Rakia New1

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

‫בס"ד‬

‫ספר הרקיעים‬ A Logical Treatise of Creatio ex Nihilo Some Secrets of the Torah in the Light of Scientific Method A Scientific Rejection of Idol Worship

By Gad Maimon, Shlomo Makmel and Pinhas Ben Avraham Elad, Israel, 5767-69

To learn, pursue and try to unify Physics, Mathematics and Kabbalah constitutes Kiddush Shamayim. The Torah is waiting for you. May you shed new light on her secrets. Rabbi David Abuchatzira

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G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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When we call G-d the ultimate form of the universe, we do not use this term in the sense of form connected with substance, namely, as the form of that substance, as though G-d were the form of a material being. Rabbi Moshe Maimon (Rambam) He has No Place, and No Boundary, and No Name. Rabbi Yitzchak Luria (Ari) Recent decades have taught us that Physics is a magic window. It shows us the illusion that lies behind reality – and the reality that lies behind illusion. Its scope is immensely greater than we once realized. We are no longer satisfied with insights only into particles, or fields of force, or geometry, or in space and time. Today we demand of Physics some understanding of existence itself. John Archibald Wheeler

Introduction Since the beginning of mankind, the quest to know what laws govern our universe and how this helps to comprehend its creation and functioning to take advantage of the use of these laws of nature in the life of humanity, was a deep concern of thinkers of all times. Similarly, the seeking for knowledge and understanding of the spiritual background of such laws were part of the same quest. Old traditions treat the laws of spirituality, society, the human mind and the laws of nature in a holistic manner. The ancients throughout the world treated physical observation and spirituality in a “mixed state”. Clearly scientific thought based on detached observation without emotional involvement in form of prejudice or false beliefs, which distort such observation’s interpretation, was and partially even today is a very difficult task to achieve. Ways and methods of scientific reasoning were refined during the last nearly three thousand years on a journey through philosophies which led to both true and false conclusions about the laws governing the behavior of our universe and the objects therein. Many theories and descriptions of ancient origin are formulated in cryptic language, where oral traditions are needed to elucidate the subjects treated. Only with the emergence of mathematical reasoning in a framework of qualitative and quantitative descriptors in form of logical and provable theorems, lemmas and corollaries, a systematic scientific edifice could be built on the basis of self-evident axioms. Basic laws of Physics were kind of known for purposes of engineering like building roads, architecture, water supply and sewage systems, but not put into a fundamental mathematical framework of rigor until the time of about 600 years ago. Before that only mathematical and geometrical edifices were built on idealized forms and shapes, leading to a mathematically idealized approximate modeling of natural phenomena. Euclidean geometry did not provide possibilities for curved coordinates. Besides this a relatively precise description of astronomy as seen from our planet Earth was available, which led to very accurate calendars like the one issued by Hillel before the destruction of the second Beis HaMikdash and very well mathematically treated by the Rambam in his Hilchot Kiddush HaChodesh, despite his cumbersome corrections to fit observational data with the flat Euclidean geometry available to him at that time. Planetary orbits were very well known since ancient times, at least back

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G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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to the times of the Exodus of Egypt and the giving of the Torah, as is explained for example in Tractate Rosh Hashanah, which was written down in the time of the Babylonian Galut straight after the destruction of the first Beis HaMikdash. So was the mechanism of the ever renewing moon of the Earth, which is a precise monthly play of light and shade. Earlier works like Sefer Raziel HaMalach still show a different picture: the orbits of the planets of our solar system begin and end in an ocean, but the sequence of the distances of these planets from the earth are surprisingly correct. Whether this is due to lost knowledge re-gained at the giving of the Oral Torah, remains speculation, at least for now. Sure is in any case, that with the giving of the written and oral Torah, which includes the Kabbalah in form of visions, prayers and descriptions from as early as Adam HaRishon, Chanoch, Avraham Avinu, and our Prophets, the full concepts of the structure of the created worlds were also given, but not always very well understood. With today’s knowledge and methods of modern Mathematics and Physics, we try to take the reader on a journey through the ancient literature of Judaism, the only original philosophy ascribing the creation of the physical, mental and spiritual worlds to a one and only origin or Creator as stated in the Torah:

‫שמע ישראל יהוה אלהינו יהוה אחד‬ Rambam (Rabbi Moshe Maimon z”l) in Sefer Ha-Mada, Hilchot Yesodei HaTorah writes the following characterization of the Creator: [7] G-d is a single entity of an oneness even more single and unique than any single thing in creation. [8] G-d has no physical form … [11] Once it is known that G-d has no physical body it will become clear that he does not experience any bodily sensations either, sensations such as formation, decomposition, occupying a physical space or size, rising or falling, a left or right side, a need to stand or sit etc. G-d does not exist in time, so he has no beginning or end. G-d cannot die, and does not live as life is known. Ari HaKadosh (Rabbi Yitzhak Luria z”l) says in Etz Chaim, as written down by Rabbi Chaim Vital z”l: “In the beginning the Or Ein Sof (Or Elyon) filled the entire Existence” (not space!), which emerged from a singular point in infinity, as space and time were not created yet. A distinction between an infinite sphere or space and a point in infinity is not possible, as will be explained later. From this state the infinite light got expelled beyond the infinite sphere and a vacuum was formed inside the sphere, into which a thread of light was drawn, finally forming the ten sfirot of the Tree of Life, which contain our physical world as well. As we will see later, dimensionality and viewpoints of observers play an important role in the understanding of this philosophy. Whether and how this agrees with modern science and what hints it gives to achieve a better understanding of the worlds we live in, physical, mental and spiritual, will be discussed in this treatise. In modern Physics evidence of creation is recovered by observation, measurement and mathematical formulation of theories describing the history of our universe. The methodology to formulate such theories underlies strict logic and must not contradict any of those measurements and observations. The formulation of such theories is done by

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G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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mathematical modeling which depends also on mathematical proof. We can mathematically model systems’ dynamics into the future or into the past. The only things needed are initial or final conditions of such system and the knowledge of all interactions during the dynamical process. Such physical reasoning and mathematical modeling lead to the theory of the Big Bang as the origin of our universe. It is supposed to have emerged from a singularity as a result of the creation of space and time, but such creation of space and time also needs initial conditions in Physics and Mathematics as well as in philosophy. It is quite puzzling, that modern Physics and Mathematics should be confirming an ancient philosophy of religious origin, but exactly this seems to be the case, if one researches carefully both the Kabbalah of the Torah and Physical and Mathematical Theory. In particular General Relativity and especially Quantum Theory with its involvement of the observer into the process of finding the truth hint to some spiritual extension of the purely physical world we try to observe and understand today. Higher worlds are described in Kabbalah, worlds of action, formation, creation and emanation, which are crowned by the world of primordial “man”. It is also taught, that those worlds contain each other from the highest to the lowest, where one can see from the higher to the lower but not from the lower to the higher [Etz Chaim]. This hints naturally on the dimensionality of those worlds, which, in a way also plays a role in the mathematical treatment of the modern model of the universe. Relativity and Quantum Theory include the role of the observer as part of and influencing measurements and observations. This is the point where the infinite number of dimensions of the mind comes into play, where besides strictly logical thinking effects and observations beyond possible physical realization or beyond logic are possible and conceivable. As an example for this we may take a picture of a flower under which we write “This is not a flower”. This seems very out of place and bordering on ridiculosity, but exactly it represents a typical case of Gödel’s un-provability theorem. What has that to do with our question to understand the different worlds and dimensions? The answer is, said picture is an example of a “projection” of an object of four-dimensional dynamic physical space onto twodimensional static space representing the “real” object. The picture is taken as a very unique and selective representation of the real object in regard to view angle, instant of time the picture is taken, size due to distance and other optical imaging constraints, and color, to name only a few constraints. All these parameters are responsible for the formation of the projection. In addition, the physical and mental state of perception of the viewer or observer plays a crucial role how this projection is perceived and recognized. This is why it is not a flower. On the other hand the mental recognition system of the brain of the observer tells clearly that it is, at least a picture of it. Now we can try to move into the other direction of dimensionality. Let us suppose a real flower in three-space, which we see in nature. We see again a projection of the flower from four-space, but now only one parameter is not perceived, its change in time. If we sit long enough in front of it, we can see its entire life from the seed growing into a plant, the flower emerging and finally being transformed into seed again. The original flower then seizes to exist.

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G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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Let us suppose we see the flower in one year at a certain place and do not know the Biology of it. We leave its presence and come back exactly a year later. On the same spot we see a couple of flowers. We may conclude, it replicated, maybe got children, conjecturing from our own life-cycle, but do we know whether the original flower from last year is still here? – No, if we have not tagged it, we cannot say, but resemblances of it are there. What do we conclude? Either it is still there or it is not. Unless we observe its complete life-cycle, we do not know for sure. So at least one dimension, time in this case, constrains our perception of the truth. But it is still a flower, isn’t it? – Maybe it is not, if we do not touch it, we will not know for sure. Maybe it is a replica from plastic. – So it is not a flower?! We can argue whether it is a flower or not until we know all necessary details and criteria to recognize the observed object. Whether we arrive at a conclusion depends on the criteria used in the definitions of the object itself, which are, let us always remember, made by the observer(s). Now let us go even further. The four-dimensional flower in space-time is a projection from a world of higher dimensionality. It has a life-force, which is called in Jewish philosophy a Nefesh, which is the lowest level of spiritual or mental dimension of the soul. We refer here to the Baal Shem Tov as cited in [Sefer Tanya, Shaar HaYichud, Chapter 1]. He states that even a stone has a life-force that makes him exist, and this life-force is always renewed in every instant of time by the Creator. Suppose we know all the Chemistry and Biology to synthesize the flower in the laboratory. Will it live? – We do not know, we do not have a detector system for Nefesh, or do we? – Can we develop it and how? – How do we define Life? At this point the infinite number of dimensions of the mind comes into play. We still know very little about detection methods on these levels. Information Theory tries to find answers, so do Physics, Mathematics, Biology and Chemistry. The pace of these sciences is breathtaking, but still, in Physics we battle with a clear understanding of what are space, time, mass and charge. May we soon shed light on this, with the help of the information the Creator has given us, but we have so far failed to understand. In Physics we have detector systems to observe, man has senses to observe, but what are the detectors in higher dimensions or worlds? How do they work? -- Questions that belong to Information Theory, a branch of Mathematics. We will encounter them again on the journey this book is taking us on. In the following chapters we will give a brief overview about the views of Science and Torah on the creation of the universe. We will elaborate on physical principles and mathematical concepts underlying current theory how our world works, and on the principles of Torah and its Kabbalah, to be precise, on the principles of the world of Adam Kadmon or primordial man which contains all other worlds mentioned above, spiritual and physical. The observable physical world is said to be a projection of the higher spiritual worlds, which gave rise to our assertion that physical and in particular mathematical principles should hold and be represented in the descriptions of those worlds. Furthermore, the questions of the singularity of a Creator and its existence as well as the inevitability of the emergence and existence of the One and none other will be thoroughly discussed. We will try to explore Physics, Mathematics and Information Science to find answers to some age old questions, still hidden in the Secrets of the Torah, namely its

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G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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Kabbalah. Let us shed some light on the traditionally handed down secrets and reveal some answers to these questions. This book will be incomplete despite of our quest for completeness wherever possible, but as Kurt Gödel has proven, anything attempted to be proven in finite dimensions by finite man will be incomplete in an infinitely dimensional world. Some of the questions and secrets light will be shed on are: • • • • • • • • • • • •

Before the creation of space and time, what did exist, or what represents such Existence? Why is the existence of One as the beginning of all worlds inevitable? Are actions beyond the observable laws of nature possible or do actions beyond nature not exist? Are miracles or actions as a result of the will of a creator possible? Can laws of nature be temporarily influenced or changed by such will or are such influences or changes part of laws of nature which we not yet fully comprehend? What are the structures and mechanisms of the higher, spiritual worlds? What role do the human mind and consciousness play in the system of physically observable and physically non-observable worlds? Is sentient being or life inevitable for the existence of a universe or system of worlds? What is the reason of creation? Is communication with the creator possible or only a myth? What are angels, persons or psychological forces? Are the Laws of Nature Divine Will or created by chance?

With these questions in mind, let us embark on our journey.

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G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

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1 Absolute Nothingness, Non-existent? The main belief in Judaism is that there is one Creator who brought everything into existence from nothing. We call this ‫ יש מאין‬or creatio ex nihilo. The oneness of the Creator is a commandment of the Torah that is interpreted as an immutable oneness or absolute oneness. This presents us with a formidable paradox, because in regard to the Creator the definition of a space-time or any other multi-dimensional space related to the Creator before Creation constitutes already a violation of the conditions given above by Rambam. According to that, the Creator is absolutely simple and perfectly One without any shape, structure or attributes. Hence the “Existence” referred to in Sefer Etz Chaim, as cited below, being filled with the “Infinite Light” (Or Ein Sof) could not fill any space at all. There is no geometrical shape spanning up entities like space or time not comprising any structure in the mathematical sense, may the entity be physical, spiritual or anything beyond that. Bear in mind, that before the emanations were emanated, and the creatures were created, the Upper Simple Light had filled the entire Existence. And there was no empty space whatsoever, namely as empty air, a hollow or pit. For everything was filled with that simple boundless light and there was no such part as head and no such part as tail. That is, there was neither beginning nor end, for everything was simple or smooth light balanced evenly and equally in one likeness or affinity, and that is called the Endless Light. And when, in His simple and smooth Will, the desire arose to create the world and to emanate the emanations, to bring to light the perfection of His deeds and His Names and His appellations – which was the cause of the creation of the world – behold he then contracted Himself in the middle point which is in Him, precisely in the middle, He contracted the Light. And the Light has withdrawn to the sides around the middle point, and there has remained an empty space and a vacuum surrounding the exact middle point. And the Light has withdrawn to the sides around the middle point. And behold, this contraction was equally balanced around that middle empty point in such a manner that the vacuum was circular and in complete balance and sameness all around.

The descriptor of such entity before or at the onset of Creation must be called “absolute nothingness”. This seemingly contradicts the statement of “absolute oneness” demanded by the Torah, but let us examine the possibility of considering an entity mathematically describing nothingness. The Empty Set contains no elements whatsoever, and it needs no space to fill. As we consider further, along the lines of Etz Chaim, that all the Divine Light filled the “existence” and said nothingness is after the 2nd Tzimtzum contained in a boundary which is spherical and infinite from which the light had been expelled, there are two possibilities for such a boundary: a) a sphere with its radius going to zero, will construct a point, albeit in three dimensions; b) a sphere of infinite dimensions with any radius (it can go to infinity), which surface area and henceforth its volume tends to zero1, which constructs also a point, now in infinitely many dimensions. Furthermore such infinite dimensional sphere is indistinguishable from a sphere of zero dimensions for reasons which will be explained below (the point being in infinity, if the sphere is the one and only available).

1

The volume of a sphere of infinite dimensions approximates zero. See proof in the Appendix.

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G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫בס"ד‬

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Information Box 1: N-dimensional Sphere The -hypersphere (often simply called the -sphere) is a generalization of the circle (called by geometers the 2-sphere) and usual sphere (called by geometers the 3-sphere) to dimensions . The of points (

-sphere is therefore defined (again, to a geometer; see below) as the set of ,

, ...,

-tuples

) such that (1)

where

is the radius of the hypersphere.

Unfortunately, geometers and topologists adopt incompatible conventions for the meaning of " sphere," with geometers referring to the number of coordinates in the underlying space, and topologists referring to the dimension of the surface itself ("the defined to be the set of all points "the -sphere object described by

in

is

-dimensional sphere

is

satisfying

,"

). A geometer would therefore regard the

(2)

as a 2-sphere, while a topologist would consider it a 1-sphere and denote it geometer would regard the object described by

. Similarly, a

(3)

as a 3-sphere, while a topologist would call it a 2-sphere and denote it . Extreme caution is therefore advised when consulting the literature. Following the literature, both conventions are used in this work, depending on context, which is stated explicitly wherever it might be ambiguous. Let

denote the content (i.e.,

sense) of radius

-dimensional volume) of an

-hypersphere (in the geometer's

is given by

(4)

where

is the hyper-surface area of an

-sphere of unit radius. A unit hypersphere must satisfy

(5)

(6)

But the gamma-function can be defined by

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G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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(7)

so (8) (9)

Special forms of

for an integer allow the above expression to be written as

(10)

where

is a factorial and

is a double factorial.

Strangely enough, the hyper-surface area reaches a maximum and then decreases towards 0 as increases. The point of maximal hyper-surface area satisfies

(11)

where

is the digamma function. This cannot be solved analytically for

numerical solution is maximum hyper-surface area.

, but the

. As a result, the seven-dimensional hypersphere has

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G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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Case a) has to be discarded, because it has the limit of being finite dimensional, while case b) fulfills all possible conditions of infinite radius and infinite dimensionality, and has the highest possible symmetry a geometrical object, besides absolute nothingness, can have. Since we considered this geometrical object as spherical in all dimensions, and its volume tends to zero, it still can contain something, let us say its center point. Let us consider the infinite-dimensional sphere enveloping this center point which is containing all energy necessary to create a universe2. It can be called: • • •

cyclic, without beginning or end containing an empty set in its middle point having the highest possible symmetry

Etz Chaim describes this as containing a simple, indescribable light, which at the onset of creation got expelled to As an example for relativity of space, we want to look at our solar system. If an observer is located the outside surface of the said sphere on a planet, all other planets and the Sun will and then the inside of the sphere space appear to rotate around him, no matter whether he got “inflated” containing a “reshimo” is on Earth, Mars, Jupiter or any other of the planets. If he leaves the solar system and looks at of spheres to be created. The it from outside, he will perceive all planets orbiting mechanism of the expulsion in a still around the Sun. We can now assign a sphere to each orbit, and the orbits will be represented by undefined and unstable system of the spheres the radius of which will represent the point in infinity that represents a distance from the observer. They will always be sphere with infinite radius depends on concentric with the center at the location of the observer. The order of those concentric spheres the effect how the system is being will then depend on the location of the observer. stabilized, as will be discussed in Similarly we can argue for spheres that have detail in the course of this treatise. different dimensions and are nested into each other, the dimensionality of the observer and his One possible explanation for such an location in those dimensions will determine the expulsion mechanism is first the volume of the sphere he perceives. For example, if relativity of space that has at least one he is three-dimensional, and he resides in dimensions 1, 2 and 3 he will perceive a solution for turning the sequence of voluminous sphere as in the same way as if he is in the still latent spheres into one with dimensions 204, 306 and 1002. He will always Malchut inside and then change perceive the volume of the sphere according to his dimensions as voluminous, because he will number position to have Malchut outside. those dimensions as 1 to n. All others will then Furthermore one can imagine that at appear according to the plot in Information Box 1. the stage of the system being not stabilized yet such inside and outside is not yet defined as well as any sizes or dimensionalities. We will try to discuss this situation in more detail when we will have gained more insight into both the scientific and kabbalistic propositions in the literature. Information Box 2: Relativity of Space

How can an infinite-dimensional sphere with infinite radius, explained above as having an infinitely small volume, be inflated in volume to create a space to contain a void or vacuum as described in Etz Chaim? The answer is, the symmetry of the object described above must be broken, until a sphere of reasonable volume is created3, but this is not so simple. First of 2

Why this system contains energy is for quantum mechanical reasons which will be explained later when we will talk about uncertainty relations. 3 For an explanation of symmetry breaking, see the Appendix.

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G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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all we have to consider a mechanism that breaks the symmetry and second, we have to discuss how it is possible to break the symmetry effectively to create a voluminous space for a physical world as we know it, where this volume can be very small like for instance have an order of magnitude of the Planck scale. If the symmetry is broken from an infinite dimensionality, a voluminous space is only achieved if a finite number of dimensions is left over after the symmetry reduction. This poses a mathematical dilemma, because infinitely many dimensions have to be partitioned into at least one finite dimensional subset and at least one infinite dimensional subset. Two other possibilities would be to partition the infinite set of dimensions into infinitely many finite sets or a finite set of dimensions (spheres) containing infinitely many subsets of dimensions (spheres). This last possibility is favored by the Kabbalists4. We will discuss this in the next chapter in more detail. For now, it shall suffice to remark that for a finite dimensional observer the volume of a sphere of the same dimensionality as that of such observer does not depend on the observer’s subset of dimensions particular location inside the infinite set of dimensions. The observer will always perceive the volume of such sphere as if all other dimensions he is unable to perceive do not exist. We shall call this “relativity of space”. With the advent of creation, our empty set containing absolutely nothing constitutes without its boundary of an infinite-dimensional sphere absolute unity with the intrinsic property of containing light or energy, whose properties are yet undefined. Why this light or energy is an intrinsic property of our empty set as a precursor of space and time has to do with the peculiar geometry we are confronted with at the onset of creation5 and will be explained in the next chapter. For now, may the reader accept this as fact. Appropriate spheres (sfirot) of different dimensionality can be pre-created by preparing the “inflated” space (after breaking symmetries) according to the Ari-zal’s and Chaim Vital’s (Otzrot Chaim) proposal of engraving a “reshimo” into such space, but immediately the question arises why such pre-creation is necessary, and why could the Creator not proceed to create the sfirot directly? A possible answer to this is, the Creator needed to create the concept of plurality to create any tangible structure, and hence the “reshimo” was created as a conceptualization of plurality. This is also true for the dimensionality of space, because such dimensions are countable. Above we have seen how difficult it is to understand absolute nothingness. The critical reader might now ask the question whether this nothingness at the onset of creation contradicts the commandment of the Torah that asks for “absolute oneness” as the source of all being, while another might argue that “absolutely nothing” very nicely fulfills the request for structureless indescribability of such a source. Both readers have very good reasons for their argumentation, but should now read on extra carefully. Prior to any creation no whatsoever concepts or structures existed. Mathematically we can see this state of affairs only as an empty set representing an “absolute nothing”. This set needs for the above mentioned expulsion of the infinite light (Or Ein Sof) a boundary of highest possible symmetry. This boundary already is presenting us with a fundamental 4

See Sefer Etz Chaim 1:1-4, and Sefer Otzrot Chaim 1:1 We have here to do with a very small volume of space-time so that time is squashed into a very small length. This leads to the creation of energy according to the relationship ΔE Δt ≥ ħ/2 as will be explained later. 5

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G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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paradox. The nothingness exists in no environment, is not having any structure and is neither represented by anything nor distinguished from anything, space, time, energy, or any mathematical-physical concept whatsoever, but constitutes One absolute nothingness. How can such nothingness then suddenly have a boundary and light or energy which can be expelled to outside this boundary? And where to is it expelled if there is no environment the absolute nothingness is in and where comes suddenly an oneness from? – We try to suggest an answer. As we will see later, Mach’s principle which is the precursor of the principle of relativity explains that space is created by its contents and needs not to be a prerequisite for placing anything created like in the Newtonian view of the world contained in an absolute and rigid space. Furthermore, Sefer Yetzirah 1:7 states: ‫עשר ספירות בלי מה נעוץ סופן בתחלתן ותחילתן בסופן כשלהבת קשורה בגחלת שאדון‬ ‫יחיד ואין לו שני ולפני אחד מה אתה סופר‬: Ten sfirot of nothingness, their end is embedded in their beginning and their beginning in their end, like a flame in a burning coal, for the master is singular, he has no second, and before One, what do you count? In the state of absolute nothingness no means of distinction and no structure exist, so this nothingness is the one and only nothingness available. We therefore can postulate the absolute nothingness being identical with absolute oneness, and the concept of One did not have to be created, it is an intrinsic property of absolute nothingness. In this state, numbers need not be created, and counting is impossible for lack of any second entity or concept besides the absolute nothingness. This is denoted by “before One, what do you count?” – a very clear hint how to get to an acceptable solution to the above conundrum. Let us for this purpose conjecture the identity of absolute nothingness (non-existence) with absolute oneness (existence) and see which of the two is able to “survive” alone: We can look at the absolute nothingness as an absolute oneness, because we have no distinction of this absolute nothingness from something or nothing else. Suppose, if there is not one absolute nothingness, there must be either a) no absolute nothingness or b) more than one absolute nothingness. Case a) can be rejected, because if there is no absolute nothingness there can be only either somethingness or a relative nothingness, which must be relative to some other nothingness or somethingness and be distinct from it; since there is a distinction, there is something, so the nothingness is not absolute. Case b) can be rejected for the same reason, that there must be a distinction or distinctions between the absolute nothingnesses, which would constitute already something. A further trivial case would be that there is something besides the nothingness, which takes the absoluteness of the nothingness away. From that we can conjecture, that absolute nothingness can only exist once, and hence, absolute oneness is an intrinsic property of absolute nothingness. Since absolute oneness does not allow any boundaries or structures and demands highest symmetry, the absolute nothingness is not distinguishable from the absolute oneness. We further conjecture, that the absolute nothingness’s property of being absolutely one makes non-existence impossible. It follows, that a) if absolute oneness does not exist, only plurality can exist; b) if absolute

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G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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nothingness does not exist, only absolute oneness or plurality can exist. Hence, if absolute nothingness and absolute oneness do not exist, only plurality does exist. Plurality cannot exist without a space at least of natural numbers. This shows that since before creation absolutely nothing existed, there was only one absolute nothingness which cannot exist without being exactly one, but exactly one or oneness can exist on its own, without any nothingness. Hence the origin of existence is ONE, since only absolute oneness can exist as an only entity, and absolute nothingness requires oneness for its absolute existence. The same conjectures are valid for absolute non-existence (equivalent to absolute nothingness) and absolute existence in oneness (equivalent to absolute oneness). A further reason for existence superseding non-existence or negative existence is the intrinsic asymmetry of NOT (‫ )לא‬or negativity as such which is also shown in the asymmetry in the Baryogenesis in favor of matter over antimatter. A nice example to make this plausible is that additions or subtractions which are commutative in regard to multiplication, behave as follows: +.+=+ +.- = -.- = + This or similar reasoning might be underlying the idea of Parashat Beshalach (Shemot 17:7), commented in Idra Rabah 83, punishing the questioning of the identity of Existence in favor of Non-Existence, which is also a clear rejection of a negative existence of the Creator. Sefer Yetzirah 2:6 states: “He formed substance out of chaos (‫ )תוהו‬and made nonexistence into existence …” The concept of absolute oneness or unity of which absolute nothingness is part of, is at the same time part of the concept of existence, which we want to call “somethingness” (cf. Sefer Yetzirah 2:6 as cited below). This somethingness can be described in absence of any space and time as either a point or, with some caution, as our infinite-dimensional sphere lacking any volume as discussed above. Before we look deeper into this issue, let us first consider how from absolute nothingness, which constitutes absolute oneness, space could be defined. Above we proposed inflation of a finite-dimensional space from that infinite-dimensional sphere by symmetry breaking. The Ramchal (Rabbi Moshe Chaim Luzzatto) describes the formation of a reshimo of the sfirot in a void space evolving from a singularity. This space, as we have remarked already, does not need to have a large volume, it can be infinitesimally tiny. How can this happen? To distinguish between two basic entities or properties in the state of absolute nothingness we need to take two things into account: • •

The identity of absolute nothingness with absolute oneness The identity of oneness with somethingness

If we take these two identities together we can deduce, that absolute nothingness and absolute oneness (somethingness) represented by, say, a point can coexist as the same system unless any action occurs. Since this point does exist in a space of no dimensions or no space, it has

13

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‫בס"ד‬

‫ספר‬

no coordinates. We can say it lies in infinity. As is very well known to mathematicians, such point in infinity represents a circle or sphere with infinite radius, dependent on the number of dimensions involved. To explain this, consider a circle with two points marked on it on opposite sides, i.e. the points are the intersections of a straight line containing the middle point of the circle and intersecting with the circle. Suppose the radius of the circle becoming infinite. The circle approximates in the two intersection points straight lines, but they meet at the respective antipodal point forming a circle. This can be done in three dimensions with planes and spheres and in higher dimensions with hyperplanes and hyperspheres.

Information Spheres

Box

3:

Fluctuating

We see here schematically, how the sphere of infinite radius fluctuates between the point in infinity and the infinite sphere. We constrained the fluctuation to two dimensions, because we only want to clarify that The sphere fluctuates around the point in infinity so that it is a tangential point of the sphere The radii of the resulting spheres end in different points different from the middle point of the sphere with infinite radius. Hence, we can conjecture for ten differently dimensional spheres containing infinitely many sets of ten spheres that the radii will end in infinitely different points, and if the condition is met that the outermost sphere represents the inner boundary of the Infinite Light, then the next smaller infinite sphere’s radius will not meet the middle point of the entire system which is determined by the outermost sphere.

From this we can conjecture, that our point representing oneness represents an infinite sphere and both are not distinguishable or as we say in Quantum Physics, the system fluctuates between the two states point and sphere. With this, primordial space is already created, as well as at least one second dimension, so that this space at least consists of the dimensions 0, 1 and 2 as we will see in the kabbalistic view of Creation with the creation of the letters ‫ ו‬,‫י‬ and ‫ד‬. We have to remind the reader that such a space is still not distinguishable from our point in infinity, because it is at that stage fluctuating wildly between voluminosity and zero volume, so to say at infinite frequency, since time does not exist yet 6, as will be explained later. Still we have to explain, how the point in infinity which represents an infinite sphere could be transformed into a space that is stable, expelling all energy (light) out of such space. If we assume that the laws of Physics were valid from the onset of creation, and there is no 6

Since time is not defined as a dimension yet, but is just one of many latent dimensions, one can not define a frequency with which the system is fluctuating or oscillating. This leads to infinite frequencies if one considers time zero and energy as infinite, which is one of the reasons for very rapid inflation or explosion of such a system.

14

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observation (measurement) or philosophical reasoning preventing such assumption, we can conjecture the following: Since it is very well known in Physics, that quantum effects prevailed at the very onset of the existence of the physical universe, let us assign state vectors (wave functions) to each of the observables defined above, namely absolute nothingness, point in infinity, infinite sphere, energy and time. Additionally we can assign non-commuting operators to each physical quantity, namely space, energy and time, which are some of the dimensions of our sphere system. We have to take into

Information Box 4: Essentials of Quantum Mechanics Quantum Mechanics is a fundamental branch of Physics covering phenomena of the microscopic realm like elementar particles, atoms and molecules, and of the macroscopic realm such as the universe. It generalizes all classical theories such as mechanics and electrodynamics, atomic and nuclear physics and condensed matter physics, but does not provide yet any generalization of general relativity. Niels Bohr determined that it is impossible to describe light adequately by the sole use of either the wave analogy or of the particle analogy. Therefore he enunciated the principle of complementarity: light is a particle and a wave, like position and momentum are paired and cannot be determined at the same time with full precision. The particle-wave duality was formulated by de Broglie in 1924 and the uncertainty principle that limits the precision of measurements of complementary properties of objects was discovered by Heisenberg in 1927. Such complementary properties are responsible for the necessity of the interaction of an observer with the observed phenomenon. Historically, Schrödinger described quantum phenomena with his wave-equation, while Heisenberg used matrix mechanics to describe the same phenomena. Both their results were equivalent. In 1930, Dirac combined Heisenberg’s and Schrödinger’s approach into a single quantum mechanical description of state vectors. The relevant uncertainties for the understanding of our book are wave-particle, positionmomentum and energy-time. At a measurement of any property of a particle, its complementary property becomes meaningless, as the wavefunction “collapses”. To achieve this, a demarcation needs to be made between the observer and the observable to terminate any entanglement of the two. For a full popular explanation of Quantum Theory please refer to the Appendix.

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‫בס"ד‬

consideration, that in Quantum Theory we can assign two different states to one physical reality, where observation determines, which state is representing such reality in question. In our case, the obvious result of observation is, that we have permanently the state of infinite space and an immensely large energy prevailing. The question to be resolved is, how the formerly ambiguous system arrived at exactly those observed properties and what caused time and energy to exist. An extensive explanation of those questions will be given in the next chapter, but for the moment it seems to be that the “freezing” of the ambiguous system into a definite one needs some action to be performed, which for example can be an observation, which causes the system to “freeze” or as we say in Quantum Theory, leads to the collapse of the wave function (Copenhagen mechanism). The wave function collapse can either be happening spontaneously or through a defined action. At the moment of our discussion this is not yet clear. For spontaneous collapse a probability has to be defined or another reason has to be found, why the system would prefer to freeze. The defined and willed action needs a separate entity to act or at least a subset of the system needs to act. Another possibility is that the whole system wills the action. The possibilities of such freezing mechanism by quantum decoherence and/or delocalized counterpropagating wave functions will be discussed as well. This will lead to a better understanding, whether and how any willed action is necessary to bring a stable system like our universe into existence and to sustain it. We will discuss this issue in detail below. Any action needs a new concept to be created, either cause and effect or probability. We will discuss in detail, whether there is any minimum causality necessary to start any action in the above sense even if we base a physical theory on fluctuations and probability. Philosophically this arises one of the toughest and most fundamental questions: Is causality as we observe it on a macroscopic scale a must also in the quantum world of microscopic and mesoscopic systems or is it sufficient to collapse our ambiguous system into a stable one purely by chance? A most important effect of such collapse is the choice of the values of Planck’s constant, the elementar electric charge and the velocity of light in vacuo which all together are represented by the fine structure constant with a value of 1/137. This is the only fundamental constant the value of which cannot be derived by any theory and cannot be mimicked by any condensed matter system. To shed some light onto this issue, we should remind ourselves: In Physics, the discussions are centered on the following problems:

•

•

•

Einstein-Podolski-Rosen paradox or the measurement paradox of Physics: If one of two complementary properties of an observable is measured, the other becomes unreal. A quantum particle’s properties can only be observed half; all complementary information gets lost. Causality or probability: In quantum mechanics, properties of actions of particles can only be described probabilistically, and sometimes time-reversal effects are observable; only in the classical limit causality can be shown. This leads to paradoxes. Spontaneous or deterministically willed action and symmetry breaking; is will itself at all deterministic? – In Physics we speak about spontaneity when e.g. an exact place or time of an event cannot be determined; as we shall see later, a willed action can produce the same spontaneity arising from observation, because only the action resulting from the will can be observed.

16

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• • • •

‫ספר‬

‫בס"ד‬

Lacking unification of General Relativity and Quantum Theory. Thermodynamic origin of time and with that its existence depends like space on the distribution of matter and its dynamics; does this mean that a spiritual space cannot exist without a physical space and vice versa?7 Light and time as links to un-accessible worlds or parts of our universe. Validity or invalidity of the anthropic principle: if the world were not in a highly structured but extremely unlikely state, we should not exist and be here to observe it.

In Kabbalah, the discussions are centered on the following problems:

• • • • • •

Simplicity and oneness of the Creator: both simplicity and oneness are of the utmost extreme, so that no structure or attributes can be applied to that Creator. Namelessness of the creator vs. names used to describe the creator (or its creation) and possible implications of Idol Worship by the inappropriate use of such names: such names describe only certain aspects of the Creator or His Creation. Problematics of names and attributes related to different stages of creation and different world levels. Role of sfirot, vessels and light in creation. Divine will and reshimo principle: before light can interact e.g. with free space to form a vessel, that space needs to be prepared by a structure called reshimo. Way and time of the decision for Adam Kadmon to emit light; is this spontaneous action?

Up to now, we only have established the intrinsic properties of nothingness and oneness, and no initiation process for creation, or better, stabilization (“freezing”) of any space or world has been established, except the possible processes as proposed in Etz Chaim and some vague spontaneous action as proposed by science. To follow along these lines, we need to establish very carefully, what has to be created to facilitate such a process. Examples for such facilitating entities are, in order of fundamentality [‫ דף ג' פרק ו‬,‫]ספר אלימה‬:

• • • •

The will to change state of existence; Cause and effect (or alternative like self-observation or self-consciousness of a “selfexcited circuit” universe)8; Initiation of symmetry breaking (causes partitioning automatically), causes the creation of natural numbers; Concept of light and its definitions (energy, constancy of its speed in vacuo etc.).

A possibility is to carefully look at the dichotomies mentioned above to explain the state of affairs at the onset of creation, where clear definitions and distinctions, which are part of the concept of plurality or at least duality, are not yet made. We have: 7

As we will see later, information and with that spiritual entities need a physical carrier to be actively exchanged or interactive with other entities. According to quantum field theory the vacuum can constitute such a physical carrier. 8 Since what is regarded as cause and what as effect depends on the observer, and in Quantum Mechanics it has been proven theoretically and experimentally that causality as it is known in daily life can be violated. As we will see in our later discussions, such “relativity of cause and effect” can also be shown in a classical environment.

17

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• • • • •

‫ספר‬

‫בס"ד‬

Absolute nothingness and absolute oneness; Non-existence and existence; Point and circle (sphere); No space and no time exist and despite of that infinite light is available; No causality, but probability and statistical causality and time may exist, as proposed in Quantum Theory and Information Theory9.

Let us first look carefully into the Physics of the Big Bang with all its open questions to see whether we can reach a more enlightened view of the beginning of our worlds we live in. After that we will look at the view of the Secrets of the Torah, how the process of creation is described there.

9

Violations of causality are only a reversal of same and depend on the observer and the statistical behavior of the phenomenon observed.

18

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‫ספר‬

‫בס"ד‬

2 Space, Time and Energy, Created at Will or Inevitable? 2a: Emergence and History of the Physical Universe, a Scientific Model Information Box 5: History of the Universe as we look back into it 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Planck epoch Grand unification Inflation causes Big Bang Baryon genesis Weak and electromagnetic forces separate Protons and neutrons created Electron-positron pairs annihilate Nucleo-synthesis Decoupling of light from matter Protogalaxies and first stars

10-43 sec 10-35 sec 10-33 sec 10-11 sec 10-5 sec 1 sec 3 min 300,000 years 1 billion years

For later discussion please note that we have seven epochs from the Big Bang to the existence of first stars, while we have three epochs before the universe had any significant size. We also have seven significant spontaneous symmetry breakings (3. – 9.) during the formation of our observable universe, where the symmetry breakings after the Big Bang are connected with a cooling of the universe.

Physics explains, according to measurements and observation, that the physical world emanated from a singularity, a point, where all physical forces and objects were unified at an energy density, which is hard to grasp. The entire universe, concentrated into a very small sphere, contained a “substance”, which unified all particles and space-time. This is known as the Planck state of the universe and the grand unification of all laws and objects of physical space. In Kabbalah this is referred to by the expression “ineffable infinite light”. This state lasted about 10-43 seconds after the point started expanding. Up to 10-35 seconds, the universe inflated to nearly half of its present size in a process faster than the speed of light. This shows that inflation of space-time, not matter or energy, took place, hinting to a process similar to that described in the old Sfarim of Kabbalah. Although the properties of the Big Bang are very special, as we will see below, we now know that the laws of Physics provide a mechanism that produces exactly such a bang: cosmic inflation. What makes inflation possible is a high energy density that cannot be rapidly lowered. Such a state is called a false vacuum, where vacuum indicates a state of lowest possible energy density. For a period of time, where time emerges out of the fluctuation of the Planck state of space-time, the false vacuum acts as if the energy density cannot be lowered. This creates a negative pressure causing a repulsive gravitational field, which is the driving force behind inflation. With the onset of such inflation time as we know it is created. Only a small patch of the anyhow at that time small universe needs to be in a state of false vacuum such as in a random fluctuation, and it will enlarge by many orders of magnitude, while other regions remain microscopic. Typical expansion factors are in the order of at least 1025. There is no upper limit to the amount of expansion. Eventually the false vacuum decays, and the energy that had been locked in it is released, producing exactly the Big Bang as it started, containing a hot soup of particles10. As we will see in our later discussions, gravity plays a very special role in this scenario and is also responsible for the 2 nd law of

10

We will discuss the implications of Inflation in detail in our later discussions.

19

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

‫בס"ד‬

thermodynamics that gave us the direction of time, at least macroscopically in the physical environment we are in. Another mechanism proposed in Physics to create matter as we observe it is spontaneous symmetry breaking at the beginning of the universe. As an example for such symmetry breaking, let us look at the time before 10-12 seconds after the Big Bang. There an exact U(2) symmetry held in which leptons and quarks were all without mass, electrons and neutrinos were the same, and W- and Z-bosons and the photon could be “rotated” into each other. Then at 10-12 seconds, the temperature dropped below a critical value, making the choice of the now prevailing gauge bosons (W-, W+, Z0, γ). Within three minutes nuclei of atoms of the chemical elements were formed. From then onwards, matter plasma prevailed for about 300,000 years. Then a decoupling of matter and radiation took place, which allowed the formation of stars and galaxies as we know them today. Let us look now in detail at the Physics at the onset of creation. Particularly interesting is the specialness and uniqueness of the Big Bang emerging from a singularity with an immense amount of energy.

20

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫בס"ד‬

‫ספר‬

In

Information Box 6: Relativity Principles

the

For a popular treatment of Einstein’s special and general relativity principles please consult the Appendix. For the understanding of the following arguments we need to know the implications of the Lorentz transformations which are a feature of these relativity principles because of the constancy of the speed of light in vacuo as demonstrated and proven by the Michelson-Morley experiment. When a rigid massive body moves with a velocity of about half the speed of light or more, space contracts and time dilates more and more as its speed approaches the speed of light. The mass of the body will increase the more it approaches the speed of light. It is another feature of these Lorentz transformations that if space contracts, time will dilate and vice versa.

beginning we have an immensely strange geometry. Space and time are squashed into an infinitely small sphere with a mass distribution of a δ-function. According to the general relativity principle, such a scenario is unique for our universe as it is not Lorentz invariant. It also immediately follows from t ≈ ħ/E, where t is the time, E is the energy and ħ is Planck’s quantum that E reaches infinity. In practice and along the lines of observation as a means of wave function collapse as discussed above, before any action took place, the following scenario prevailed: Quantum fluctuations are a feature of Heisenberg’s uncertainty principle as applied to field quantities. Hence, if we try to measure the space-time metric precisely, same will wildly fluctuate. The same happens, if the system observes itself or is self-conscious. Whether this was the case, we do not want to answer now. The question arises, what would happen, if such metric is constraint by the sheer microscopic size of the available space (cf. John Wheeler’s suggestions of 1950 and later)? In case of a space-time singularity or even in case of a size of the space of the order of magnitude of the Planck scale (10-35 m and 10-43 s), such metric’s fluctuations would very likely lead to a wild 21

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

‫בס"ד‬

explosion. One could imagine, if space-time is such constraint, the uncertainty of the energy (mass) of the system causes fluctuations from zero to infinity. Such fluctuations have to be understood in a very special way, since, as we said, space and time at the beginning of the universe were not formed yet in the way we know it. Hence, such fluctuations of the dimensions of space-time have to be understood rather as having some sort of yet undefined properties in the way that their magnitude is at the same time infinitely small and infinitely big or somewhere in between. Only through an action like observation or similar interaction the system’s dimensional properties can become defined. Such action is to be understood in the same way as we explained it above with the point in infinity and the infinite sphere. We will discuss this issue below in our discussion of the scientific and the kabbalistic views of creatio ex nihilo. This issue is also the very central problem of Quantum Physics and known as the measurement problem of complementary observables underlying the uncertainty principles of Heisenberg. In this discussion philosophical implications of causality, locality and the act of observation or measurement (which is related to the collapse of the wavefunction of the observable) will be uncovered. According to the General Theory of Relativity, time is a dimension of space fully interchangeable with the other dimensions of that space. The Lorentz gauge dictates, that if space contracts, time dilates. If now all dimensions including the time are pressed into a singularity, this condition breaks down. The only way out of this dilemma is that time was either a space-like dimension and spontaneously changed its property, or the system was a wildly fluctuating space-time with its energy content as wildly fluctuating between zero and infinity. Again assuming that the laws of Physics are valid in this state, we have to consider laws related to the energy of such a system, namely the laws of thermodynamics. The second law of thermodynamics dictates by its mere existence, that the Big Bang must have had absurdly low entropy, which can have many different forms. This suggests very special conditions for the Big Bang. Evidence for the early universe being in a thermal state is the close resemblance of the universe’s background radiation of the Planck black body radiation curve. This is observed experimentally by the 2.7 K background microwave radiation, which is the remnant of the flash of the Big Bang. Further evidence can be found in nuclear processes in the early universe. There prevails a thermal equilibrium of its matter in conjunction with the rapid expansion of the universe. Hence, it must have been in a highly organized state of low entropy. Inflationary expansion provides a completely homogeneous highly organized state. One could argue that soon after the Big Bang the universe was small, so its degrees of freedom were very limited, so only low entropy was possible. This is not the right view, in particular regarding the still possible infinite dimensionality, which must be affected by the fluctuation, the dimensionality then also fluctuating between zero and infinity11. In such a highly fluctuating undefined state, the gravitational degrees of freedom, which depend on the mass12 as an energy form of the universe, have not been thermalized with the other parameters of matter and electromagnetic states which are involved in the thermal state of the 11

It is not entirely clear whether this would affect the entropy of such a fluctuating system. One has to remind oneself that inflation, explosion and rapid cooling all happened in about 10-12 seconds. 12 The question is whether such mass had gravitational interaction at that stage or whether such mass could be defined as such in a stage of Grand Unification, is pretty open and any answer would be highly speculative. If mass was not de-coupled it cannot contribute to the thermal state like the de-coupled ones. Hence the following argument above is a very valid one.

22

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‫ספר‬

‫בס"ד‬

universe. This means, mass was not yet de-coupled of the other properties and henceforth the gravitational degrees of freedom provided a huge reservoir for entropy like in a black hole 13 as a cluster of gravitational matter. This different behavior of gravitation (high entropy in clustered masses as opposed to high entropy in spread out gas) gave us in Inflation and the Big Bang the second law of thermodynamics as we observe it, and with that the deterministic forward movement in time. It makes time an arrow. Gravity had a very special status at the beginning of the universe, different from that of any other field. Rather than sharing in the thermalization like all the other fields gravity’s degrees of freedom were lying in wait, so that the second law could come into play as these degrees of freedom begin to be taken up. Gravity’s behavior seems to have been different from all the others, but why? Answering this question is entering the speculative area of Physics, and since at the very beginning of the universe definitely quantum effects dominated the scene, we have to go right back to the fundamental questions of Quantum Theory and to the most pressing question regarding gravitation: what is mass and how did it emerge? At the moment of the writing of this book there are only theoretical explanations or better, proposals to explanations. The most favored mechanism for giving mass to particles and making them into matter is the Higgs mechanism, but until now the Higgs boson, which is one of the four gauge bosons, eluded any conclusive experimental verification of itself. At this very moment the high energy Physics experiment ATLAS at the Large Hadron Collider (LHC) of CERN in Geneva, Switzerland starts getting into the stage to produce data very soon, so that the existence of the Higgs particle, supersymmetry and related issues can be either verified or the door to some new unknown Physics may be opened, which may require us to again re-think our perception of how we understand the Physics of the world(s) we live in.

13

Please consult the Appendix for a popular description of black holes.

23

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

‫בס"ד‬

Information Box 7: Configuration Space A configuration space is the space physical and other spaces or systems of spaces are based on. It contains all possible histories of such spaces and evolves with the dynamics of such spaces. Those spaces are also dependent on the dynamics of their respective contents. For example, if a space contains three point particles, we can plot all possible configurations in time as single points on a curve on configuration space. Such path represents a particular history of that three particle space. If several sets of spaces show a particular dynamics, such dynamics can also be represented by a path on configuration space. Hence, configuration space can also be understood as the space where the wave function of our entire universe “settles down” on, and it represents then all possible histories of such wave function. Configuration space evolves as every other space with the dynamics of its contents. The same conditions are valid for phase space which contains all possible phases of its contents.

Concerning the probability of the occurrence of the Big Bang, conventionally one assumes a phase space describing the thermal and other conditions leading or not leading to a universe as we observe it. The “box” in such phase space for the occurrence of our Big Bang is ridiculously small with a probability value of about 1:1010^123, so it would require a nearly infinite precision to choose all necessary parameters to let such a Big Bang happen. This fact is often used to argue in favor of an intelligent Creator. Strictly speaking, such phase space also needs to be created or has to emerge, as all space is in a highly fluctuating state, and that includes such phase space as well, if one is to take the term creatio ex nihilo seriously. Thus we can argue that phase space was just as small as the singularity, so no precision at all was needed. The question still remains, what happened with the high entropy of a normally thermally homogeneous system. A possible answer to this lies with the above mentioned anomaly of the thermodynamic state of the Big Bang and its

24

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

‫בס"ד‬

consequences, namely on the not yet thermalized gravitational degrees of freedom at its very beginning. Quantum theoretically, these special conditions dictate that configuration space also underlies the same conditions as physical space in the beginning of Creation. We will discuss why this should be the case in our discussion of scientific and kabbalistic views of the role of such configuration space and its history since the inception of creation. This will be important for the discussion of the kabbalistic view of Creation, because we can interpret the vacated space before the introduction of light as the configuration space of the still not stabilized set of worlds which includes the reshimo of all sfirot that will ever exist. Let us now explore how the second law of thermodynamics causes time to behave as we observe it. We should remember that we can mathematically model systems’ dynamics into the future or into the past. The only things needed therefore are initial or final conditions of such system and the knowledge of all interactions during the dynamical process, but there arises a fundamental difficulty caused by the second law of thermodynamics. Consider heat flowing from hot to cold until thermal equilibrium is reached. In this case a retrodiction is impossible, because one cannot determine from a system in thermal equilibrium, which of the originally thermally unequal sides of the system becomes hot and which cold, spontaneously. Similar to this, if a system is in a fluctuating indeterministic state, it is not possible to predict with certainty or by strict causality, in which state the system will be when it stabilizes or as we called it, “freezes out”. This difficulty arises, because of the statistics we use to predict and retrodict the behavior and status of a physical system. The Second Law states, that entropy grows with time. Re-ordering the system costs huge amounts of energy, while to bring the same system into disorder costs no or a lesser amount than to order it. This constitutes an asymmetry between the ordering and disordering processes, which is expressed in the asymmetry of time, which is in contradiction of time symmetry assumed in both General Relativity and Quantum Theory. So, what has gone wrong here with our Physics?14 The answer to this question lies in the global properties of the universe, whether it is finite or infinite and whether we consider the presence of black holes in the universe as part of such universe or as “gates” to another world or parts of another world altogether, in different or adjacent dimensions to our universe. In order to have a discussion that is completely according to general covariance of General Relativity, it would be necessary to have no special choice of time coordinate with respect to which the universe is “evolving”. This seemingly contradicts the requirements laid down by the second law which gives time its specialness, but we learn on the other hand that inside a black hole the space and time coordinates swap roles. So, does the second law jump coordinates? A detailed discussion of these possibilities we want to spare for later, when we have looked onto more facts in both Physics and Kabbalah. In opposition to the Big Bang a black hole has maximum entropy by concentrating all gravity in one point. Subramanian Chandrasekhar said about black holes: “The black holes of nature are the most perfect macroscopic objects there are in the universe; the only elements in their construction are our concepts of space and time. And since the General Theory of Relativity provides only a simple unique family of solutions for their descriptions, they are the simplest objects as well.” The configuration of a black hole is described by ten parameters:

14

As we will see later, this time symmetry has been upheld by the latest quantum mechanical experiments (delayed choice and quantum erasure). This however does not render the 2nd law of thermodynamics invalid.

25

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

• • • •

‫ספר‬

‫בס"ד‬

Kerr metric a and m , where a x m = total angular momentum (G = c = 1); 2 parameters Direction of spin axis (φ, θ); 2 parameters Position of center of mass (x, y, z); 3 parameters The black hole’s three-velocity (vx, vy, vz); 3 parameters, where the time is surprisingly only implied in the velocity

The difference between the Big Bang and a black hole is that in the Big Bang the time is squashed to zero as is space, despite the high concentration of energy, while in the black hole the time is stretched to infinity while space is contracted to very small distances. This is the reason why the Big Bang explodes immediately and the black hole does not, it may evaporate with time. A still open question is: where does all the massive material and information 15 go – out of our universe? Only the gravitational field of a black hole, and with that indirectly its mass, remains observable. For future discussion, let us keep the following facts in mind: The growth of entropy from a very low entropy of the Big Bang, as matter was distributed into expanding space, to cluster gravitationally and finally collapse into black holes with maximum entropy defines the arrow of time. It begins in the Big Bang passing very fast and ends in black holes stretching to infinity and not passing at all. Hence, the reason for time as we observe it is the distribution of matter and its dynamics, which is in accordance with General Relativity. A second fact is that in the standard picture, the universe initially expands very rapidly away from the Big Bang, but it is incorrect to think of an explosion away from a central point. A more appropriate image is, in two spatial and one time dimensions, the surface of a balloon as it is blown up. Each point of the surface gradually recedes from each other point, as time passes, and there is no central point in the universe model, as the surface of the balloon represents the entire universe. Thus, the center of the balloon does not count as part of the expanding universe, nor does any other point that does not lie on that surface. Whether the singularity of a black hole lies on it we leave open for now. Hence, we can conjecture that any worlds of different dimensions from our physical world also lie on such surfaces and the point of origin is isolated from those worlds. In N dimensions, if one dimension is time, N – 1 become dynamic, but then the N – 1 must move along the one. As a remark, we suggest to keep this fact as it is established by Physics in mind for the description as it is rendered by Kabbalah. Henri Poincaré and Norbert Wiener state that a cognizant being could not exist in an entropydecreasing universe, because one needs a uniform flow of evolving time to be able to communicate. This statement is based on the very simple fact that with a reverse order of events and back-flowing time or with an ever changing direction of time communication as we know it would become very strange as would the dynamics of physical entities. The special cases of exactly reversed time, infinitely stretched time (timelessness) and infinitely contracted time still need a very careful analysis in regard to their consequences in the physical, information-theoretical and also kabbalistic realms. For now we can say that in the physical world an exact re-tracing of a history is impossible, if inside that history irreversible processes took place and information or other entities got lost and were transformed into 15

Any information entering a black hole is lost. When the black hole finally evaporates, this information is not reconstructed.

26

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‫ספר‬

‫בס"ד‬

energy. The same is surely true for information spaces, and it is very likely that the same is valid for any other spaces or worlds such as Atzilut, Beriah, Yetzirah and Assiyah. We have, as we have seen above, a wildly fluctuating system, where all its dimensions “oscillate” completely irregularly between their extremes. This happens in an unsynchronized manner, which gives rise to the conditions for inflation. Exact parameters and boundary conditions underlie the laws of statistics and not causality. This means, at the time and place in the not yet stabilized space-time, where the conditions for a false vacuum are given “first”, the inflation starts and gives rise to the Big Bang. Strictly speaking, such “first” needs time and space to have some extent, even on a minute scale of about 10 -34cm and 10-43 seconds, and the energy density there needs to be not lowerable for at least that amount of time. After inflation, space-time stabilizes and the temperature of the system lowers itself drastically, making possible all observed symmetry breakings in the process of the Big Bang. It is hard to conceive of an alternative theory that could explain the basic features of the observed universe. Not only does inflation produce just the kind of Big Bang that is as special as the observed one, but quantum fluctuations during inflation could have produced exactly those non-uniformities which were the seeds of cosmic structure. These non-uniformities can be observed directly in the cosmic background radiation with an amplitude of about ten parts per million16. At this point, we want to remind the reader about the Kabbalistic view of the beginning of the universe as an inflating space that stabilizes with the “birth of time”, which we will discuss after we exactly analyze these ideas of the Kabbalists. Information-theoretically the emergence of time is essential for observation as such observation must be transformed to communicable information, as we will see later. How this and Poincaré’s and Wiener’s conditions for useful communication of information agree or contradict the experimentally verified violations of the order of time as demonstrated by delayed choice, barrier tunneling and quantum erasure experiments, still remains open for further discussion. We will later attempt to propose a solution to this conundrum.

16

We do not particularly favor Inflation, for cosmic strings also explain non-uniformities, but they cannot account for the large-scale homogeneity and the flatness of the universe.

27

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‫ספר‬

‫בס"ד‬

2b: The Kabbalistic View The Ari z”l describes the first phases of creation in Sefer Etz Chaim as follows: Bear in mind, that before the emanations were emanated, and the creatures were created, the Upper Simple Light had filled the entire Existence. And there was no empty space whatsoever, namely as empty air, a hollow or pit. For everything was filled with that simple boundless light and there was no such part as head and no such part as tail. That is, there was neither beginning nor end, for everything was simple or smooth light balanced evenly and equally in one likeness or affinity, and that is called the Endless Light. And when, in His simple and smooth Will, the desire arose to create the world and to emanate the emanations, to bring to light the perfection of His deeds and His Names and His appellations – which was the cause of the creation of the world – behold he then contracted Himself in the middle point which is in Him, precisely in the middle, He contracted the Light. And the Light has withdrawn to the sides around the middle point, and there has remained an empty space and a vacuum surrounding the exact middle point. And the Light has withdrawn to the sides around the middle point. And behold, this contraction was equally balanced around that middle empty point in such a manner that the vacuum was circular and in complete balance and sameness all around. It was not in the shape of a cube, which has straight angles, because the Boundless also withdrew His Light in a circular form equally on all sides. This is due to the fact that the Endless Itself is equal. That is, since the Endless Light is in complete omniparity, it follows that It must contract Itself in omniparity on all sides. The reason for this is that the Infinite Light was symmetrical with a complete symmetry, so that it felt compelled to contract itself on all sides. And it is known that geometrically there is no figure of such symmetry as the sphere – certainly not the rectangle, with angles jutting out, nor the triangle, nor any other figure. He was therefore compelled to contract Himself to the shape of a sphere, there being no symmetry greater than that of a sphere. In the Zohar Parashah Bo, “a vessel in the sphere which is Yud”. There is a further reason: that is, for the sake of the emanations which in the future will come forth in the place of that empty void space. And behold, after the contraction mentioned above, It drew from the Endless Light one line direct from His circular Light from above downward, and it gradually descended by evolution into that hollow or vacuum. The Upper Head of the line was extended from The Endless Himself, and it contacted Him. Verily, the end of that line below did not contact the Endless Light. The line was drawn and extended below, and in that vacuum He emanated, created, formed and made all the collective worlds. Prior to the four worlds, there was only the Endless, in the form of “He is One”, in a wondrous concealed unity, for it is beyond the power or capacity of even those angels who are near Him to conceive of it. They have no conception of the Endless, blessed be He. There is no intellect created which could conceive of Him, since He has No Place, and No Boundary, and No Name. And lo, as the Infinite Light extends in a direct line in the midst of space, it does not extend and disperse immediately to the bottom; but rather slowly, slowly. That is, at the beginning, the line of the light started to flatten out; and at the beginning of this spreading out of the line in all directions – in the mystic meaning – it dispersed and extended and became a sort of wheel, completely round and detached from the Infinite Light, which imbues it from all sides. If it becomes attached it returns to its previous condition, it disappears in the Infinite Light, and its strength is NOT seen at all, and all becomes Infinite Light as it was at first. The sphere is therefore close to that of the Infinite and not attached to it. The only main connection, or joining of the sphere of the emanation with the Infinite that causes the emanation, is by means of the abovementioned line through which the light descends and extends from the Infinite, influencing the sphere. And the Infinite surrounds and encompasses it on all sides, being but a iota removed from it on all sides, for that also is of round, encompassing aspect, as mentioned before, so that the illumination by the Infinite of those receiving the emanations must come through this line only. For if the light spread round on all sides, the recipient of the emanations would be like the giver Himself, that is, limitless and boundless. Furthermore, even that line, too, is very narrow and fine and does not make a wide connection, so that the light extended to the emanated is in fixed amounts and measures. Because of this, the emanated is called the Ten Attributes (Yud Middot), and the Ten Sfirot, to show us that there is a fixed amount and measure and a limited

28

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‫ספר‬

‫בס"ד‬

number, which does not apply in the case of the Infinite. As it is written in the Zohar Parashah Pinhas: “The thirteenth command is the reading of the ‫ שמע‬but it has no measure or specific Name in the way that every Sfirah has a specific name for its measure, its boundary and its limit”. And since the line is thin, they will receive abundance only to the extent it is required, as they are the recipients of emanations, rather than the givers of emanations. And behold this first sphere, most closely attached to the Infinite, is known as the Crown (Keter) of Primordial Man (Adam Kadmon). After it, the line is extended and continued this way, then coils round in a sphere and becomes sphere number two within sphere number one. This is known as the Wisdom (Chochmah) of Adam Kadmon. The line extends then downwards again, coiling round to become a third sphere within the second. This is known as the sphere of Understanding (Binah) of Adam Kadmon. In this way, the spheres are made one within the other, up to the sphere number ten, known as the sfirah of Kingdom (Malchut) of Adam Kadmon. Here is revealed the nature of the ten sfirot, which were emanated by way of the ten mystic concentric spheres. All this is an aspect of the ten sfirot, which includes all aspects of all the worlds; but in fact it is explained – and it is a simple explanation – that many kinds of worlds were emanated, created, formed, and made a million or a billion times over, all being equally in the middle of the empty space already referred to, with Nothing outside it.

Sefer Etz Chaim explains the inflation of space and the expulsion of light from same space as the first creative action of the Creator. Here we are introduced to the concept of Tzimtzum, the self-constriction of the Creator’s light. This involves one of the most important philosophical concepts of Kabbalah, as well as one which has been a source of confusion to many scholars. The Zohar 1:15a, which is the opening statement of Bereshit, states: “At the head of the King’s authority He carved out of the supernal luminescence a lamp of darkness. And there emerged out of the hidden of hidden the Mystery of the Infinite, an unformed line, imbedded in a ring … measured with a thread …” The Bahir 25 cites Rabbi Berachia saying that “the light was like a beautiful object for which the King had no place in which to put it”. Only after a “place” was provided could the light be revealed. This suggests that the light, besides the absolute unity, is intrinsic to the singularity at the beginning of the creation process, which is justifiable by Quantum theoretical argument as we have seen above. Time and space are squashed into the singularity, and according to the relation t ≈ ħ/E we create besides wild fluctuations a veracious explosion. We need to be careful in saying light and unity are intrinsic rather than separate properties, as we would destroy the absolute unity, if we said otherwise. The solution to this difficulty is to regard the light as a product of the fluctuations. Before we discuss this issue, let us look at the effects the inflation of space was involved with. The process of carving out or engraving a reshimo17 into the vacated space took place with the creation of space and time at the expansion from the infinitely small into the infinitely big, which is mathematically imbedded into each other18. A conformal mapping of an infinitely small sphere or point into an infinitely big sphere in finite dimensions is possible and part of complex number theory. An explanation was given above. The engraving of the reshimo can be seen as a symmetry reduction with that information is discarded, in this case all the information lying outside of the reshimo. The lost information is transformed into energy or light, as we will see in detail later. This engraving process can be directly connected with the creation of the concept of natural numbers out of nothingness. With the expansion or inflation into infinite space and the 17

The concept of a reshimo is explained in Otzrot Chaim as an imprint made onto space without substance, more or less as a sort of memory that, when interacting with light, brings the “planned” object into being. 18 May the reader be reminded that the structure of the sfirot and space-time was still latent at that stage. Only with the filling with light of the reshimo structure the space-time and its contents were stabilized.

29

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‫ספר‬

‫בס"ד‬

creation of a void inside the light of Ein Sof, we have an empty set within an empty set, which defines the number 1, which is according to our definition above equivalent with an empty set. With the creation of the reshimo structure, ten empty sets were imbedded into each other after the following rule: The empty set can be written as Ø = { }, where the brackets delineate a set. If we associate Ø with the number 0, we can further define an empty set within an empty set {Ø} = 1, since this set contains one element, namely an empty set. The next number is then defined as {Ø, {Ø}} = 2; {Ø, {Ø}, {Ø, {Ø}}} = 3; and so on to infinity. This rule to create the natural numbers ex nihilo was developed by Cantor and Peano. According to Otzrot Chaim, the dimensional order of the sfirot in the state of reshimo is the following (lowest to highest dimension), cf. also Zohar Bereshit B:

•

•

Malchut (Kingdom), Yesod (Foundation, Procreation), Hod (Splendor), Netzach (Victory), Tiferet (Beauty), Gevurah (Strength, Strict Judgment), Chesed (Love, Greatness, Kindness), [Daat (Knowledge)], Binah (Understanding), Chochmah (Wisdom) and Keter (Crown). The sfirot denote besides the ten digits also the ten vowels of the Hebrew language. Hence they represent the complete qualitative and quantitative descriptors of anything thinkable (and un-thinkable) in that language.

Inside each of the sfirot, there exists a full set of all ten sfirot ad infinitum. Hence we can conclude that with the engraving process of the reshimo the concept of natural numbers by infinite symmetry breaking into infinitely many numbers, representable by ten different digits, resulted. With this the duality of nothing and one, which has been defined by the identities explained above, became extended into an infinite plurality. We can see that the reshimo as the precursor of the sfirot defined the natural numbers. A further source in Kabbalah is a study of the Preface to the Zohar with the Sulam (commentary of Rabbi Yehuda Leib Ashlag). It is written there, that the letter ‫ י‬is the forerunner of creation. It is the dot or point that everything started with. In our interpretation of the duality of non-existence and existence a line is created between these opposites. One can say the same about the other dichotomies mentioned above. Since these dichotomies are dependent onto each other, one cannot consider them as independent from each other. Hence these opposites form one dimension or a line separating the opposite properties of the dichotomies. This can be represented by the letter ‫ ו‬or its reshimo, which can be looked at as the first and primordial separation or ‫רקיע‬. We will see later, how such separation or demarcation between a system and its observer is essential for the system to come to a stable state, both in Physics and in Kabbalah. It is stated that the letter ‫ י‬is the root of all letters. The reshimo is the cause of the springing into existence of the vessel (letter), to be precise; the withdrawal of the light is the cause for the vessel to begin to exist. Again, information is discarded with the formation of the vessel by state reduction, and the vessel sends light back. The source of the worlds is then the second Tzimtzum, which took place after the Infinite Light was withdrawn after the same light was introduced to interact with the reshimo to form the Sfirot. ‫ י‬is called the fourth

30

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‫ספר‬

‫בס"ד‬

distinction19, which alludes to Malchut, which contains four-dimensional space-time. A later unison of the point enveloped by Malchut with its later position within Binah creates the splitting of the Sfirot into head and body, which has the appearance of ‫א‬. Its appearance can be explained with a diagonal ‫ו‬, which is headed by an upper ‫י‬, denoting upper waters, and supported by a lower ‫( י‬or ‫ ד‬as we will see later in our discussion of the letter ‫)א‬, denoting lower waters, so that the ‫ ו‬is the ‫רקיע‬. The vessel and the world have two consecutive sources, the ‫ י‬and the ‫א‬, where the first engendered the letters in concealment (reshimo), while the second brought them into being after the point rose to Binah (logical planning or blueprinting) 20. This action can be interpreted as the creation of a configuration space on which the Laws of Nature in all the worlds were defined. According to the same Preface to the Zohar the following names represent the states of creation:

• •

First Tzimtzum: Chochmah (‫)י‬, Binah (‫)ה‬, Zeir Anpin (,(‫ו = ז"א‬ Second Tzimtzum: 6 days of Yetzirah ((‫א‬

‫ = ע"ב‬72 ‫ = ס"ג‬63

} (‫ז"א)ת"ת‬

‫ = מ"ה‬45 ‫ = ב"ן‬52

• •

Malchut  2 x ‫הויה‬

First Tzimtzum: It is clearly stated, that with the first Tzimtzum the Divine Light was expelled from the original “point in infinity”, which mathematically represents a sphere of infinite radius that is still not stabilized, or as we say in Physics, fluctuating (Sefer Yetzirah 1:6): ‫עשר ספירות בלי מה צפייתן כמראה הבזק ותכליתן אין להם קץ ודברו בהן ברצוא ושוב‬ ‫ולמאמרו כסופה ירדופו ולפני כסאו הם משתחוים‬: Ten Sfirot of Nothingness, their vision is like the appearance of lightning, their limit has no end, and His Word in them is running and returning, they rush to His saying like a whirlwind, and before His throne they prostrate themselves. Here it is clearly stated that the sfirot were in a yet unstable state, unless they are “spoken” to, which can be generalized to interaction. Aryeh Kaplan comments: “It is only with regard to the generic speech that the sfirot oscillate [fluctuate], running and returning, but when there is a specific saying [‫]מאמר‬, they no longer oscillate, but rush like a whirlwind.” The running and returning speech here denotes all concepts necessary for creation as well as all ever possible mental, physical and other activities or concepts are all latently present, but not in a stabilized or condensed form as after creation. The prostrating after the specified speech of the ‫ מאמר‬can be understood as such stabilization, which alludes to the second Tzimtzum. This can be seen as a wave-function collapse by observation or a similar action that still has 19

At the time of writing, a source for such “fourth distinction” in scripture eludes us. We therefore inform the reader that this expression was used by Rabbi Yehuda Leib Ashlag in his aforementioned study of the introduction to the Zohar. He also gives no further explanation. 20 ‫בריאה‬

31

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‫ספר‬

‫בס"ד‬

to be defined. Such wave-function collapse stabilizes the system and makes the process irreversible. The exact mechanisms for such a process are described in our separate treatment of Quantum Theory in the Appendix, but the issue will be much better understood towards the end of this book. This allows the creation of the first reshimo without the necessity of the presence of time. The reshimo was created in the first Tzimtzum and needs to be voluminous only later after the second Tzimtzum where such volume is needed: in the physical world of Assiyah and in the realm of Yetzirah (formation). Whether voluminosity in the physical sense is needed in the higher, spiritual worlds remains doubtful. On the other hand the formerly established relativity of space-volume allows such spaces to appear voluminous to “observers” inside them. Additionally, the first Tzimtzum appear only as an engravement in n-space 21. Let us now analyze how it is possible to create such a thing without specifying or creating time or stabilizing the system through any interaction or observation. We have seen above in our scientific view that with the emergence of the universe, light or energy is also latently available in abundance, because of the yet in-phase fluctuation of time with space22.

1. The dichotomy of absolute nothingness being absolute ONE at the same time “creates” automatically the point in infinity, the letter ‫י‬. 2. The dichotomy of such point in infinity being an infinite sphere at the same time allows the following: it can be such sphere in all possible dimensions from zero to infinity. This builds mathematically a set of infinite spheres around a point. All these spheres are not materialized, but only latent, as they are simultaneously infinitely small and infinitely big. This is called in Etz Chaim “Reshimo”. 3. The above concepts of being and not being or small and big create a set of dualities. This very set of dualities can be represented by a line, represented by the letter ‫ו‬, which is created herewith. 4. With the creation of the still imaginary spheres of the reshimo the concept of natural numbers was also given as has been shown above by Cantor’s theorem. 5. The expulsion of the light to the outermost sphere (or point) can be explained by an energy fluctuation in form of a δ-function explained above. This is the Light of Ein Sof which provides energy for the system. In the not yet stabilized system the innermost sphere can be the outermost at the same time23, if the relativity of space as described above is taken into account. In the fluctuating state one cannot say, where and what of the system may be the observer. Hence, the light is inside the point and outside the sphere system at the same time.

21

As stated in Etz Chaim this n-space is divided into ten cardinal parts, namely the sfirot of Adam Kadmon. In-phase fluctuation means, that time is not yet distinct from other dimensions and still is symmetric, because the second law of thermodynamics is not yet in place, neither is any Lorentz-invariance. This is the case, because all interactions, i.e. inter alia the physical interactions like gravity, electromagnetism and nuclear (strong and weak) fields are still indistinguishable inside grand unification. This however does not mean that all dimensions fluctuate strictly in-phase. It means only that the time is not yet distinguishable from space and other dimensions and therefore the Lorentz-invariant dependency of space and time does not exist yet: So, if space shrinks, time not necessarily expands synchronously. 23 Cf. ‫ "וזהו בערכנו אנחנו בני אדם היושבים‬,‫ דף יד‬,‫ שער א דרוש עגולים ויושר ענף ד‬,‫ספר עץ חיים‬ ‫ וכל מה‬,‫ אדרבה עולם העשיה הוא הקליפה החופפת על כולם‬,‫ אבל בערך א"ס הסובב הכל‬,‫בו‬ ‫שנתקרב אל הא"ס הוא יותר פנימי‬..." 22

32

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‫ספר‬

‫בס"ד‬

This allows to have created n-dimensional space and infinite energy, which allows now creation on the level of emanation (‫)ע"ב‬. For an explanation of this name please refer below to the second Tzimtzum. Whether the energy really needs to be infinite from the very beginning is questionable as we will see in the description of inflation of the physical universe. For infinitely dimensional space it will definitely have to be infinite, because it is quantized. Second Tzimtzum: Etz Chaim states that a line of light was drawn into the reshimo to manifest the spheres, which can be interpreted as a “freezing” (according to the Copenhagen interpretation the wavefunction of the fluctuating precursor of the universe collapses) of the latent structure of the first Tzimtzum into a configuration space which allows basically the creation of anything there could be thought of. The implications of such a ”freezing” into configuration space like conscious observation or conscious willing will be discussed in the next chapter. The following conditions are known:

1. The light from Ein Sof proceeded from the outer infinity (from outside the sphere with infinite radius) to fill the reshimo sequentially from outside to inside until it stopped before the original point leaving it untouched. In Kabbalah the introduction of the line of light and its stopping are caused by Divine Will, while in Physics such a process needs an observer-interaction or objective state reduction process24. This clearly is the creation of time, because it represents the onset of dynamics in the classical limit. The light drawn into the sequential manifestation of the sfirot was not supposed to touch the inner original point because a unification of such light would have made the whole structure latent again as is explained in Etz Chaim (this constitutes the second ‫)רקיע‬. This unification would constitute an uncertainty of the location of the Infinite Light and with that an entangled or evolving state and not a reduced state of the world system just created. As we will see later, such a state of affairs enables the undoing or quantum erasure of a state reduction as demonstrated in quantum erasure experiments. Surprisingly, the conditions given by Kabbalah are very similar to the conditions of Physics. 2. The sfirot were manifested in such a way that • The sfirah of Keter was next to the light of Ein Sof; • Next to that were the sfirot of Chochmah and Binah with Zeir Anpin; • Last the sfirah of Malchut, left without light inside, so the middle point of the beginning including its remaining light was separated from the worlds. The physical world is on the surface of the sphere, while the Sitra Achra (other side) of that sphere represents the world of the Klipot and dwells in darkness. • The sfirot separated with the introduction of light which then can be seen as “concentric” spheres with a middle point, while the ‫ צינור‬still falls short of the distance between the original radius of Keter and that of the Or Ein Sof. Now we have the concepts of space and time defined as well as the concept of numbers. It naturally follows from the above, that a configuration space on (or in) which all the worlds could be defined mathematically was also created, as well as energy was brought into being. 24

This issue needs careful elaboration, as the question remains: how did the Creator effect these actions? The possibility of inevitability of these occurrences needs to be taken into consideration, too.

33

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‫ספר‬

‫בס"ד‬

The configuration space comprises the created void including the border to the infinite light. The space around the original point as well as the realm of the expelled light does not count as configuration space according to our definition. We do not want to include the infinite evolving part of the Total Existence and its infinite light into such configuration space. We rather propose the border between such configuration space containing all creation and the Creator with his light as the demarcation and henceforth stabilization of both the realms of creation and the Creator as opposites to be able to interact. Strictly speaking such demarcation does not affect the absolute oneness of the Creator, because as we learned above, opposites form one dimension or set of dimensions. In this case we conjecture the possibility of one set of all possible dimensions made up of all possible observables on the side of the creation and all observations on the side of the Creator. We will see later how by such observations alone it is possible for the Creator to interact with all observables in any manner whatsoever, leave free will and influence of the creations untouched in their realm and sustain and guide the creations at the same time. The totality of Creator and creation together remains henceforth one single entity, but now in a stabilized state allowing further creation, formation and action, as distinct to the state before space, time, matter, morality and all other created concepts were in a grand unification but yet undefined. This Total Existence is now divided into a part of a manifest state reduced part that is stable, represented by the vacuum with the sfirot system and the created worlds and the ever evolving part of the expelled Infinite Light. Both are separated by a ‫רקיע‬, represented by the border of ‫כתר עליון‬ to the Infinite Light. This can be interpreted as the configuration space of all worlds including that of Adam Kadmon. According to Y.L. Ashlag’s study of the preface to the Zohar, in a second withdrawal of light, the letters were formed as vessels. This happened as the light overtook the already existing letters ‫ ו‬,‫ י‬and ‫ ה‬as Binah was created during the first Tzimtzum as well as ‫ז"א‬, which is denoted by ‫א‬. Now the following process took place: The creator now consciously had the vessels created latently in the brain of Chochmah and Binah (Abba and Imma): The letters of Zeir Anpin (Partzuf Tiferet and Malchut), which here belongs to the spiritual worlds, contain both the letters of the ‫א"ב‬. Zeir Anpin was included in Chochmah and Binah. At the second Tzimtzum the light pervaded the Sfirot only up to Binah, where it terminated. Rabbi Ashlag’s study of the preface to the Zohar explains, that the point (or screen or curtain) of Malchut rose to Binah creating an immature Partzuf and remained there. Hence, the light stopped at Binah. The effect of this was that at Binah, the two points met and formed the line mentioned above. This is the creation of the second ‫רקיע‬. It has to be remarked, that the two points are in essence the same point (before and after Malchut moved). The implications of this are manifold. With the creation of the second ‫ רקיע‬a principle of opposites, which permeates all creation, is brought into existence. While in the first ‫ רקיע‬the opposites were not distinguishable and only a polarization or fluctuation took place, now the opposites were separated and “frozen in” (consciously observed). This constitutes the most important aspect of symmetry reduction in this process. Now spaces and realms could be defined as described in Sefer Yetzirah: a set of worlds could be created, one of which is the physical world. Still the question arises whether the worlds, which at the same time represent the stages of creation, were created consciously and willingly or by statistical chance. Logically, emanation, creation, formation and making or action must follow that order, and hence, these worlds were created in this order inevitably. The worlds of Adam Kadmon and Atzilut

34

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

‫בס"ד‬

however do not follow such logic, because no time in our sense exists there, only an order of time. This would agree to our conjecture that only after the emanation of space-time and all other dimensions the creation and formation processes can follow the (time-asymmetric!) laws of Nature. It still remains open to discuss how order of time violations are possible to be observed on the level of the lowest of the worlds, Assiyah, the world of making and action25. Sefer Yetzirah 1:5: ‫עשר ספירות בלי מה מדתן עשר שאין להם סוף עומק ראשית ועומק אחרית עומק טוב‬ ‫ועומק רע עומק רום ועומק תחת עומק מזרח ועומק מערב עומק צפון ועומק דרום אדון‬ ‫יחיד אל מלך נאמן מושל בכולם ממעון קדשו ועד עדי עד‬: Ten Sfirot of Nothingness: Their measure is ten which have no end, a depth of beginning, a depth of end; a depth of good, a depth of evil; a depth of above, a depth of below; a depth of east, a depth of west; a depth of north, a depth of south; the singular Master G-d faithful King dominates over them all from His holy dwelling until eternity of eternities. And 1:13: ‫בירר שלש אותיות מן הפשוטות בסוד שלש אמות אמ"ש וקבעם בשמו הגדול וחתם בהם‬ ‫ שש חתם תחת ופנה למטה‬.‫ חמש חתם רום ופנה למעלה וחתמו ביה"ו‬.‫ששה קצוות‬ ‫ שמנה חתם מערב ופנה לאחריו‬.‫ שבע חתם מזרח ופנה לפניו וחתמו בוי"ה‬.‫וחתמו בהי"ו‬ ‫ עשר חתם צפון ופנה לשמאלו‬.‫ תשע חתם דרום ופנה לימינו וחתמו ביו"ה‬.‫וחתמו בוה"י‬ ‫וחתמו בהו"י‬: He chose three letters from among the Elementals, in the mystery of the three Mothers Aleph Mem Shin, and set them in His great Name and with them, He sealed six extremities. Five He sealed above and faced upward and sealed it with ‫יהו‬. Six He sealed below and faced down ward and sealed it with ‫היו‬. Seven He sealed east and faced straight ahead and sealed it with ‫ויה‬. Eight He sealed west and faced backward and sealed it with ‫ויה‬. Nine He sealed south and faced to the right and sealed it with ‫יוה‬. Ten He sealed north and faced to the left and sealed it with ‫הוי‬. From these two verses we can learn a few aspects of the creation of the space-time we are observing in our universe. 1:13 defines all three spatial dimensions and six orientations of physical space-time, while in 1:5 two more dimensions with four orientations are defined, but not “sealed” as the spatial ones. From this we can conclude the dimensions being in the state of a reshimo there, while in 1:13 the action of “sealing” can be interpreted as an observation and henceforth the dimensions named here were stabilized26. Note carefully that the time and moral dimensions are only mentioned in 1:5 as “depths”, their orientations being defined by sfirot representing opposites. We see, as commented by Aryeh Kaplan, that “space-timemorality” is defined as a five dimensional space with five pairs of sfirot as denominators of its orientations. The spatial dimensions are additionally sealed by permutations of the three 25

We refer here to the quantum mechanical experiments that violate such order of time, which are discussed below. 26 Let the reader be reminded that here we are not talking about Newtonian space-time. The sealing of dimensions takes place in relativistic space-time, so that under special conditions like e.g. in a black hole such dimensions are freely exchangeable. The sealing denotes the names of directions and not their lengths or positions.

35

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

‫בס"ד‬

letters making up the Tetragrammaton. According to Sefer Raziel 12a (31), the primary order of these letters is ‫יהו‬, because the ‫ י‬includes the first four letters of the alphabet since it has the gematria 10. After the first four letters ‫ ה‬and ‫ ו‬follow. In the system of the letter permutations the letters ‫ י‬and ‫ ה‬are determining the orientations while the ‫ ו‬is the neutral letter whose position determines the axes of the dimensions and henceforth the origin of the coordinate system denoted by the Tetragrammaton. Opposite permutations of the first two letters denote opposite orientations. Concerning the ‫ ו‬as a separator or origin between opposites, the Sefer HaBahir 30 states: “They said to him: But what is ‫ ?ו‬He said: The world was sealed with six directions. They said: Is ‫ ו‬not a single letter? He replied: It is written (Tehillim 104:2), He wraps himself a light as a garment, [He spreads out the heavens like a curtain].” In Kaplan’s commentary we can find the ‫ י‬defining the beginning of time, which is the past, while one ‫ ה‬of the Tetragrammaton is supposed to denote the future, while the other one is used for the definition of spatial dimensions27. Up to now, nothing is said about the moral dimension of Good and Evil. Instead the relation of the three letters of the Tetragrammaton to the three “mothers” (‫ )אמ"ש‬is pointed out, which alludes to the separation of opposites in two ways:

• •

The ‫ א‬denotes the ‫ רקיע‬between the upper and lower waters, and breath or air28; The ‫ מ‬denotes water and the ‫ ש‬fire, which are opposites;

These opposites are separated by the ‫א‬, which contains the separator ‫ו‬. We suggest the “sealing” process in the manner using opposites defining dimensions spreading orthogonally to the ‫ ו‬as a separation, distinction or demarcation (‫ )רקיע‬is essential for the stabilization or “freezing out” of a latently created space of whatever generalized dimensions as we will see later in our discussion of the measurement problem of Quantum Theory. The fact that time is not sealed but only given a beginning with the ‫ י‬may show the asymmetry of macroscopic time as determined by the 2nd law of thermodynamics. It is also the malleability of time as seen in relativity that affects space. Let us quickly see how spacetime29 is affected by the distribution of matter and radiation. As we have seen earlier, the contents of a space determine its voluminosity, while the dynamics of those contents determines the flow of time and of course the time as a dimension of space-time. All dynamics of all possible spaces and their contents originated in the still not stabilized ‫י‬, and from there an arrow of time was created for all worlds with demarcations. As mentioned above, the 2nd ‫ רקיע‬gave rise to a second source besides the ‫י‬, namely the ‫א‬, which is the source of all letters. ‫ י‬was responsible for the creation of the letters in concealment (reshimo), while ‫ א‬served as their source in reality or in the stabilized creation. A set of names for the Creator depicting the different worlds or universes was created herewith also in the manner as stated above (Havayah)30: 27

That the time has not been sealed in the future like the spatial dimensions may allude to its malleability as we see it in General Relativity, where it is also freely interchangeable with other dimensions. The spatial dimensions represent physical reality in the sense of substance while the time as well as morality are only “felt” in form of dynamics (time) or as mind-sets (morality). 28 In Hebrew, the word for “direction” is the same as for “air”, ‫רוח‬. 29 Strictly speaking, it is the voluminosity of space-time we are referring to here.

36

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

Chochmah Binah Zeir Anpin Malchut

‫י‬ ‫ה‬ ‫ו‬ ‫ה‬

‫ע"ב‬ ‫ס"ג‬ ‫מ"ה‬ ‫ב"ן‬

‫בס"ד‬

‫ספר‬

Atzilut (Emanation) Beriah (Creation) Yetzirah (Formation) Assiyah (Making, Action)

‫יוד הי ויו הי‬ ‫יוד הי ואו הי‬ ‫יוד הא ואו הא‬ ‫יוד הה וו הה‬

The ‫ א‬only appears in the lower part of the name ‫ס"ג‬, in the ‫ואו‬, which is showing that the origin of the worlds is Zeir Anpin, the body of the Etz Chaim, or Adam Kadmon or any full set of the ten sfirot. An arrow of time we will have only after distinctions and classifications are made in Binah of any world, otherwise we have only statistical time or an “order of time” as we will discuss at length later. To be consistent, one must now ask a question concerning the existence or creation of the ‫ה‬, if there is only ‫י‬, ‫ ו‬and ‫ א‬present. The answer is, from the ‫ א‬of “‫( ”ע"ב דס"ג‬lower part of the ‫)א‬. Combined, the ‫ ד‬and the ‫ ו‬give a ‫ה‬31. The ‫ ד‬represents two dimensions, while the ‫ו‬ represents one; together they represent three dimensions of physical space. The Tetragrammaton then represents seven dimensions, because the ‫ י‬represents zero dimensions. We will see later that Malchut must have seven dimensions for this reason, and because in the view of Malchut being the shell of all worlds, seven dimensions provide the biggest possible volume so that all higher dimensional spheres that have a smaller volume will fit into the sphere of Malchut in the appropriate order, Keter being the smallest one. The rest of the letters were formed according to Sefer Yetzirah 1:11: ‫שלש מים מרוח חקק וחצב בהן כ"ב אותיות מתוהו ובוהו רפש וטיט חקקן כמין ערוגה‬ ‫חצבן כמין חומה סיבבם כמין מעזיבה ויצק עליהם שלג ונעשה עפר שנאמר כי לשלג‬ ‫יאמר הוא ארץ‬: Three: Water from Breath. With it he engraved and carved 22 letters from chaos and void, mire and clay, He engraved them like a sort of garden, He carved them like a sort of wall, He covered them like a sort of ceiling, And He poured snow over them, and it became dust as it is written: “For to snow He said, ‘Become earth’”. We will come back to this in our discussion of the philosophical implications of Quantum Theory. For our discussion now the created letters are five letters of the Hebrew alphabet, all of them representing three groups of letters: mothers (‫)א‬, doubles (‫ )ד‬and Elementals (‫ ה‬,‫ ו‬,‫)י‬. As we saw above, according to Sefer Etz Chaim the interaction of the light drawn into the thread from the outer light of Ein Sof towards the center point with the engraved structure then manifested the ten sfirot of nothingness, from which the world of Adam Kadmon 30

Insofar as the Creator is concerned such names should not be used to address Him as they denote only parts of His creation and not Himself, G-d forbid. As it is stated in Etz Chaim and elsewhere, He has no name. Denominations like the Tetragrammaton etc. are merely used as variables in blessings and prayers, not as the Creators real name. This is one of the reasons it is forbidden to pronounce the Tetragrammaton. Its letters are also His creation, not Him. This issue will be discussed in the framework of our treatment of idol worship. 31 Cf. Raavad on Sefer Yetzirah, also Gra on Sefer Yetzirah 1:2.

37

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

‫בס"ד‬

emanated together with the worlds of Atzilut, Beriah, Yetzirah and Assiyah, which includes the physical world. The reshimo of the sfirot was filled with light in a sequence, so that we can say, this was the onset of primordial time, which with the same action “froze out” ndimensional space-time. This primordial time is to be understood rather differently than the time we know in our physical universe. It is rather a sequence of time created by the dynamics of the filling of the reshimo of the worlds with light. The sequence was created by the evolutionary bringing into a stabilized reality the system of the sfirot, sfirah by sfirah, as presented in Etz Chaim and elsewhere. In contrast, our time is an arrow of time given by the thermal conditions and the dynamics of the distribution of matter in our universe; it is dependent on the second law of thermodynamics32 and valid on the surface of the sfirah of Malchut. In the study of the Torah the difference is known as the order of time (‫ )סדר זמן‬and time (‫)זמן‬. A detailed account of this is given in Otzrot Chaim and in Etz Chaim as well as in the Sefer Yetzirah, Sefer HaBahir, and Sefer Pardes Rimonim and in the Zohar. We have to remind ourselves here about the fact that the Kabbalistic treatment of Creation and Formation is only qualitative and does not define the boundary conditions of spontaneous symmetry breaking or “system freeze-out”. In Quantum Theory we will see that the conditions of those are mainly dependent on the thermodynamic conditions prevailing in the early universe, manifested in the form of phase transitions and other critical phenomena. From these mechanisms we can conclude, how in the higher dimensions of the higher worlds such phase transitions took place. Such a process of evolving and reducing states is described in detail in Etz Chaim33. T he Ari z”l writes in Etz Chaim a remarkable condition of the Tzimtzum: The resulting vacuum, in which the worlds would be located, had to be as symmetric as possible to allow creation. In addition, no vertices or other singularities were allowed, i.e. the whole structure had to be differentiable, as cited above (Etz Chaim 1:2). In terms of the Physics of such space-time or vacuum he asserts full isotropy which due to very recent ideas need not be an intrinsic property of our universe, if observed from outside. Observed from inside, however, we can postulate isotropy34. Then a line or pipe of light (‫ )צינור‬was drawn from the outer light into the spherical vacuum, as it is written, by evolution, which denotes its interaction with the engraved structure of the sfirot in a defined course of time, bringing them into reality. Remarkable is, that the line of light only touches the outer light and not the light of the ce nter point, since then there would be no directions or dimensions possible as well as the freezing-out of space-time would have been reversed like we know this effect from very recent experiments which confirmed quantum erasure. In this case the information and energy flow from the source to the detecting and registering system was not interrupted by producing communicable information distinct from the source of information, so this information could be changed even after detection. That means the system never got out of the undefined state, in kabbalistic terms, there was no ‫רקיע‬. Here the separation of the light 32

In quantum mechanical experiments violations of the orientation of time are measured as separated events at instants of time. A reversal of the continuous evolution of time was not observed, as we will see below. 33 Cf. ‫ שער מטי ולא מטי‬,‫ספר עץ חיים‬ 34 Simulations with condensed matter like liquid Helium which mimics the quantum behavior of the universe hint to anisotropy. This could explain the asymmetry of time and the 2nd law of thermodynamics in the classical limit of the universe.

38

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

‫בס"ד‬

of the original source ‫( י‬point in the center) and the light that got expelled to the outside of primordial space and drawn back through the ‫ צינור‬is accomplished by not letting the latter light reach back or connect with the light of the point. We will discuss this effect which seems so equally fundamental in both the kabbalistic and Physics account of the onset of creatio ex nihilo. So far, the creation of space and time in Beriah, Yetzirah and Assiyah seem to crystallize. Etz Chaim speaks about the creation of Adam Kadmon with the main partzufim Arich Anpin, Zeir Anpin, Chochmah, Binah and Malchut, while Sefer Yetzirah elaborates on the role of the letters as denominators of formation. Etz Chaim 1:2 goes on to describe the creation of the world of Adam Kadmon and the other worlds as follows: And behold, each world has its own ten sfirot. And each individual sfirah in each world is composed of ten distinctly separate sfirot. Each one is in the form of a sphere, one inside the other, and one after the other, endless and innumerable; one inside the other like the layers of an onion, like a picture of wheels. We now come to explain the second aspect of the ten sfirot, namely the Light of Righteousness, in form like three lines in the shape of the supreme man… It extends from the top downwards, enclosing the ten sfirot in the mystic similitude of the upright man standing upright and comprising 248 limbs imagined from the ten sfirot, both in totality and each sfirah separately – of the ten without end in the same form as the ten sfirot which are as spheres. This aspect is termed “the image of Elokim”, … Torah Bereshit 1:27: “And Elokim created man in His Image, in the image of Elokim”, and almost all of the Zohar and the Tikunim HaZohar are concerned with this second aspect alone, as indicated elsewhere. … it is quite obvious that the largest of these spheres, encompassing all the others, is the wheel of the Crown (Keter), which is more closely attached to the Infinite than the others, and is therefore more excellent and laudable. But the second wheel, known as Wisdom (Chochmah) has a space between it and the Infinite, which is the wheel of the Crown, so that its degree of superiority is one less than that of the Crown. Similarly, the wheel of Understanding is double the distance away from the Infinite that is two wheels away, so in grade it is inferior to Wisdom. Thus, the nearer to the Infinite is the world’s sphere in space, the more superior it is and the greater its excellence, down to this world, which is in the very center of all the spheres, within the void space mentioned above. It is far removed from the Infinite, farther than all other worlds, so that it is so material, so mundane, that it has no peer, being in the middle of circles. Understand this well. There is also a second reason, connected with the first. As has been explained, the line extending from the Infinite stretches then to form a sphere, expanding further down wards and circling up to the very last of all the spheres. And the first sphere at the beginning of the line is superior to, and more excellent than all the spheres below it, as it comes from the top of the line, and furthermore it is illumined, being in the highest place – the highest sphere of all, known as “upward”. The sphere next inside is middle and center – the lowest of them, illumined from the bottom of that line, is known as “downward”.35 1:4… Similarly, all were required by the Holy one, blessed be He, with which to create the world and perfect it – the brain at the center, with layers surrounding it, all worlds likewise, one within the other, so that each one surrounds the next…The innermost is the outer shell, and surrounding the rest of the brain…

Again here we see (1:4) relativity of space, and definitely the differences of the spheres in dimensionality (1:2), as there is no up and down in space. The Ari z”l tries exactly to explain that, but in very cumbersome language. He refers to different degrees of superiority. As we have discussed earlier, this means that one can see from a superior sphere to the lower ones but not vice versa, in our opinion a clear hint to the different dimensionality of the spheres. 35

See also Sefer Yetzirah Chapter 1 on this issue.

39

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫בס"ד‬

‫ספר‬

How did this spiritual creation affect the level of Assiyah and the physical universe? It is said, and one can deduce this from the dimensionality theorem and the passages cited above that the physical world including man is a projection of all the higher worlds. This means that if one follows logic, the physical world inside Assiyah must be together with Assiyah a projection of Yetzirah, which is itself a projection of Beriah, which is itself a projection of Atzilut. This means also that due to different dimensionality these projections, when looked upon them separately, will look different. Even self-similarity may not necessarily be obvious. These worlds known to us either by scientific observation or by handed-down tradition work differently, their “Laws of Physics” look different, but that does not necessarily mean that the underlying common principles of Mathematics will after thorough examination yield different “Physics” for the different worlds 36. The idea of projections rather lets us expect “common laws of functioning” or if we want to define it like this, “Physics”. Definitely, we are not only looking at our physical universe alone, but together with the spiritual worlds we know from tradition, also at the realm of the mind, may it be the human mind or the “mind of the worlds we live in”. In the following chapters we will try to understand the different worlds according to mathematical consistency, which may include besides strictly logical processes also effects and observations beyond logic. We remind the reader of the existence of Information Theory, which examines systems inter alia on logic, provability and computability. This is in the “hard sciences” the border to processes of the mind, which, as we will see, can conceive physically non-realizable objects.

A non-realizable geometry:

object

in

Despite of the impossibility to construct such an object in physical real space we can do it still in our mind. A good question for the reader to answer: What is the minimum number of dimensions where such a 3- D projection of the object into real space becomes feasible?

36

Higher dimensions than the ones we can observe have more degrees of freedom than what we are used to. Only this can be a reason that in those higher dimensions the laws of Physics would appear strange to us.

40

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

‫בס"ד‬

2c: Discussion of Kabbalistic and Scientific Point of View 1. Geometrical and other mathematical conditions: The process of the first Tzimtzum as described in Sefer Etz Chaim and elsewhere has certain conditions attached to it, which can shed light on the Physics of the creation of the physical world. Those conditions are:

1. When you are in the realm of a sfirah, you can see all the realms of this sfirah and of all lower sfirot relative to that one you are in. 2. When you are in the realm of a sfirah, you cannot see all the realms of the sfirot higher than that one you are in. 3. The relative surroundings (other, visible sfirot) of the sfirah you are in seem to envelop your sfirah or vice versa. 4. The entering light fills the engraved structure of the reshimo sequentially, where the sequence is the rank of symmetry from highest to lowest, also according to their rank in dimensionality37. 5. The entering light does not touch the original source, which is the point at the beginning. 6. The sfirot are exactly spherical, any vertices or singularities or edges are not allowed. 7. The appearance of volume underlies the laws of relativity of space as defined above. Let us now explore, under what conditions these statements are true in the mathematical sense. Due to statements 1 and 2 the sfirot must differ in dimensionality, because we have here a purely mathematical structure. A set of three-dimensional spheres as they are very often perceived, would allow the view to the higher sfirot in the same way the lower ones are perceived. The only condition where asymmetric perceptionality as stated in these conditions is valid is a regular order of dimensionality. Supported is this by the statement in Etz Chaim that there is a ranking of superiority between the sfirot. Due to statement 3 a relativity of space must prevail. As the planetary motion of a solar system appears to the observer as if he is always in the center, the “visible sfirot” also follow that rule. Group symmetrically from sfirah to sfirah in descending order of dimensionality, symmetry is broken in the sense, that below each transition between sfirot the lower one is no longer invariant under the full group transformations as it was above the transition. The same criteria apply when assemblies of sfirot move up or down relative to others. Certain symmetries are broken, such that a sfirah is now only invariant under a subgroup of the relevant higher group symmetry transformations. While the subgroup describes the remaining symmetries of the lower sfirah in question, the co-set space R = High/Low characterizes the broken symmetries, i.e. those transformations that change the “ground state”, which is the lowest possible energetic state of a system, in its perception. The co-set R represents the manifold of internal states or, as it is called in Mathematics and Physics, the degeneracy space. According to 4, the symmetries are broken sequentially in a proper order of time, as the light interacts with the reshimo. This sequential symmetry breaking is a parallel to the symmetry breakings of the physical universe after the onset of the Big Bang. Since we have to understand this “explosion” as a rapid filling of the Riemann sphere with energy and matter as described before rather than as a central explosion from a central point in three37

The light not necessarily followed in this process time as a continuum, but rather an order of time.

41

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

‫בס"ד‬

space, this can be alluded to the filling with light of the respective sfirah representing that Riemann sphere. In 5, we state the entering light is not touching the center point, as stated in Etz Chaim. This has two implications in Physics, one being the establishment of a demarcation between the entering light and the center point, and the other a possible reunification of the center point with the light from outside would reverse such a demarcation and reinstate the dichotomy of the original point-sphere system. An experiment for demonstration of such a reinstating process is the quantum eraser we will explain extensively later. Vertices or sharp edges as mentioned in 6 would constitute lines and points in the system and allow relative coordinates of those objects which make the original point in infinity system just another point in such coordinates and with that a defined space. That would make the point-sphere fluctuations impossible, because only a point in infinity in no space can constitute such fluctuations, and for the system to be self-emerging until stopped by the bringing in of the light from outside the system it is necessary to have the point-sphere system in a space-free environment enabling creatio ex nihilo. Philosophically we can argue this may also be the real reason for the validity of general relativity: space-time wraps around its contents rather than the contents being put into a rigid Newtonian space. The relativity of space or its apparent voluminosity depends on the viewpoint of the observer as stated in 7. This means, volumes of sets of dimensions or spheres of different dimensions will appear different to observers in different spaces made up by different or partially overlapping sets of dimensions. Any motion within these spaces will therefore look entirely different to different observers. For example a moving object in dimensions 1, 2 and 3 may appear to the observer in this space moving moderately while for an observer in the dimensions 1, 2, 3, 4, 5 and 6 the same motion may appear much more vehement as the voluminosity of that space is greater than in the former three-space. In the contrary, an observer who resides in 3 to 25 with his physical dimensions in 23, 24 and 25 will observe no movement at all and possibly will not even be aware of that particular object for reasons of resolution of his sensing system, because for him dimension 3 is one of the small volume dimensions. We can speak of a sequential symmetry breaking during the interaction with the engraved reshimo structure of the world created during the “drawing back from the expelled light into the vacated space” until the state of the physical universe was reached. All higher symmetries relative to the symmetry group of the physical world still exist and certain interactions between their “phases” (sfirot) are possible38. We use here the word “phase” for a sfirah to connect the principles of Physics with those of Kabbalah in the sense that the sfirot can be mathematically modeled with the same methods as the phases of the observed universe, which includes also in science realms of consciousness and other non-material subspaces. Before we further analyze the creation process in respect to both sfirot and physicalmathematical phases, there should be a reminder to the fact, that all sfirot can contain the whole set of sfirot “ad infinitum”. Let us discuss the writings of Sefer Etz Chaim as a manifestation of symmetry breaking and propose a possible scenario. In the beginning (point in infinity / sphere with infinite radius) existed the highest possible symmetry as well as the highest and lowest possible dimensionality indistinguishable from each other. All possible combinations of infinite and finite sets of sfirot were contained in the then prevailing fluctuation. With the expansion into 38

Letters connecting the sfirot could represent partition functions distinguishing between these phases of different symmetry or dimensionality.

42

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‫ספר‬

‫בס"ד‬

a void with a boundary separating the light of Ein Sof to the outside of a void that contains the engraved structure of the reshimo, the first set of symmetry breakings was effected. With the bringing in of the ‫ צינור‬containing a string of light coming from the now expelled Or Ein Sof, the structure was “frozen” into a stable structure which can be seen as configuration space of all the worlds to be created including the vacua (yes, there is more than one vacuum) of the observable world(s). This proposed configuration space deduced from information provided by Kabbalah may be regarded as the platform for inflation and was brought into existence by the following symmetry reductions:

•

• •

•

Singularity to duality: our point in infinity becomes a void with a boundary and the light gets expelled outside the boundary. The system is still in an evolving state and not stabilized. The symmetry breaking is effected by the separation of light and “empty” space, but at this stage the symmetry breaking is still reversible. The smoothness and high symmetry of the light and the point-sphere system mentioned seems to be in accordance with the low entropy of our universe at the pre-inflationary stage. Plurality is invoked by the reshimo of the sfirot system, but also in a reversible manner. With the bringing in of the string of light preferred directions and an asymmetry of space were created and the system was stabilized through the demarcation between the center point and the end of the string of light. The emphasis of Etz Chaim on the sequential entering of the light into the reshimo system as well as the asymmetric location of the string of light may be interpreted as the emergence of time. This asymmetry of the resulting space-time also “freezes” the number of dimensions of the system. A naturally emerging number of such dimensions, however, is not determinable and may well lie in infinity. We have now a defined region of spacetime within the demarcations between the system and the middle point as well as the formerly expelled Infinite Light on the outside of the system39. The outside of the system is now fully disentangled from the center point system while it is still entangled with the formerly expelled light which is connected with the sfirot system through the thread of light. The Infinite has now two aspects: the totally detached center point and the connected Infinite outside. This will be a very interesting subject for further discussion when we have learned more about the underlying physics. The sfirot system of the worlds is now established and allows further symmetry reductions within each sfirah. Sets of sfirot make up different worlds that have the remarkable property to be connected with each other and the Infinite through the thread of light and the ‫ צינור‬which allows entanglement over the boundaries of the sfirot and the worlds created40. The sfirah of Malchut of the main sfirot system is now ready to receive the Creation of our physical universe on its surface41.

39

Inside and outside are not in a fluctuating state anymore but are dependent on the viewpoint of the observer. 40 We regard this as a possibility of communication gateways to the “higher” worlds, be it physically or through the faculties of the mind. We regard divine service as such way of communication but remark that the exact mechanisms of such service are not fully understood and desperately need further research. 41 According to our interpretation any worlds are contained on the surfaces of sfirot or sets of sfirot, not within their volume, otherwise we create a mathematical blunder regarding special and general relativity.

43

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‫ספר‬

‫בס"ד‬

All this structure needs not to occupy a large volume. It can have a size of the order of magnitude of some Planck scales, because up to now it is not filled with anything except the primordial Light which in the physical realm is now in the state of grand unification. With the asymmetry of time and the boundary between the Infinite Light and the worlds system the platform for inflation is now ready. With the onset of inflation time as an arrow in its classical physical sense begins to exist as opposed to the Planck state where we have an evolving system with symmetrical time which is reversible and statistical. All we need now is an irregularity to start inflation. Since the system freezeout was connected with the loss of complementary information, we need to take into account that such “lost” information is transformed into e.g. thermal energy42 which is correct according to inflation theory which contains a heating up phase of the universe before the Big Bang. Observational evidence for a small positive vacuum energy of the universe exists 43 which is an asymmetry between the positive field energies of the standard model and the negative gravitational field energy. It is very interesting that the conditions described in Kabbalah have a cosmological constant as a consequence. This tiny energy surplus has, due to quantum mechanics, a complementary observable – time. In our tiny universe at the onset of inflation the necessary irregularity may be delivered by this uncertainty. To prove this is subject of ongoing research by one of the authors and others. The process of inflation in particular is an interesting fact in regard to the writings of Kabbalah. So, let us now systematically investigate what the Kabbalistic writings unravel about these first phases of the emergence of our universe, and what Physics has to say about it. With the stabilization of the empty space44 or vacuum which at this stage was still tiny as described above, the platform for creation was brought into existence. We spoke about “freezing of the system” by the formation of a first and second partition (‫)רקיע‬. Such a partition separates something, makes a demarcation between opposites, in short, creates a dimension. The demarcation between the point symbolizing oneness and the expelled infinite light made it possible for the two opposites to communicate or interact without being entangled. Above we spoke about an unstable, fluctuating and relatively undefined primordial state, which got stabilized by the action of separation. In Physics, this is the separation of energy and space-time, unfolding a multi-dimensional space, whose at least one dimension is time, while in Kabbalah the introduction of the ‫צינור‬, which made space asymmetric by symmetry reduction and with that stable, because the light of the point and the expelled light could not anymore unite and un-do the stabilization, and its sequential filling with light (creation of time) unfolded a space-time. In Kabbalah, the creation of the demarcation or firmament (‫ )רקיע‬is symbolized by ‫א‬, the first “mother” of the letters of the Hebrew alphabet. We have seen above, how from that and the Tetragrammaton four worlds were created. One can say, this is how G-d made it and let it suffice, or we can decide to find 42

We shall see this later in detail when we will talk about information theory and state reductions. A.G. Riess et al. (Supernova Search Team Collaboration), “Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant”, Astron. J. 116, 1009 (1998); arXiv: astroph/9805201. 44 This could be seen as happening after inflation, since the bringing in of the Line of Light stabilized an inflated void. It would be interesting to see whether such inflation process took place causing the Planck state to be replaced by Grand Unification, ultimately leading to Baryo-genesis and with abrupt cooling of the universe lead to the U (2) symmetry breaking and formation of the four gauge bosons at the time of the decoupling of electromagnetism. 43

44

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

‫בס"ד‬

out, how he did it and what principles and laws of nature he created with that. Let us first look at the role of a demarcation or partition (‫ )רקיע‬in Torah, Mathematics and Theoretical Physics. “Chochmah is found from nothing” (Iyov 28:12, Proverbs 3:19), i.e. from the concealed Chochmah which is called the Depth of Chochmah. Along these lines the nothingness needs to release Keter and Chochmah / Binah to make a partition in itself to “exist”, i.e. to make a difference between “non-existence” and “existence”. The first partition therefore is the first symmetry breaking to polarize the two opposites of “non-existence” and “existence”. This existence from said polarization creates the first “duality”. This is true, but those two exact opposites constitute the extrema of one dimension and hence, the law of oneness is not violated, they together make ONE, initiating a partition, whose concept holds throughout creation: the definition of created concepts or physical or even massive entities by their opposites. Some examples are: • •

• • • • • • •

The physical directions of three-space (up-down, South-North, East-West) Time (past-future) with the constraint that time has a beginning and not really an opposite that would define it. In Physics its complementary is energy. Only from our point of view past and future are opposites partitioned by the present. Substance (matter-antimatter) Electric Charge (positive-negative) Magnetic Charge (North-South) Illumination (light-darkness) Morality (good-evil) The 28 times of Ecclesiastes 3:2-8 Living creatures (male-female)

to name only a few. Examples of opposites are given in the formation process described in Sefer Yetzirah everywhere. Those dualities seem to be inherent in the entire Jewish philosophy of Creation, only the Creator is unmistakably One. Kabbalah speaks for instance of a world of Kedushah and a world of Tum’ah which are exact mirror images of the worlds of Atzilut, Beriah, Yetzirah and Assiyah on both sides. Nevertheless they are asymmetric by their information and light content. The only dimensions and field energies in Physics which seem not to be created alongside this otherwise ubiquitous principle of duality are gravity45 and time. There is, as far as we know, no repulsive force in gravity, except for the state of a false vacuum during inflation and that with a good reason: this universe could not exist with it, and so could not the second law of thermodynamics46. Time is asymmetric according to the 2nd law of thermodynamics and cannot run backwards continuously, so it has no opposite47. 45

As we shall see later, gravity is also the only form of interaction that allows an objective state reduction that makes an observer obsolete. One can interpret this as the means of the Creator to keep His Creation in a stabilized unentangled state. 46 Or could it? – The only reason for this argument is Norbert Wiener’s condition for a universe supporting intelligent sentient life which would make no sense without a macroscopic arrow of time. We will discuss this argument in favor of the anthropic principle at the end of this book, but we tell the reader now that we have our doubts about its validity.

45

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‫ספר‬

‫בס"ד‬

We saw above that at the onset of the Big Bang there was (at least in the physical world’s precursor) prevalent the Grand Unification and before that the Planck state. Energy and space-time were fluctuating wildly as we said, if the system is observed or otherwise interacted with. We also presumed that the laws of Physics did never change and always existed in the form known to us. With the very special conditions of the Big Bang described above, we have to answer two essential questions: If quantum mechanics was valid, what made the separation of space-time and energy stable as it is today? We need a measurement or other observation, if not conscious observation to do that, so what happened so long before we existed? Let us try to find some answers to these questions. 2. Philosophical discussion of quantum theoretical treatment of “existence”: The freezing of the wavefunction or collapse is a stabilization of the state of the system as measured at the instant of observation. For spontaneous collapse either a probability has to be defined or a cause for such collapse has to be found. For a causal explanation at least one of the following entities has to act as a cause: • • •

The whole system concerned A subset of the system An entity outside of the system

Another essential question is the definition of reality in Physics. In their groundbreaking paper Einstein, Podolski and Rosen (EPR) defined physical reality like this: “If, without in any way disturbing the system, we can predict with certainty (i.e. with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.” They arrive in their analysis of this problem of determinism in quantum mechanics at this conclusion: “The description of reality as given by a wavefunction is not complete.” The condition for completeness here is: “Every element of physical reality must have a counterpart in the physical theory.” Since orthogonal noncommutative operators (observables) like location and momentum cannot be measured together with the same precision (when the momentum of a particle is known, its coordinates have no physical reality), one of the observables is not real, which is a contradiction to the above theorem. John Wheeler proposed an experiment of so called delayed choice, where it should be shown, whether this finding is correct or not. We will discuss this and related experiments later, after we discuss the philosophical aspect of the EPR finding, that Heisenberg’s uncertainty relations are correct. The same discussion has to be applied to the question of knowledge of past and future in quantum mechanics. The question is now, what constitutes a phenomenon related to an observable and what has consciousness of the observer to do with it? John Wheeler writes: We cannot speak in these terms without a caution and a question. The caution: “consciousness” has nothing whatsoever to do with the quantum process. We are dealing with an event that makes itself known by an irreversible act of amplification, by an indelible record, an act of registration. The question: Does that record subsequently enter into the “consciousness” of some person, some animal or some computer? Is that the first step in translating the measurement 47

Or has it? – Delayed choice, barrier tunneling and optical phase conjugation experiments justify that doubt for now, but do not prove any continuous time reversal.

46

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‫ספר‬

‫בס"ד‬

into “meaning” – meaning regarded as “the joint product of all evidence that is available to those who communicate”? Then this is a separate part of the story, important but not to be confused with “quantum phenomenon”. – From this question we turn to the question: Is the elementary quantum process an act of creation of any other kind required to bring into being all that is? – At first sight no question could seem more ridiculous. How fantastic the disproportion seems between the microscopic scale of the typical quantum phenomenon and the gigantic reach of the universe! Disproportion, however, we have learned, does not give us the right to dismiss. Else how would we have discovered that the heat of the carload of molten pig iron goes back for its explanation to the random motions of billions of microscopic atoms and the shape of the elephant to the message on a microscopic strand of DNA? Is the term “big bang” merely a shorthand way to describe the cumulative consequence of billions upon billions of elementary acts of observer-participancy reaching back into the past? – An old legend [he means the Torah] describes a dialog between Abraham and [G-d]. [G-d] chides Abraham, “You would not even exist if it were not for me!” “Yes, Lord, that I know”, Abraham replies, “but also You would not be known if it were not for me.” In our time the participants in the dialog have changed. They are the universe and man. The universe … says, “… I supply the space and time for your existence. There was no before before I came into being, and there will be no after after I cease to exist …” How should we reply? Shall we say, “Yes, oh universe, without you I would not been able to come into being. Yet you, great system, are made of phenomena; and every phenomenon rests on an act of observation. You could never even exist without elementary acts of registration such as mine”? – Are elementary quantum phenomena, those untouchable, indivisible acts of creation, indeed the building material of all that is? Beyond particles, beyond fields of force, beyond geometry, beyond space and time themselves, is the ultimate constituent, the still more ethereal act of observerparticipancy? For Dr. Samuel Johnson the stone was real enough when he kicked it. The subsequent discovery that the matter in that rock is made of positive and negative electric charges and more than 99.99 per cent empty space does not diminish the pain that inflicts on one’s toe. If the stone is someday revealed to be altogether emptiness, “reality” will be none the worse for the finding… Are billions upon billions of acts of observer-participancy the foundation of everything? … The very fact that we can ask such a strange question shows how uncertain we are about the deeper foundations of the quantum and its ultimate implications… Could it be that all the time we have been missing the central point, the use of the quantum phenomenon in the construction of the universe itself? …

Eugene Wigner cites Descartes’ “Cogito ergo sum”, so that mind and thought are primary. Existence in Wigner’s sense is directly connected with interaction or observation (as a secondary effect thereof) as George Berkeley said: “Esse est percipi.” – Or as Wheeler puts it: “G-d willed it? Why demand of science a cause if cause there is none?” – Let us counterargue for now: Since the source of all is One and not absolutely nothing, the coming into being of at least the potential of a universe or some wildly fluctuating space(-time) came into being inevitably. How this system stabilized and defined its dimensions and what level of self-consciousness is minimally needed for that, and what type of separations have to be made and how, and what sort of being this self-conscious being or system has to be to bring into existence and stabilize itself and its creation, remains an open question, which is neither answered by the allegation there is no primary cause nor that some ineffable being separate from this system willed it. Both would contradict the “oneness-condition” of the Torah explained by the Rambam and our earlier proof that absolute nothing cannot be or be alone and one. As soon as the slightest dynamics emerges, even in form of fluctuations or noise, time starts to exist and with that energy that leads to a rapid expansion of the system. We need to pose the question differently: What is an elementary act of creation? – Let us go with Wheeler: “There is an untouchable interior of an observed phenomenon. Until the act of detection the phenomenon is not yet a phenomenon. The quantum phenomenon is independent of consciousness insofar the translation of the observation into meaning is meant as observation. Before that translation the observation has already been made.” – He allows a registration of the event without acclaim to meaningful interpretation as an observation, which makes sense insofar as a phenomenon can be observed but need not to be interpreted in the correct way, so despite reality may be distorted, the measurement or observation has been registered. How this fits into the EPR statements is partly questionable, but the question whether reality can be determined completely has Gödel’s incompleteness theorem hovering over it. With the conditions inside a black hole for instance, where time and space swap roles,

47

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‫ספר‬

‫בס"ד‬

we know that space and time are not the ultimate categories in the description of nature. Only the interplay between space, time, interactions and observations together with information theoretical considerations can bring us any further in reaching satisfactory descriptions of what we call reality. With all this in mind let us return to our primary issue: creatio ex nihilo. Wheeler states, we need to look at the creation of the universe as out of nothingness, not out of vacuum! – Vacuum fluctuations and virtual pairs of particles are too much structure for that. It is remarkable, how this statement resembles the Rambam’s definitions of the Creator. Also Leibniz remarks on this issue: “Omnibus ex nihil ducendis sufficit unum.” – We immediately can deduce from that the oneness of the all encompassing origin as we saw and have proved before. So, how do we explain within the quantum realm a stabilization or freezing out or collapse of the wavefunction of primordial configuration space? – We need a partition, a ‫רקיע‬, between the quantum and the observer; otherwise the quantum has no counterpart. Observer-participancy of quantum theory is the mechanism for the universe to come into being. Or we can put it also this way: the necessity of the quantum as we see it comes from the requirement that, via observer-participancy, the universe should have a way to come into being. Hence, we can propose on the grounds of what we have proved above about our forced explosion that we can also try to derive quantum theory from the requirement that the universe did not have a choice but to come into being. Now our argument has become nicely elliptic up to the question of ultimate stabilization of space-time structure. Wheeler asks how much arbitrariness is there in this kind of demarcation or partition between universe and observer (who by his very nature is part of that universe), arbitrariness for the location of that line between “system” and “observing device” and “observer”. He says, existence, not position is important for such a partition. And he states: “What we have the right to say of past space-time and past events is decided by choices of what type of measurement to carry out, made now.” People who believe the universe is a machine functioning according to immutable laws which are completely deterministic in Laplace’s sense have to be told that this is a cracked paradigm. Quantum mechanics allows us to know one of two complementary orthogonal observables but not both at the same time. As Wheeler puts it: “Of the initial-value data that Laplace needed, the principle of complementarity or indeterminacy says half do not and cannot exist”. Again, this leaves us with the only condition for “existence” to come into being: the partition between the “existing” system and the observer. He argues further along the lines of our proof that absolute nothingness can only exist as oneness and becomes henceforth meaningless by the line of distinction that rules it out, that the universe evolved in the past from phenomenon to phenomenon, observed today after it gave rise to observership, after having reached regularity and structure out of the statistics of many phenomena, to be a self-excited circuit. Whether he is right or not, including or excluding a Creator who evolved with his universe and such universe being a subset of His, very recent experiments have shown the correctness of one principle, observer-participancy and a demarcation between observer and observed system (universe) suffices to create everything: the building of law (of Nature), and space-time as part of law, and out of law substance. But, he cannot prove or disprove the way of building law: whether it is by pure statistics of myriads of phenomena, and its wave-function package collapsed to stabilize it spontaneously or by a defined

48

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‫ספר‬

‫בס"ד‬

conscious will. It is still open, at which point the system “froze” – to get the universe we have, the chances are one in 1010^123! Sefer Yetzirah 2:6 states: ‫יצר ממש מתוהו ועשה את אינו ישנו וחצב עמודים גדולים מאויר שאינו נתפש וזה‬ ‫סימן א' עם כולם וכולם עם א' צופה וממיר ועשה את כל היצור ואת כל הדבור שם אחד‬ ‫וסימן לדבר עשרים ושתים חפצים בגוף אחד‬: He formed substance out of chaos and made non-existence into existence, He carved great pillars from air that cannot be grasped. This is a sign, Aleph with them all, and all of them with Aleph, He foresees, transforms and makes all that is formed and all that is spoken: one Name. A sign for this thing: Twenty-two objects in a single body. Aryeh Kaplan comments that chaos was engraved and carved from water, which comes from Chochmah, the basis of all physical creation. It is supposed to be the most primitive root of water as it exists in Atzilut, the realm of the sfirot. Chaos was formed out of this and matter from chaos. – In our opinion chaos is a system underlying statistical and not causal laws. Hence, the view of quantum theory seems also to be favored by Sefer Yetzirah for the beginning of the universe as quantum theory is favored by Physics to describe the processes of bringing matter into existence and last not least the (microscopic and mesoscopic) behavior of matter itself. The chaos can be seen as an evolving state where details are indistinguishable, and only by a state reduction (Binah) such distinctions and with that order can be achieved. This constitutes an entropy reduction which requires the input of energy. The creation of the 22 objects is referred to in Sefer Yetzirah 1:11: ‫שלש מים מרוח חקק וחצב בהן כ"ב אותיות מתוהו ובוהו רפש וטיט חקקן כמין ערוגה‬ ‫חצבן כמין חומה סביבם כמין מעזיבה ויצק עליהם שלג ונעשה עפר שנאמר כי לשלג‬ ‫יאמר הוא ארץ‬: Three: Water from Breath. With it he engraved and carved 22 letters from chaos and void, mire and clay, He engraved them like a sort of garden, He carved them like a sort of wall, He covered them like a sort of ceiling, And He poured snow over them, and it became dust as it is written: “For to snow He said, ‘Become earth’”. Chaos and void here allude to the initial state of creation of the physical universe in its Planck state (Genesis 1:2). With 2:6 above we see that substance was formed from chaos, which contains no information, but is pure material. The void is considered pure content of information48 that does not relate to any substance. Both are not differentiated and therefore included in Chochmah. With void the 22 letters could be engraved on chaos. The bottoms of the letters were engraved like a garden, the sides are carved like a wall and the tops are added as a ceiling. According to the Ramak (Rabbi Moshe Cordovero) this alludes to the creation of space (Pardes Rimonim 3:5). Raavad in his introduction to Sefer Yetzirah 2a says that both chaos and void are intermediate to actuality and existence. Quantum theoretically this would mean they describe the unstable or not yet “frozen-out” system to be formed. Hence, such 48

We say here content of information to maintain non-physicality as required by Kabbalah. To become real information, this content has to be encoded onto a physical carrier as we will discuss later.

49

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

‫בס"ד‬

descriptors must refer to a space on which the later stabilizing creation, namely all the worlds from Adam Kadmon down to Assiyah, are constructed onto: configuration space. It is possible to subdivide such configuration space into several configuration spaces, which are then interrelated by at least the one main configuration space. Let us now explore how such configuration space allows constructing a world or a universe. The (well-behaved) solutions of the stationary Schrödinger equation that describe the characteristic structures of atoms, molecules and condensed matter are determined by the complete structures of the configuration spaces on which they are defined. This shows first that the governing equation does not necessarily contain time, and that all possible behaviors of any elementar particle, atom, molecule or what is made of them can be described in a timeless manner49 as also general relativity treats time just as another exchangeable dimension of the physical world. That means simply that with the engraving of the letters and through their combination the structures of the configuration spaces must have been predetermined and brought into existence before the formation process of creation. If we assign a configuration space to the entire creation, i.e. all possible worlds, then the shape of such configuration space determines the laws of the “Physics” of such entire creation. Such configuration space encompassing all creation should be a subspace of the entire infinite dimensional Total Existence, so that the One from which everything emanated and emanates comprises the entire creation. Tikun 57 in Tikunim states: “There is no place devoid of Him, not in the upper worlds or in the lower worlds.” (cf. Sefer Tanya, Shaar HaYichud 7:166). Time evolves as any other physical law50 and maybe all other laws like for example the axiomatic of Mathematics due to the geometry of that configuration space, which not necessarily has to be entirely static and rigid. According to General Relativity and Quantum Theory it would be very probable that it is as malleable as our physical space-time. It is also conceivable that such geometry of configuration space could be influenced from a space this configuration space is a subspace of.51 Hence, any temporary and willed change of such geometry may change the prevailing laws of Nature temporarily and constitute anomalies regarded by us as “miracles” or “divine intervention”. Another possibility is that configuration space might be influenced by actions performed in the physical universe and/or in the worlds accessible by the mind in form of prayer, practical Kabbalah or the like. This could have consequences which may be beneficent or detrimental to this universe and the accessible higher worlds. Utmost caution has to be exercised in two ways concerning this issue:

•

Traditional methods how to influence or ask for influence of any powers like angels and other spiritual beings with the quest for change of circumstances need to be carefully understood before one embarks in using such techniques. Halachic restrictions should be strictly observed and in every case professional guidance is highly recommended, and even then utmost caution is recommended, because individual interventions may be detrimental to the whole.

49

This can be done as long as there is no state reduction. As we will see later, this is valid for all physical laws except the numerical value of the fine structure constant which comprises the electric charge and Planck’s quantum, because this prevailed right back to the very onset of time. 51 The “Total Existence  ONE” being infinite dimensional allows any subspace also to be infinite dimensional. 50

50

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

•

‫ספר‬

‫בס"ד‬

Modern applications of mind-stimulators or other ways of influencing or G-d forbid mind-changing agents for the purpose of invocation of “heavenly powers” and their use for personal gain or other advantage is strictly not recommended. The same needs to be said about the use of living or deceased persons for similar personal goals as well as the use of Kabbalah Ma’asit for one’s own interests.

The still open question is, how the conditions of stabilization or “freezing out” of the Total Creation (not the Total Existence) were determined and what caused the system to stabilize. This refers to the name ‫ אל שדי‬and the saying of the Creator “‫ ”די‬to finalize the process of stabilization. We leave this question for the moment alone and allow to first look at other experimental evidence. 3. Experiments of interest and their philosophical consequences: Time and space are modes by which we think and not conditions in which we live. During the elementary process of radiative loss, the molecule suffers a recoil of magnitude hν/c in a direction which is only determined by “chance”, according to the present state of the theory. Albert Einstein Recent decades have taught us that Physics is a magic window. It shows us the illusion that lies behind reality – and the reality that lies behind illusion. Its scope is immensely greater than we once realized. We are no longer satisfied with insights only into particles, or fields of force, or geometry, or in space and time. Today we demand of Physics some understanding of existence itself. John Archibald Wheeler

With this citation in mind, we want to show some experimentally verified discoveries that promise to give us the opportunity to suggest further thinking in Physics under reference to the Torah and its secrets and vice versa. The results of delayed choice experiments and group delay in barrier tunneling experiments have been performed and published very recently. Their results show agreement with Quantum Theory as explained above. Quantum erasure obviously also suggests the time reversed recovery of information even after the measurement has been done. Suggestions and objections have been raised concerning the issue of quantum entanglement and its implications concerning the validity of the conjecture that the speed of light as an upper limit of communication or information exchange would render such experiments contradicting quantum theory, but both types of experiments have proven otherwise: Quantum mechanics is right with all the philosophical implications discussed above. Wheeler’s and Wigner’s points of view have been proven: objects on a microscopic level measured over macroscopic distances behave acausal. – Our physical universe as we observe it, at least in its beginnings and definitely its microscopic constituents now, underlies the laws of quantum behavior, not causality in the Einsteinian, Newtonian or Laplaceian sense. This suggests that causality as we perceive it may only be a mirage, induced by the second law of thermodynamics,

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camouflaging reality. The details and reasons for this hypothesis we will discuss after we looked carefully at the experiments and their possible interpretations. A very recent delayed choice experiment was performed by V. Jacques, A. Aspect et al. taking relativistic space-time separation into account, meaning the photon has long passed the beamsplitter (or double slit) when the choice is made whether to measure the wave or particle property of the photon, which should exclude entanglement through the source of the photon observed. This realization of Wheeler’s gedankenexperiment demonstrates beyond doubt that the behavior of the photon in the interferometer depends on the choice of the observable measured, even when that choice is made at a position and a time such that it is separated from the entrance of the photon into the interferometer by a space-like interval. In Wheeler’s words, since no signal traveling at a velocity less than that of light can connect these two events “we have a strange inversion of the normal order of time. We, now, by moving the mirror in or out have an unavoidable effect on what we have a right to say about the already past history of that photon.” It can, with this information, be said that Nature behaves in accordance with quantum mechanics even if there is a seeming tension with relativity. Two other effects also seem to contradict relativity: barrier tunneling and optical phase conjugation. In the following we will look closer at these two effects and what seems to appear to happen in regard to the light cones of these events. As a fourth effect anomalous dispersion in a medium might be considered, but at this moment great caution has to be exercised, as relativity only considers the very front of the light-wave as having maximum and absolutely constant velocity in vacuum. Experiments with resting or trapped photons also raise some fundamental questions about the interplay of relativity and quantum mechanics. Barrier tunneling is surprising scientists with a very strange behavior concerning the propagation velocity of particles going through a potential barrier, which is called the Hartman effect: The average duration of a tunneling process does not depend on the width of the barrier, but only on its (energetic) height. This implies that for large opaque barriers the effective tunneling-velocity can become arbitrarily large: τeff. = ħk / (κV0), but it seems to be that the tunneling time is proportional to the wavelength of the tunneling particle. According to relativity, cvac is the upper limit of velocities particles can reach and information can be transmitted. R.C. Tolman in 1917 believed to have shown that the existence of particles with v > c would allow to send information into the past. We refer here to V. Jacques’ and A. Aspect’s experiment, where this actually seems to be the case. One has to carefully investigate, how these seemingly reverse time effects can be seen from other reference frames, such as explained in several publications on phase conjugation experiments. The question there still remains open, how the produced and reconstructed picture is “known” by the phase conjugating mirror. G. Privitera et al.52 champion an argument against the measurability of particles moving backwards in time so that macroscopic observers who are forced to move forwards in time cannot perceive something moving backward, but see it as moving forward with its additional charges reversed – they see an anti-particle. A superluminal electric charge will appear as a 52

Preprint arXiv: quant-ph/0412146v1 19 Dec 2004, G. Privitera, G. Salesi, V.S. Olkhovski, E. Recami, Tunneling Times: An Elementary Introduction.

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magnetic monopole moving backwards53. We argue similarly, other charges will appear as their complementary orthogonal ones, if they themselves are superluminal. Hence, it seems to be that charges (in their extended meaning also as topological charges) change into their orthogonals when crossing the “light-barrier”. Similarly, with the crossing over an event horizon of a black hole, space-time coordinates of a particle change also into their orthogonals. In non-resonant tunneling the speed of the tunneling particle does not depend on the width of a spacer (consisting of regular space) between the barriers. This sounds rather strange, because one could imagine the two barriers being infinitely far apart from each other. Would they then not act like single barriers? – And if not, what lets the two barriers know from each other, or how does in the case of two barriers the particle know there is a second barrier ahead, so that with that knowledge it keeps on traveling faster than the speed of light outside of any barriers, so one cannot argue for an imaginary wavefunction either? – Does that mean, also according to Wheeler’s delayed choice experiment that a photon sent from a galaxy 1.5 million years ago “knows” about our detector which will exist in its future and be in its path? This is highly speculative, but would strongly ask for an explanation along the lines of Barbour’s interpretation of configuration space. Kabbalistcally it would favor hashgacha pratit of the particle, but in a restricted sense that only if such detection device is moving into its path it will know it, which is again dependent on the free will of the observer. Furthermore it looks suggestive that corresponding anti-particles move opposite to particles. Could this be the solution of the conundrum of “knowledge before it happens”? If some but not all of the dimensions of the “brother”-particles would change into their orthogonals this could actually make sense. The changing of the meaning of coordinates (dimensions) of observed objects into different ones must open the gate to “other worlds” as it is in the case of a black hole. The only difference to this case is that some of the dimensions keep accessible to observers in this physical world, while in a black hole the only “communication line” is the gravitational field. Hence, in this light we can conjecture, the judgment about what is cause and what effect is not independent of the observer. In fact, in case of cause and effect inversion, with a dependency on the observer, all observers could see cause and effect valid in their reference frame in the proper chronological order. Further we can conjecture from the influence of the observer on the observed phenomenon, as shown in our delayed choice and quantum erasure experiments, that there exists an influence of the consciousness of observing entities on the physical world and its time-like behavior and vice versa, because we do not know of any phenomenon in which one subject is influenced by another without exerting an influence thereupon. This is the key to possible observation of interactions between the observable physical world and the “higher” or “parallel” worlds as described in Kabbalah.

The effect of optical phase conjugation is still open to discuss along the lines of “swapped meanings” of dimensions. If we look at complementarity, space coordinates and momentum are orthogonal to each other, similar to a superluminal charge that becomes a magnetic monopole moving at subluminal speed. Thinking that orthogonals of superluminals are real (slow) observables, could also give some plausibility to uncertainty relations as well as to light or the photon as a particle constituting the demarcation between worlds with swapped coordinates54. Again, we have time, or better, its defining quantity cvac involved here as an observable of both types of “worlds”, ours and the one whose dimensions are swapped. If we 53

One could argue that magnetic monopoles are not observed in nature, but it is conceivable, that superluminal electric charges have no divergence. One has only to modify Maxwell’s equations accordingly. We will do this for the interested reader in the appendix.

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want to say so, the photon travels in the ‫ רקיע‬separating these space-times or “worlds”, but it is able to participate in interactions in both “worlds”. Are there other such invariant observables like the photon in Physics? – It remains to be seen. Kabbalah, at least it seems so, knows only light as a common observable in all the worlds. According to all these experiments there seems to be a grave violation of relativity as it exists:

• • •

The sequence of time and maybe even the flow of classical time seems to be violated; Causality seems to be broken in the sense that not the observed object but the observer’s choice determines the outcome of the measurement even after detection; There seems to be irreversible evolution of our universe macroscopically insofar as the second law of thermodynamics is concerned, but there is obviously reversible evolution insofar as microscopic entities of our universe are concerned.

Let us go back to Bohr’s definition of a phenomenon: it is unambiguously communicable (not necessarily communicated) information. As an example for this he stressed: “I am absolutely prepared to talk of the spiritual life of an electronic computer, to state that it is reflecting or that it is in a bad mood. The question whether the machine really feels or ponders, or whether it merely looks as though it did, is of course absolutely meaningless.” Why are we speaking of a spiritual life of a computer here? First, we conjectured according to Bohr that any communicable measurement result closes the measurement process. The double delay experiment by V. Jacques et al. showed also very clearly that the choice does not need to be made by a human being, but by an electronic device which makes the choices and records the phenomena. After the recording process, which transforms the measurement data into a communicable set of information, the measurement outcome could not be reversed. This is also clearly shown in the delayed choice quantum erasure experiments so far discussed. Ergo, Bohr was right all the time. From all the above we can conclude the retroactive reconstruction of information by erasure of information complementary (orthogonal) to the reconstructed information is possible under violation of a forward-in-time causality. For the realization of such a process the observation not necessarily has to be made by a human conscious being. Communicability of the information seems to be the most important property of the produced, erased and reconstructed information rather than its communication to a sentient being. Evidently, as Eugene Wigner argues, there are enormous gradations between consciousnesses, depending on the elaborate or primitive nature of the structure on which they can lean: the sets of impressions which an ant or a microscopic animal or a plant receives surely show much less variety than the sets of impressions which man can receive. Hence, electronic devices designed to receive certain impressions and to recognize them as such, are valid receptors of observed information with enough “consciousness” to qualify as “first observers”, despite they might be very simple and primitive devices. Recalling the situation at the onset of Creation, the implications this fact has philosophically and scientifically is the possibility of a very simple self-observing Total Existence in the state of un-defined dimensionality in yet undefined space-time. We refer here to our citation of Etz Chaim 1:2 above that states: 54

We remind the reader of the photon traveling on the demarcation between the observable space within the relativistic light cone of our space-time and e.g. Rindler space.

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“When in His simple and smooth will the desire arose…” – How simple can such a “will” be to be able to observe itself to stabilize a structured universe in the state of fluctuation between a point in infinity and an infinite dimensional sphere with its number of dimensions also fluctuating between zero and infinity? What are the minimum conditions for such a “measurement”? What is the simplest form of self-observation?55 In Etz Chaim and in Otzrot Chaim the creation of vessels or substance, here represented by letters of the Hebrew alphabet, takes also place by a specified process of observation. In this case the observer is Adam Kadmon in the first phase of the creation process, which we will describe in the following section. Another conclusion follows logically and very clearly from the above: under certain circumstances, the apparent indeterminism of the object due to the measurement back-action can be undone by the action of a local operation on the probe, which does not mean that both orthogonal observables have been simultaneously measured in one and the same process. This quantum erasing is a manifestation of the non-locality of quantum mechanics, which herewith has been proven. A further implication is the apparent disruption of the order of time. The possibility of un-doing an event, however, does not necessarily mean that an exact backtracking of time took place. It may be mentioned here as well that phase conjugation experiments do not prove such exact backtracking. There can be a complete reconstruction of a formerly distorted wavefront, but whether the conjugated wave really backtracks exactly the incident wave remains open. Furthermore, the possibility of the relativity of cause and effect has to be looked at more closely. As we stated before, for two different observers in two different reference systems cause and effect may be interchanged. We suggest the following gedankenexperiment: Suppose two sources of sound capable of releasing loud bangs of different sound, are located at a distance from each other. Each of the sources contains a sensor that can be activated by sound and triggers the bang to be released. If one source is triggered, the sound-wave will travel spherically away from it and after some time trigger the other source of sound. Suppose the exact front of the wave triggers the second bang. There exists a geometry where the wavefront of the second bang arrives at an observer before the wavefront of the first bang. If the observer has the knowledge that one bang causes the other, he will conclude that bang 2 caused bang one, which is according to another observer who, let us say, stands on the side of source 1 opposite to the side where we find source 2, false, since he will state that bang 1 caused bang 2. The reader is reminded that this effect will be increased, if the sensors are placed somewhere near the sources, but in between them and the triggering signal is transmitted from the sensor to the source electrically or by light, which both travel faster than sound. One can say in this case, if the observers do not know the wiring of the experiment and have no way to find out, but only know that one bang causes another, their observations are both correct. Now let us consider a similar experiment with light of different color (wavelength) instead of sound. We place two lightsources a distance apart from each other in the same way that one light source triggers the other. Even if the sensors are placed in between them and the transmission from the detector to the trigger would be at the speed of light, an observer 55

We suggest self-observation for the reason of absolute oneness of the Creator.

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placed in such a way that the triggered lightsource is located between him and the triggering lightsource would in the most extreme possible case see both signals arriving at his location at the same time. Hence he would still be able to deduce the correct causality, knowing that the triggering lightsource is further away from him than the triggered one and knowing that the fastest velocity for signal transmission is that of light. Let us now place a tunneling device between the triggering lightsource and the sensor of the triggered lightsource. Due to the Hartman effect as discussed above, the light of the triggering lightsource would arrive after the light of the triggered one and arise in the observer the impression of an inverted causality. In both cases, the impression of an inverted causality depends on where the observer is located relative to the experimental arrangement. Another important condition for the perception of an inverted causality is the lack or availability of certain information about the exact experimental set-up. It is therefore highly questionable, whether an experiment such as that with two lightsources would be sufficient to accept causality inversion as a result of that experiment. If, on the other hand, one discusses the experiments on the basis of either a constraint dimensionality of the observers or allows for the lack of information the same way Einstein did with his man in the elevator, we think such experiments, and in particular the one with light, can illustrate the phenomenon of causality inversion very nicely. It also becomes clear that a proper time reversal in the form of back-flowing time 56 does not and does not need to take place to show this effect. As we remember the delayed choice and quantum erasure experiments and compare the results with these gedankenexperiments of causality inversion we see again the already mentioned result that the order of time seems to be reversed rather than the continuous flow of time. This inevitably must lead to the question whether we observe in these experiments a “backflow” in time or causality or rather a reversal of distinct instants of time as perceived by a particular observer. Similar to Einstein’s “man in the elevator” who is deprived of knowing that he is continuously accelerated interpreting this as being in a constant gravitational field, our observers are deprived of knowing the exact wiring of the experiment, i.e. the exact flow of events with time represented by the shortening effect of the transmission time of the triggering light coming from the “real” triggering source. So he interprets the sequence of the different lights as inverted. Note that for the other observer the events occur in the “right” sequence, but both observers experience the events, whether inverted in causality and time sequence or not, in a perfectly logical chronological order. The observer never has the feeling that time flows backwards. The observer who perceives the causality inversion lacks the knowledge that by insertion of a tunneling junction the triggering signal “overtakes” the emitted light of the first lightsource, and hence his perception and interpretation of that perception is flawed as well as that of the second observer who will perceive an anomaly in the speed of light of the triggered light source. Only the “independent” third observer who set up the experiment knows the “true” sequence of events and hence the order of causality, if one can speak about this as such. We have to be very careful about that, because the perception of the one observer records something else, a totally reversed causality. In the light of the different perceptions we need to ask whether it could be possible that in the case of other observed sequence-of-time 56

This has to be understood in the sense that the arrow of time would be reversed.

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reversals such overtaking effects are responsible for the “flawed measurement” or whether there exists really relativity in the sense of the Einsteinian simultaneity paradox57. Let us now take a good look at our delayed choice and quantum erasure experiments. In Wheeler’s delayed choice experiment carried out by V. Jacques et al. the choice whether to measure wave or particle property of the photon is made after the photon passed the beam splitter (or double slit). Hence, under “normal causal” circumstances the outcome of the experiment should not be changed by the choice, but it does. It appears here that the already written history of the photon is re-written; or is also here some signal overtaken by a faster one like in the tunneling experiment above? The same question has to be asked for the quantum erasure experiment, where already registered information is “quantum erased” and replaced by other information complementary to the first. We need to look carefully at the space-time conditions for the photon before and after it passes the beam splitter. Jacques claims in his publication58 a space-like separation of the choice from the passing of the beam splitter, but makes no remark about a separation in the time-domain. The question remains whether there could be an “overtaking signal” governing the outcome of the experiment setting causality “right” via any superluminal or other effect and “reality” is only “camouflaged” by that. We will discuss this later in a chapter presenting open questions and suggesting new experiments that can help to shed some light on these questions. The only conclusion we can reach for now is that causality and order of time as we know it and interpret it in daily life as well as in our view of Creation both physically and spiritually are seriously threatened as means for explanations of what we believe to observe or to have observed. The experiments clearly show that perceived or measured causality can be, under certain circumstances, even under non-relativistic and non-quantum conditions, inverted due to the reference system of the observer, but under circumstances where quantum behavior dominates like at the onset of Creation before an arrow of time could emerge, such causality and order of time violations were part of the Existence. To be more blunt, in this state of affairs no causality or time existed, everything was in an evolutionary state and completely reversible and time-symmetric. The Rambam59 clearly states about the arguments and proofs of the Mutakallemim, who pursued an atomistic and probabilistic theory of Creation: “They denied the nature of the existing things, misrepresented the properties of heaven and earth, and thought that they were able to prove the creation of the world, but in fact they were far from proving the creatio ex nihilo, and have weakened the arguments for the existence, the unity, and the incorporeality of G-d. The proofs of all these doctrines must be based on the well-known nature of the existing things, as perceived by the senses and the intellect.” In the second part of his work 60 he analyzes the views of the philosophers inter alia concerning an eternity of the universe. He clearly states that time and space have a beginning. Before that there existed only an absolute nothingness. He does not propose the same solution for a proof of the unity of the Creator as we have done above, but argues in a much more cumbersome way in favor of the 57

An explanation of special and general relativity is given in the Appendix. Pre-print arXiv: quant-ph/0610241v1 28-Oct-2006. 59 Moreh Nevuchim Part I Chapter LXXVI. 60 Ibid. Part II. 58

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same proposition. He also clearly argues for a definitive beginning of all Existence, while strongly advocating causality and counter-arguing probability or statistical theories. Neither the Rambam nor the Mutakallemim could have had any knowledge of the quantum nature of the Physics of the universe and beyond in the form we know it now since about a year after the above mentioned crucial experiments have proved the exact behavior of our world. Whether the principle of quantum theory of evolving, entangled and reduced states of physical objects was totally unknown, we doubt strongly, as clearly demonstrated in Etz Chaim’s ‫מטי ולא מטי‬. We think, some passages in Sefer Yetzirah as discussed above, also strongly support this view. In the light of current scientific knowledge we want to propose, the ways in which we see causality and the order of time must be fundamentally revised to get a clear understanding of what is presented to us as the paradoxes of Nature and the “Worlds we live in”. We think that the experiments discussed above give rise to postulate interactions which elude direct observation and that the choice of the method of such observation as well as the level of completeness of the knowledge of the observer about the exact conditions of his observation play a most important role for the outcome of such observation and its interpretation. Let us return to John Wheeler. He states61 that “we decide what the photon shall have done after it has already done it. In actuality it is wrong to talk of the “route” of the photon. For a proper way of speaking we recall once more that it makes no sense to talk of the phenomenon until it has been brought to a close by an irreversible act of amplification62.” He writes: The “Past” in the light of the delayed choice experiment: To use other language, we are dealing with an elementary act of creation. It reaches into the present from billions of years in the past. It is wrong to think of that past as “already existing” in all detail. The “past” is theory. The past has no existence except as it is recorded in the present. By deciding what questions our quantum registering equipment shall put in the present we have an undeniable choice in what we have the right to say about the past. What we call reality consists of a few iron posts of observation between which we fill in by elaborate papier-mâché construction of imagination and theory. Space-time in the pre-quantum dispensation was a great record parchment. This sheet, this continuum, this carrier of all that is, was and shall be, had its definite structure with its curves, waves and ripples; and on this great page every event, like a glued down grain of sand, had its determined place. In this frozen picture a far-reaching modification is forced by the quantum. What we have a right to say of past space-time, and past events, is decided by choices – of what measurements to carry out – made in the near past and now. The phenomena called into being by these decisions reach backward in time in their consequences … even to the earliest days of the universe. Registering equipment operating in the here and now has an undeniable part in bringing about that which appears to have happened. Useful as it is under everyday circumstances to say that the world exists “out there” independent of us, that view can no longer be upheld. There is a strange sense in which this is a “participatory universe”.

That this is a participatory universe we have experimental evidence for, evidence that causality and the order of events not only can be, but always are and must be influenced by the choices of the observer or experimenter. Jewish philosophy states a few facts that are in favor of a permanent observation bringing things “into existence”. Kabbalah also speaks about human participation in the Tikun HaOlam. Rabbi Shneur Zalman of Liadi63 states: “It is written: Forever, O G-d, your words stand firm in the heavens (Tehillim 119:89).”

61

J.A. Wheeler, W.H. Zuker (eds.), Quantum theory and measurement, Princeton 1983. This constitutes, as we explained earlier, a communicable information. 63 Sefer Tanya, Shaar HaYichud VeHaEmunah Chapter 1. 62

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He writes further:

The Baal Shem Tov of blessed memory has explained that “Your word” which you uttered, “Let there be a firmament in the midst of the waters…” (Genesis 1:6), these very words and letters [i.e. the creating forces that bring everything into existence ex nihilo] stand firmly forever within the firmament [‫רקיע‬, sic] of heaven and are forever clothed within all the heavens to give them life as it is written, “The word of our G-d shall stand firm forever…” (Yishayahu 40:8) … For if the letters were to depart for an instant, G-d forbid, and return to their source, all the heavens would become naught and absolute nothingness, and it would be as though they had never existed at all, exactly as before the utterance “Let there be a firmament”. And so it is with all created things, in all the upper and lower worlds, and even in this physical earth… This same thought was expressed by the Ari, of blessed memory, when he said that even in inanimate matter, such as stones or earth or water, there is a life force – that is, the enclothing of the “Letters of speech” of the Ten Utterances which give life and existence to inanimate matter that it might arise out of the naught and nothingness which preceded the six days of Creation (Etz Chaim, Shaar Man U’Mad, 3).

Interesting in this passage is that it again emphasizes the importance of the firmament or ‫ רקיע‬as the most vital condition for existence as such. We explained above that such a distinction, very much like the demarcation between observed object and observer must exist to be able to uphold Creation. This upholding would reverse, if such demarcation would disappear. Such a statement is not only remarkable; it might be the key to understand our experimental paradoxes and shed a lot more light on the view of the Torah and its secrets, how Creation actually took place. From our experiments we learned they are participatory throughout, whether they are of quantum mechanical, relativistic or classical nature. In every case there is an observer involved. In Classical Physics we always speak of reference frames, be it in mechanics or electrodynamics, from where a phenomenon is observed. We try to make sure that if the reference frame does change the Physics of the observed phenomenon does not; therefore, we invented gauge theories, invariant transformations and so forth. Relativistic Physics was developed as a result of the quest to unify the invariant transformations of electrodynamics and mechanics. The reason for that was the invariance of the speed of light in vacuo, which was experimentally demonstrated by Michelson and Morley. The same light gave rise to Quantum Theory, but in a very different manner it gave rise to Relativity; in fact theories that do not fit to each other and we have at the moment no satisfactory unification of them. Newton considered light to be a beam of particles able to bounce back from a mirror as they get reflected. During the first half of the 19 th century the wave-nature of light was demonstrated by interference and diffraction experiments. This later enabled optics to be integrated into electromagnetism. The study of black body radiation, inexplicable by electromagnetic theory, inspired Max Planck in 1900 to propose the quantization of energy. Using the elementar charge as a constant he derived what today is known as Planck’s Quantum h. Einstein generalized this hypothesis in 1905 and proposed that light consists of a beam of photons, each possessing an energy hν. He showed how the introduction of photons made it possible to understand the photoelectric effect in metals. 1924 Compton proved the existence of photons. Since both wave and particle nature of light, and later electrons and other elementar particles, was experimentally verified, the dualism of Quantum Theory was born, first looked at as a paradox. Discussions mainly between Bohr, Einstein and Heisenberg, with earlier contributions by Sommerfeld, Schrödinger and Planck gave way to a very slow acceptance of duality and complementarity instead of causality64. Later in the 1950s up to today these discussions were more and more refined but without fundamental experimental success. Only now in 2007 we for sure have experimental proof that Quantum Theory as it developed over one century is 64

… Causality as understood in the old unrevised sense of “common sense”.

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‫בס"ד‬

right, up to now. General Relativity is also right, up to now. Both do not fit together, up to now. – We think, we do not need a revolutionary new theory to match the two, we should only try to understand better what is causality and how does it work, and what is complementarity and how does it work; and – how do they work together? – Maybe our good old “Secrets of the Torah” can help us to understand our Physics a little bit better? – Or, if the reader wishes, the Physics can help us to understand the “Secrets of the Torah” also a little bit better? This new theory will be definitely one of both quantum-complementarity and relativistic causality65. We definitely think we have demonstrated up to now that both cannot be understood separately, only to a certain degree. Relativistic causality can only be applied to a system that has state reduced, while quantum-complementarity is influenced by the process of state reduction itself. The choice, which of the complementary information to receive, is made by the state reducing system. The reference frame of the state reducing system or observer definitely has to influence the process of state reduction according to the laws of relativity. In gravitationally induced objective state reduction breaking an entanglement the Killing vector of the equation describing the evolving state becomes ill-defined. The system breaks apart. Hence, relativity definitely plays a major role in the process that holds our universe in a stable reduced state and hinders entanglement to spread. This process, surprisingly precise, is also the phenomenon that is said to uphold Creation according to Kabbalah: if the ‫ רקיע‬would be taken out only for a moment, all Creation would revert to the state it was before the six days of Creation66. Since gravity and the curvature of space plays a major role in this type of state reduction, we think it is an important clue for us where quantum theory and general relativity are linking together. The questions of how consciousness is involved in state reductions and how gravity may be connected to consciousness are a very interesting subject we shall discuss in the course of this treatise, but rather as an outlook on ongoing and future research than as definite conclusions. We find that Kabbalah can help here to understand the interplay between geometry as mathematical structure, information as a spiritual and physical phenomenon and quantum behavior. Kabbalah tries to explain the functioning of the physical and spiritual worlds while Physics tried to avoid this for a long time, until Quantum Theory came along and made the consciousness of the observer part of the experiment or observation. Only the production of communicable information constitutes the irreversibility of a measurement, and with that the mind of the observer participates in the process. How does it participate and what exactly constitutes this mind? A question not to be answered by Science alone as well; Kabbalah may shed some light on this as well, but let us first discuss reversible state reductions to understand the question better. In the delayed choice quantum eraser experiment of Y. Kim et al. 67 the reconstruction of an interference pattern of a double slit experiment has been shown after the information through which slit the photon passed through was erased. This erasure could be delayed until after the observation of the original photon was done. At first sight it seems that the choice to observe or to erase the path information of the secondary photon can change the position where the 65

… Causality as understood in a new way of being “relative”, dependent on an observer and from where he looks at it. 66 Cf. Sefer Tanya, Sha’ar HaYichud. 67 Preprint arXiv: quant-ph/9903047v1 13 Mar 1999, Y. Kim, R. Yu, S.P. Kulik, Y.H. Shih, M.O. Scully, A Delayed Choice Quantum Eraser.

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signal (original) photon is recorded on the detector, even after it was recorded. We need to note, in this experiment the total pattern never shows interference, only subsets of signal photons whose entangled counterparts have been detected allow a recovery of interference by erasure. Hence, no signals are sent back in time, only a backwards causality results from erasure. The experiment also allows to be interpreted with forward causality, if one interprets the observations of the interference patterns in terms of the initial measurement of the signal photon affecting the probabilities of the later measurement of the counterpart photons. Again we have to do with relativity of causality, depending on the way of observation. Another result was obtained by the eraser experiment: Complementary information can only be recovered from entangled states; un-entangled states do not allow such observations. The Wheeler experiment avoids entanglement and henceforth does not allow any erasures. It does not allow quantum information to accompany classical information and therefore does not demonstrate all the features of violations of classical physics and all the properties of what is considered communicable information. To understand the implications of this, let us now look at all the aspects of quantum entanglement. The Schrödinger equation provides us with a precise evolution in time for an entity (i.e. particle or similar), an evolution that depends critically upon how the phase varies from place to place. If we ask the wavefunction where the particle is, by performing a position measurement, we lose this phase information. After the measurement we have to start over again with a new wavefunction. If the result is the position of the particle, the wavefunction peaks very strongly at that position, after which it disperses in accordance with the Schrödinger evolution. That means the wavefunction peaks at the measurement bringing the measured observable in form of a Dirac δ-function, if this is done with maximum possible precision. So we learned, the particle wavefunction disperses by evolution and peaks by state reduction (measurement). When more than one particle is present in a system to be observed, the dispersion of the wavefunctions leads to a phenomenon that is quite puzzling: quantum entanglement. Hereby a system of many particles needs to be described as a single holistic unit with its holistic wavefunction, which we want to call Ψ. Particles that are identical, are always automatically entangled with one another, although this can be happening in two very distinct ways, depending on the nature of the particle we are dealing with 68. The wavefunction Ψ would represent the observed property (position or momentum etc.) of all particles of the system, so it is really a function on the configuration space of the system of particles. The Schrödinger equation will tell us how Ψ evolves in time, so Ψ = Ψ (t). This simple space-time asymmetry of the Schrödinger approach hides something deep that is still missing from our quantum picture of things. A proper relativistic treatment of multi-particle systems makes the formalism very complicated, so time is treated by Schrödinger nonrelativistically as a background coordinate. This is a good approximation of the truth in the non-relativistic realm under omission of gravity, but we should keep this in mind with some caution. The first mystery of quantum entanglement is the phenomenon itself. We have to come to terms with it in a manner that we can comprehend the strange effects which are such an important part in the workings of our universe. The second mystery is why we barely notice entanglement in our direct experience of the world, if it is such a ubiquitous effect. 68

Depending on the symmetry of the wavefunction of the respective particle, which is dependent on the nature of its spin, we have bosons and fermions, which become entangled in different manners.

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Entanglements tend to spread, so that eventually every particle in the universe must become entangled with every other. So why do we not experience an entangled mess, with no resemblance to the almost classical world we perceive? Evolution of the wavefunction makes things worse, so it is no help to answer this question, but state reduction might do the trick. If we make a measurement of a state of a particle we cut the one entangled with it free of its entanglement, so it possesses now a state vector and wavefunction of its own. It seems that measurements or observations all the time cut through entanglements. The performance of a measurement requires the setting up of an experiment for quantum effects avoiding entanglement or worse, increasing entanglement. In practice, this is not the case; so do entanglements average out or has Nature a way of continuously doing state reduction without the need of an observer? – Averaging out would not convince us because of lacking evidence for that. So, when, where and how do we have to interpose state reductions within the evolution of the wavefunction? This is called the measurement paradox of Physics. Another puzzle is the simultaneity of entanglement effects, which does not sit very comfortably with the requirements of relativity, where such simultaneity only can exist if it is instantaneous. For Kabbalah and Chasidut the cutting through entanglement could be an example for the direct observation of the continuous upholding of Creation as written by Rabbi Shneur Zalman of Liadi in Sefer Tanya, as cited above. He is emphasizing the upholding of the demarcation (‫ )רקיע‬as a means of upholding Creation. In this case it could mean the demarcation between the quantum states and a permanent observer, the Creator Himself or one of his creations encompassing our universe. The question for us remains: how does the Creator do that? Let us remember the 2nd law of thermodynamics. It seems to present us with a timeasymmetry of the universe, such that the “final” state of it is not equivalent to its initial state, as we have seen above. In Quantum Theory we do not perceive a time-asymmetry in the process of the evolution of the wave-function, while the state-reduction definitely is timeasymmetric. The 2nd law of thermodynamics is brought into existence by the distribution of matter and the dynamics of that distribution. Matter means massive objects, space-time curvature and herewith it is related to gravity. Does gravity play a role in the reduction of a state on measurement or observation? The gravitational self-energy in a mass distribution is the energy that is gained in assembling that mass distribution out of point masses completely dispersed at infinity. Furthermore we can assign to each wavefunction Ψ of the assembly of masses a superposition of states |χ> and |φ>, so that |Ψ> = w |χ> + z |φ>. If we look at a radioactive Uranium-238 nucleus as an example for such a state of an assembled mass distribution, we see its lifetime is about 10 9 years, so that with Heisenberg’s energy-time uncertainty relation we obtain 10-51 Joules as an energy uncertainty which leads to a mass uncertainty of 10-44 of its total mass. Analogous to that we can say that the gravitational (massive) self-energy is related to a decay time of TG ~ ħ / EG

62

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One has to modify Schrödinger’s equation in a way that it includes the mass distribution, taking Heisenberg’s uncertainty relation for position and momentum into account 69. This modified equation indeed shows well-behaved stationary solutions for a single particle tailing off towards infinity. We now have what appears to be a plausible proposal for an objective state reduction for superposed states like our Uranium nucleus. Such a superposed state will spontaneously reduce into one or both of its stationary constituents in an average time scale of TG according to the above relation, where EG is the gravitational self-energy of the difference between the two mass distributions. This proposal for an objective state reduction does not run into difficulties with energy conservation as others do, and it provides the timeasymmetry desired above. To come back to the upholding of Creation, which needs to be a time-asymmetric process, this proposal of a spontaneous objective state reduction may be an explanation for a balance against ever growing entanglement, so that entangled states really average out. Hence, it may be the case that the Creator places at every instant such state reductions as a result of the gravitational properties of the quantum states of matter. Such state reductions are equivalent to proper observations, so that one can say, at least partially, these state reductions bring the “observed” objects into a stabilized existence. Furthermore, there is a possibility for objective state reduction to be the initiator of spontaneous symmetry breaking. Can we assert a universe where hashgachah pratit is produced by continuously re-occurring state reductions, time-asymmetrically along the arrow of time70 produced by the 2nd law of thermodynamics and with that camouflaging the true statistical nature of things, presenting us with a deterministic appearance of the universe? – This question has to wait to be answered until ongoing research and hopefully future experiments show us the truth. We will come back to this issue and will present some gedankenexperiments in our chapter about suggestions for further research. It remains for now one question: we showed that any (not necessarily quantum) system has to be influenced from outside to possess stabilized unambiguous properties, either by observations or other wavefunction state reductions, but what is the last and ultimate provider of such state reductions to uphold a stable set of worlds including our universe – and how can that ultimate Existence be stable in itself without an additional internal or external demarcation? – One could also ask whether a single big system of worlds and the Ein Sof together as One Ultimate and Total Existence can ever be a stabilized system in some sort of equilibrium71 and exist or “live”72 for ever. We also need to wait for some suggestions regarding these questions for now and consider a few other facts first. Regarding the kabbalistic view we at least want to remind the reader that there are demarcations and even klipot within and between the worlds and that without such demarcations any stabilization of the Total Existence would become problematic and the commandment about its absolute oneness could become questionable, if it would be stable without such demarcations inside it. 69

70

This is subject to active research and henceforth still controversial. Such an arrow of time looks on configuration space like a slope on same space.

71

This equilibrium would of course only be valid if all its dynamic subsystems’ properties would average out. 72 “Living” how we understand it would not apply to such a Total Existence, as the Rambam has pointed out (see citation in the introduction). A living system in our sense needs to be out of equilibrium to develop.

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‫ספר‬

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Any system, no matter how large, is, if it is a closed system, described by a wavefunction and obeys Schrödinger’s wave equation. The next most important fact which was only realized later by Dirac, Heisenberg and Born, is that if a closed system is going to be observed, then it is not closed anymore. It is being impacted by the measurement apparatus or any other state reducing action in an unavoidable, essential way. Then the system does not obey the rules of the Schrödinger equation any more, but jumps into one state or from one state into another. This is novel and counter-intuitive, but it agrees with experiment. It is a phase transition from evolution to steady state, which is not inconsistent at all. Under the influence of an interaction like a measurement, observation or objective state reduction the evolving state described by Schrödinger’s equation gets replaced by one of its solutions describing the state which became reduced. In case of an objective state reduction this happens on initiation of the evolving system itself, for example by the Killing vector becoming ill-defined and the system reduces to a new set of states with a well defined Killing vector. This latter process can be interpreted as self-observation. It is also conceivable that within a system of many entangled or evolving states there is a possibility to partially reduce the system while its remainder is left untouched by any state reduction which results in a partially evolving and a partially reduced system. It is furthermore conceivable that the Total Existence with its Infinite Light and the Creation inside the vacated space with its realm of Adam Kadmon and the four worlds may constitute such a partially reduced system. Such a self-observation of a single and unique Total Existence is possible even if the information produced in the state reductions is left uncommunicated. The condition for such information being produced and keep the respective states reduced is that such information is deemed communicable, not necessarily communicated. Furthermore it was believed until recently that Schrödinger’s equation only applied in the microscopic realm where signals had to be amplified by macroscopic systems on which one could use Classical Physics to describe them. Recent research showed, as we have seen in the experiments discussed above, that macroscopic quantum tunneling has been exhibited in the laboratory, and it is no longer believed that one can draw a line between the macroscopic and microscopic realms. They must be governed by the same laws of Nature and, as we have seen before, it is not relevant where the line or ‫ רקיע‬is drawn, but whether it exists at all or not. If it exists, it would allow the laws of Nature to appear different on each side of it. This obviously seems to be the case if one looks at the macroscopic realm where the laws of thermodynamics and relativity prevail, while if one considers the microscopic realm both thermodynamics and relativity seem to make no sense anymore. To shed some light onto this, let us go back to the Einstein-Podolski-Rosen (EPR) paradox. Quantum mechanics obviously not only in its mathematical formalism but also in experiment does not satisfy the locality principle of relativity. In particular the experiments violating causality and/or the normal order of time suggest quantum entanglement: when something has an effect on one of two entangled particles, the wavefunction of the other particle changes simultaneously. The simultaneity becomes ambiguous in relativity insofar such simultaneity needs either a preferred reference frame or can happen only if signals are exchanged instantaneously73. Otherwise, in the case of a limitation of information exchange speed, there will always be frames of reference which place one event first, and others which place the other one first. In case of entanglement of such events it is difficult to explain their correlation without invoking some sort of causality, but it cannot be the “normal” one where 73

Such an exchange of information cannot be Lorentz-invariant and contradicts relativity.

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‫ספר‬

‫בס"ד‬

one event can be clearly said to cause another; rather each of the events depends equally on the outcome of the other, regardless of which one might look like it happens first. This implies at least two things. Either the Quantum Theory is incomplete, and incorrect in its assertion that the second particle does not have a property before it is measured, or else the measurement of the first particle somehow determines the state of the other, however far away it is. Einstein called this a “spooky action at a distance”. Spooky because there is no known mechanism for such an interaction, and because it would entail that things can be affected by events which, in some frame of reference, have not happened yet74. One solution to this conundrum is instantaneous interaction at a distance, the other entanglement via the history of the entangled particles75. Since macroscopic entanglement is a fact, we can take Schrödinger’s equation as exactly valid over laboratory dimensions, including macroscopic apparatus. Then we have to explain how the wave of the measured system, when interacting with the wave of the measuring apparatus produces intermittent signals called measurements or observations. The production of such intermittent signals as a discontinuous transition from continuous inputs is the result of an interchange of limits 76. It can also be shown that describing the apparatus with a state space with many degrees of freedom and the particle with another state space containing the states it can assume only, and combining both state spaces describing the total system as a closed system leads to non-decomposable states of the total system, and hence, apparatus and measured particle are entangled. This entanglement cannot be eliminated. Probabilities can be derived from the amplitudes of the entangled and un-entangled states, and they can be observed when we do a measurement, but again, only some distinction (‫ )רקיע‬between the use of Schrödinger’s equation and the use of the probability rules can tell us when to use one or the other. The question again arises, where to put the distinction. We said above in the microscopic realm thermodynamics does not make sense, and in some way this is also true for gravity with the exception of processes related to the gravitational self-energy of the system; otherwise, they only make sense in macroscopic realms. Our proposition is therefore to examine the possibility to put the distinction at the thermodynamic limit. This allows us to leave the wave equation untouched and it shifts the place of the distinction to infinity, so that we reach the limit to Statistical Physics. It is, however, not always necessary to shift the distinction to infinity, but in the case of our universe and the spiritual worlds we were speaking about above, such shifting to infinity suggests to draw the line within the Total Existence at a place beyond the worlds including our universe and beyond the boundary between the Or Ein Sof and the vacated space. Up to now we think it is clear that with Creation of something, opposites began to exist and the distinctions between them led to worlds including our universe that are in a state of a relatively stable dynamics, as we can observe experimentally. This does not at all mean our world is in some sort of equilibrium, because this would cause dynamics to seize or exist only in selected parts of that world, finally getting into total equilibrium, representing a dying world. So the stable dynamics is in a state out of equilibrium, macroscopically evolving in time, yet decaying like our Uranium nucleus above77, rendering objective state reductions all the time, disentangling quantum states, gravitationally. Furthermore, all the above mentioned distinctions between observed and observing systems are stabilizing actions for such a 74

This could be interpreted as a confirmation of what is called hashgachah pratit, but is such an interpretation reasonable? – We shall see this in the course of the rest of the book. 75 This is known as the transactional interpretation of quantum measurement. 76 J.F. Johnson, Thermodynamic limits…, quant-ph/0507017v1 2 Jul 2005. 77 For example even a proton has a half-life: 1032 years.

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‫ספר‬

‫בס"ד‬

dynamics of our universe. As we learned before in Kabbalah, all Creation exists in a space from which the “simple infinite light” is expelled by a distinction, but still the light, the vacated space and all that is therein is part of a Total Existence, of what we may want to call the Creator. For now, we have ascertained an explanation how Creation is held in existence, but what about the Creator or the Total Existence, is it needed after all the mechanisms of the creation are in place? – Our experience with causality and time seem to magnify that question-mark, and so does the obvious self-emergence of the Planck state of the universe from the point in infinity. Is then the Creator together with His Creation one big closed system forming a Total Existence beyond time and causality at the onset of Creation? To answer these questions satisfactorily, we need to remind ourselves that we are part of that Creation, and still function very well as observers from inside the system, sentient observers, but physically finite. Therefore, any answers will remain incomplete. Besides the points to be examined further in regard to the Total Existence, there is something left that could shed some light on gravitational or similarly induced objective state reduction: space and time themselves. • • •

What constitutes the permanent observation breaking entanglement continuously to uphold the worlds? What constitutes the observation that stabilized the created space during the first and second Tzimtzum? What constitutes a reshimo in the sense that light is interacting with a part of space (vacuum) seemingly at random leaving an imprint which creates after further interaction with light a vessel (letter)?

4. Space, time and information processing as possible sources of objective state reductions: The plane of the present in space-time represents the demarcation or ‫ רקיע‬between the past and the future. Why do we say the present is a plane? – Relativity sets the dimension of time on equal footing with space and energy. Hence, space-time provides a hyper-plane in fourdimensional space that prescribes the geometry of the present from the viewpoints of all observers. This is a rather convoluted geometrical form as it contains moving frames of reference and the like. Causality in such a view is then dependent on the place on that plane (or better surface) the respective observer is on and how the sequence of events appears to him. Furthermore we need to remind ourselves about the fact that three-dimensional space may be extended by information coordinates and other useful dimensions concerning the determination of the observer’s view of causality. In this context the transactional interpretation of quantum mechanics is the most convenient interpretation as it does not give a preferred role to special observers or measurements. It gives, however, a demarcation between them, which, in the thermodynamic limit leads to exactly the macroscopically observed effects including entanglement. This entanglement gets broken at space-time coordinates depending on the frame of reference of the interpreting observer, meaning the causality of the process depends on a second demarcation, which

66

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‫ספר‬

‫בס"ד‬

separates the “straight” observers from the “inverted” ones, without altering or violating the Laws of Physics; they have to remain invariant to such reference frames. From relativity follows, there must be at least one observer who sees the “causality-pretending” events as “synchronous”, as being neither the one nor the other as he must be located on the demarcation surface that is neutral to causality. A good example for such an observer seeing “superluminal” and “subluminal” phenomena as neither cause nor effect is the photon itself, because it travels exactly on the demarcation between “straight” and “inverted” phenomenon, be this time, causality, space or any other inversion of the meanings of opposites, if the photon is not involved in tunneling effects. We also remind the reader at this stage about how different observers see particles and their anti-particles, where again the photon is its own anti-particle, just the chiralities are opposite to each other. Hence, we can propose light as a neutral mediator between opposites in general, if we generalize the term light in an appropriate manner. How that can be done will evolve from the following discussions of Science and Kabbalah, but first we need to clear up the exact meanings of causality, sequence of time and observation as well as of the term information. Information Theory78 provides us with some insight into how a proper understanding of these and related terms can resolve confusions related to the obvious relativity of all opposites and the puzzling way in how their meanings depend on the viewpoint of the respective observer. This viewpoint of the observer categorizes sequences of events and phenomena by means of distinctions which seem to be dependent on conditions dependent on how the information gathered by observations is processed by the sentient observer. Without consulting Information Theory, we may discuss the above issues at length, but never understand them. For example, the question of how primitive the process of producing communicable information for the establishment of a valid observation can be needs some rigorous treatment within this theory. Information Theory treats the production, processing and transmission of information and henceforth the for our discussion so important creation of distinctions or ‫ רקיעים‬to produce stable physical or other (spiritual) systems or phases (sfirot) or more general, classifications, in a rigorous mathematical and logical way, but a few limitations have to be taken into account. In logical treatments of categories the distinction rules for such categories are made • • •

In an always incomplete manner; On an individual basis or by agreement by asset of individuals; In a relativistic manner (viewpoint of the observer).

It follows that any categorization cannot be made in an absolutist way. For example: 78

Information Theory is a branch of applied mathematics involving the quantification and qualification of information to find fundamental limits on processing and communicating data. A key measure of information is for example information entropy that quantifies the uncertainties involved in random variables as encountered in measurements or more general, quantum state reductions. The field is at the crossroads of mathematics, statistics, computer science, physics, neurobiology, and electrical engineering. Its impact has been crucial to success of missions to deep space, the understanding of black holes and the study of linguistics and human perception, to name only a few. Much of the mathematics behind information theory with events of different probabilities was developed by Ludwig Boltzmann and J. Willard Gibbs for the field of thermodynamics and statistical physics, which is the classical limit of quantum physics.

67

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Does a + 0.i, for a = 1, 2, 3, 4, …, n belong to the natural or complex numbers? – The answer is: Since the natural numbers are a subset of the complex numbers, it belongs to the complex numbers, and because i is multiplied by zero, it belongs to the natural numbers. Despite the ambiguosity involved, the answer is absolutely correct, but incomplete, as it is individually arguable, whether the above number is belonging to the one or the other set, despite this example is one of the most absolute categorizations possible. The most definite example for indeterminism is the location of the place of a distinction between two empty sets. They can either be nested into each other, partially overlap each other or be completely separate from each other; the shape of the boundary of each of the two sets can also be freely chosen without affecting the structure at all. Categories such as sets do not exist in the physical real world, but only in the mind of an individual. This mind processes the information about such a categorization by electrochemical processes in the brain of the individual, which makes the information a physical entity in form of physical memory and the like. Mutual agreement between a group of individuals about definitions and other properties of such categorizations leads to communicable sets of information which are uniformized. Uniformization of sets of information within large groups of individuals or societies is called education. A further result of the availability of information carried by a physical carrier such as the brain is implied by the condition that without such availability of at least an infinitesimally small accessible memory time becomes meaningless for the individual in question. It is further questionable whether objects such as categories or objects within categories are completely separable. For example they are never completely separable from their context in which they are observed by either a sentient observer or a registration device. As we have seen before, such observer or registration device is unavoidably entangled with the object or category observed and provides additional context in form of his own context. Complete separability is therefore an idealized structure and exists only in conjunction with the observer or other state reduction agent such as a registration device. It follows that causality as a categorization of cause and effect is henceforth not making sense without the “complete” context of the phenomenon observed, including the level of information of the observer. We have seen this in our seemingly causality-defying gedankenexperiment with overtaking waves as described above. So, without the full context or with concealed information about the observed phenomenon causality is meaningless, and without interpretation even in the most primitive sense like the particle hit the detector or not interpreted by a communicable piece of information like a setting a bit to zero or one any information becomes meaningless. This opens, as we have seen in the quantum erasure experiment, the possibility of erasing such non-communicable or not communicated information violating the order of time. Only the interpretation of an observation renders the information in a related context produced by such observation true or false. Without such interpretation, or in a primitive form of it, registration in communicable form, any observation remains ambiguous or completely meaningless. Hence, it is not part of what is commonly defined as reality. May the reader be reminded that such definitions are also made by the observer as part of his society characterized by his particular education. The just explained processing of information by interpretation dependent on definitions and context is a set of mathematical operations in form of logical connections called reasoning and in most cases expressed by language. The most rigorous language is mathematics, in this case to be understood as a tool to make all available information about a measurement or observation in its respective context and its processing communicable to a receiving entity

68

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‫ספר‬

‫בס"ד‬

that is conditioned (educated) to be able to understand the communicable information conveyed to it. Mathematical expressions and words of other languages are chosen as descriptors by the communicating and processing (interpreting) entities’ proposed sections of reality, not reality itself. The mathematical structures described by mathematical expressions or observations of any structures described by expressions of other language, themselves are entities of realities and as such intrinsic parts of the real world, no matter how abstract or spiritual such real world may be, because at least the expressions describing such world or parts thereof are physically realized as information patterns on an information carrier such as a brain, its memory or any other “readable” information carrier or processor. Without such physical carrier information, at least in the classical sense, cannot exist and be communicated. Let us now look at the role of mathematical structures such as geometrical and other spaces in the formation of realities, even physically massive realities. As we have seen above, both in the kabbalistic and in the mathematical-physical creation process description, the mathematical structure of spaces and their dimensions are not only vital but absolutely necessary and sufficient for such creation processes of any thinkable realities or, expressed with another word, worlds. In finite or limited environments such realities have to be looked at as non-ideals. This makes categorization impossible as this requires idealized standards to form a model of said reality. Individual non-ideal real objects need then to be approximated to the idealized standard to be able to categorize them according to the model of reality, which is the case with any categorization process whatsoever. Hence, in any mental model of reality or in other words perception of reality, there is an uncertainty involved, namely the deviations of the true objects from the idealized model object or generalized or abstracted object. Such uncertainties are due to the general limitation of the precision of a description process which needs categorization to enable choices for descriptors (words or mathematical expressions) modeling any reality. This is identical to the uncertainties of quantum physics in its classical limit of statistical physics. Such uncertainties obey the laws of general thermodynamics as formulated by Boltzmann and Gibbs. In the non-classical case, such information becomes quantum information underlying Heisenberg’s uncertainty principle. Special care has to be taken in the treatment of quantum information in comparison to classical information, in particular regarding its transmission, if entanglement is involved. In case of models that use unlimited or partially limited infinities or infinitesimally small entities one has to realize that infinity is an open system in contrary to a limited or finite system which may be closed. In information theory an infinity is a system where no decision as to a stopping or limit has yet been chosen or spontaneously occurred. The common concept of a completed infinity, however, is not empirically viable. For example a line to be constructed by lining up mathematical points that are infinitely small from one starting point onwards yields a point instead of a line, meaning it is impossible to finish the construction. The line can only be constructed by connecting two points at a distance to each other or by lining up finite elements or points of “finite uncertainty”. To introduce such uncertainties and with that limiting distinctions is necessary, otherwise things constructed from infinities become indefinable. An example for this is our now well known point in infinity, whose coordinates are not definable for lack of space, and which is indistinguishable from a sphere with infinitely large radius, as we have seen above. Such point, representing oneness superseding absolute nothingness or absolute non-existence by logic argued above on

69

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grounds of the asymmetry of NOT79 ((‫לא‬, is a piece of information and with that a mathematical structure which is physical in the sense that the point – infinite sphere is a geometrical object spanning up a space containing it. Since this objects’ dimensionality is also undefined, it represents the primordial geometrical space containing infinitely much (all ever possible) and infinitely little (only the point), but not no information. As we have outlined above, general relativity shows that the geometrical properties of such space define its physical properties. The reason for this is: any information is physical, and in the case of space-curvature, even gravitational. The gravitational self-energy of that space, which is negative, then decays into inflation of space, light and massive particles by an objective state reduction taking place according to the conditions of false vacuum decay as described above. Without the intrinsic uncertainty (indefinability) of the information that is available at the onset of creation, such creation would not come to reality. With the adiabatic expansion the in the beginning very hot universe cooled down and symmetry reduction could take place by decay of the primordial grand unification into the universe or system of worlds we know today. Each symmetry reduction in the formation of the universe represents a demarcation or objective observation process. In kabbalistic language those symmetry reductions represent ‫רקיעים‬. Remarkable is that there are seven such symmetry reductions in the history of our universe according to physical observation, and there are seven demarcations or ‫ רקיעים‬in the “heavens” (‫ )שמים‬as described and extensively discussed in the Babylonian Talmud, Tractate Chagigah 12b and elsewhere. This is also referred to as the seven pillars of the world as explained in Sefer Yetzirah 4. Those seven pillars refer according to the Ari z”l to the seven lower sfirot or ‫ זו"ן‬and are represented by the seven double letters ‫ בג"ד כפר"ת‬which are either soft or hard, denoted by a point in the middle of the letter, the ‫דגש‬. Describe physical and kabbalistic ‫ רקיעים‬in detail here and discuss. Take Otzrot Chaim and Brit Menuchah into account and look for the angels and neshamot, ruach etc. Include Sefer Yetzirah in this process (Chapter 4 and 2:6). In Etz Chaim we see the worlds were created with light interacting with a reshimo of the sfirot in the vacuum of space, creating vessels, which can be interpreted as letters of the Hebrew alphabet. These letters make up a code creating each and every concept as well as each and every possible massive or non-massive entity thinkable in the worlds created. Let us analyze first generally with the help of information theory, what is behind this “creation by words” as creatio ex nihilo. Without interpretation words or mathematical or other statements become meaningless for lack of definition. As we have said above, definitions are made by the observer. So, if the worlds are created by words or statements (including geometrical statements about structures) these worlds become meaningless without at least a minimally sentient being “understanding” the words or statements by associating them with his observation. These observations can be in a “spiritual” or in a “physical” world in the theological sense of ‫ גשמיות‬and ‫רוחניות‬, as both contain information which is physical, because no (classical) information can exist without a carrier. Quantum information and its physicality still need some deeper discussion in this context, because the “spooky action on a distance” allows no transmission of classical information. Entangled states, however distant they are from each other spatially or in time, represent one single system acting as a physical information carrier. Hence, this information needs not to travel at all. Only when part of this entangled system is 79

We have shown this in our proof of ONE superseding absolute nothingness.

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observed or measured, the entanglement is broken and the information can be retrieved, classically. This now classical information travels at a speed lower or equal that of light to the observing or measuring system. Concerning the Creator (ONE) we need to remark that he has no properties, meaning that ONE is not a property but a countability which in turn is positive80 and information which is carried by (latent) space and henceforth (latently) physical until inflation of space and time takes place, to become physical and observable by his creation 81. In Kabbalah this latency is often expressed as the “essence” of an object created or a subject creating. As we will see later, in the process of creation the Creator uses some of his creations, e.g. Adam Kadmon, as vehicles for creatio ex nihilo, as described in Sefer Tanya, Igeret HaKodesh XX. Information-theoretically such an entity is already a structure, emanating vessels or letters, which are information in the same way as the structure itself. This means, the definitions of “physicality” and “spirituality” need to be subjected to further very careful thought, so we can explain, what may be the difference between the physical world and the higher worlds we are talking about in Kabbalah. Letters and words or a name (‫ )שם‬is a proposed section of reality, but not reality itself82. Without interpretation by a sentient observer or Creator this reality becomes meaningless and undefined. A letter, word or name cannot talk on itself. It can only be understood by an observer who can decipher it and is member of a group of individuals who agreed on its meaning. Alternatively the Creator himself delivers words and meanings at his whim. This solution is not proposed by the Torah, however, but rather Adam HaRishon had a say in the naming of things83. Any descriptor is constituted by symbols84, so is language, so is mathematics, agreed upon explicitly or tacitly by a group of individuals. An individual may choose to make up a word of his own as a label for an observation or a thing he lacks a short descriptor for85. Either by power of authority or by repetition (marketing) he may or not be successful in creating a novel descriptor (word) for the new item, phenomenon or idea. Such authority is again an illusion that comes only into real effect by the individuals adhering to such particular beliefs or authority. If such belief system becomes meaningless in relation to what it is supposed to describe or that its logic becomes proven false in part of it, suitable revision has to replace such meaningless parts. Such quest itself is doomed by the relativity 80

This is due to the asymmetry of NOT (‫ )לא‬as shown above. NOT or Ø or 0 are asymmetric. This raises the question whether any negation is asymmetric by its very nature, because the negation cannot exist without its positive counterpart, while the positive counterpart can exist alone with only an imaginary negation for definition purposes. Whether that assertion is also valid for opposites depends on the definition of the term “negative” in its particular context. 81 The Creator can be “seen” in his creations and in his actions. In case of prophesy he can be “heard” by the mind as stated in the Torah. 82 This can lead to the worship of names instead of worshipping the Creator who is the full and one entire existence and reality. Hence one worships a piece of information depicting one or more aspects of the Creator, which easily constitutes ‫( עבודה זרה‬idol worship). 83 See also Sefer HaShemot which is attributed to Adam HaRishon constituting the first book written in Lashon HaKodesh. 84 Symbols are signs that stand for which they stand by virtue of an habitual associate or a conventional agreement rather than because of any relation of resemblance or any causal connection. More generally, a symbol is something that stands for something for someone who uses it. The leading view in cognitive science is that mental symbols get their meaning through naturalistic of some sort that are causal. Kabbalah includes acausal cases. This will be discussed later in the information theoretical aspects of Kabbalah. 85 This was done so by Adam HaRishon on grounds of encouragement by the Creator (Bereshit 2:19-20).

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of the rules inherent to such belief systems. It has to be accepted that any description of the “truth” is inherently dependent on the reference system and pre-information standard of the observer of such “truth”. In short, a statement can be said to be true if: •

• • • •

It refers clearly to areas of external reality that are accessible to the entities communicating; The common meaning of the descriptors accord with that observed reality; There is sufficient agreement between the parties concerning what is perceived; The meanings of the terms being used can be established through an iterative process; The meaning of sufficient is determined and expressed by each party individually.

Due to the above derived uncertainties and incompleteness of any information about an object a “relaxation of rigor” needs to be introduced for statements to be regarded as complete and true: Things become indefinable if no ‫ רקיע‬is introduced. For example “true” and “provable” are not simply interchangeable. “Provable” is dependent on the perceptions of observers to be “true”, under given circumstances, given context and given boundary conditions, e.g. the “true” color of objects is dependent on illumination and the perception of the detection system. An observation of a phenomenon is “true” according to a “picture” or other data or algorithm stored in the brain or elsewhere. In the case of the observation of previously unknown phenomena the establishment of “truth” is accomplished by “proof” within “scientific methodology”. In physics a previously unknown phenomenon or effect may be “proven” to be “true” by establishment of reproducibility of the phenomenon or effect. Furthermore it should not contradict preconceived and established “truths” in form of the Laws of Nature. If such contradiction to preconceived “truths” occurs as for example in the case of Einsteinian relativity or quantum mechanics, only reproducible experiments preferably using more than one experimental method or effect may convince of the “true”value of such new phenomenon. If we check any perceived measurement or observation process information-theoretically we can compare the following phenomena in physics, computer science, mathematics and simple everyday reporting of events: • •

• • • •

Uncertainty in measurement of complementary properties of an observed object; An endless loop in a computer program caused by complementary, mutually exclusive or contradictory inputs; Improvability of a theorem or other mathematical statement due to ambiguosity or complementarity of statements within the theorem itself or occurring during the proof process, like for example elliptic integrals; Ambiguous or elliptic statements describing a phenomenon (not necessarily only a physical one); Self-contradictory statements or paradoxes; Non-computable expressions.

In all these cases the introduction of initial or final conditions, boundary conditions or other demarcations (at least one ‫ רקיע‬is necessary) and the discarding of a subset of information are necessary to get stable solutions or bring a computing process to a “natural” stop or

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explain a phenomenon or expression or make same computable. Even the delayed choice quantum eraser underlies these “laws of information accessibility”. There we change our choice of what to measure even after the measurement event took place in the detector, but we always lose half of the information. This means quantum information can be transferred between entangled states at a distance because those states really appear as one and not two particles. Only after this entanglement is broken, the chosen information can be retrieved, not before that. Hence, quantum information is exchanged in the entangled state instantaneously while classical information is exchanged after the breaking of the entanglement. Barrier tunneling seems to be a mixture of classical and quantum information as it takes a finite time for a particle, even a rest-mass free one like a photon, to cross the barrier. As a general rule we can therefore state: A loop or unobserved phenomenon or phenomenon before an objective or induced state reduction allows retrieving information from the system to characterize the phenomenon while information complementary to the retrieved information is lost or useless and has to be discarded at the moment communicable information about the observation or measurement is produced. Let us now examine the conditions and processes involved in building a demarcation or ‫רקיע‬ for the purpose of making a measurement, observation or objective observation or state reduction. We can have internal actions such as evolving boundary conditions that dictate the conditions of such making of a ‫ רקיע‬such as change in temperature of the system as inductors of spontaneous state reduction or external actions like observations or measurements taken at the time and place of such intended ‫רקיע‬. This latter process requires Decision Making. It is essential to distinguish between the definitions of “decision”, “decision process” and “choice”. Furthermore a clear definition of “action” is needed, besides those for “time” and “intelligence”, “reasoning”, “consciousness” or “self-consciousness”. “Movement” is what we call “time”. In the universe or the worlds inside the Total Existence any dynamics, change or movement emerging from physical entities including information and its carriers causes time or at least an order of time. In case of matter the movement of its distribution in the universe according to the 2nd law of thermodynamics causes the “arrow of time”, as we have seen above. “Intelligence” and “consciousness” relate to information and its processing. “Machines can never make mistakes” as stated by Alan Turing in 1950 in his treatises about sequential computing machines and intelligence have to be refuted because of ubiquitously occurring bit-flips which are due to the quantum mechanical behavior of the information carriers in computer chips. Even in an electromechanical computing machine based on relays (in Turing’s time) a spontaneously and randomly failing relay can cause such bit-flip. Today software has to be designed robust enough to avoid failing of a program or mistakes in the output created by such program due to such flips 86. Through this we see that due to the physical and henceforth non-ideal nature of any information carrier “intelligence” cannot be a measure of how little mistakes are made or how “right” decisions of such an intelligent 86

Learning software, neural networks and fuzzy logic are good examples for such robust systems, but they show too clearly how fallible “artificial intelligence” can be.

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system are. Similarly we have to treat the term “consciousness” here with a lot more caution and in a more rigorous manner than done in colloquial terms. Historically, “intelligence” has been viewed as the capacity or ability to learn. When that ability or capacity is evaluated in relation to one’s chronological age employing standardized tests, the result is a numerical value known as IQ. The problem that has plagued IQ tests is that IQ must be something more than merely a test score or else it would not be worth measuring. There are those who suggest that the term “intelligence” carries with it an evaluative connotation, where its meaning presupposes mentality in the sense of mental ability and it indicates a high level of mentality. Alternatively, its use in the context of “artificial intelligence” raises the possibility that, even if machines are incapable of possessing “ordinary intelligence”, they might still be described as intelligent machines by virtue of their capacity or ability to learn a task successfully and reliably and carry it out as well. Where to draw the line qualitatively between intelligence of a human or animal being and that of a machine and whether such line factually makes any sense or is only a product of human arrogance or prejudice we cannot and do not want to answer here. May it suffice for purposes of decision making to define intelligence as capacity and ability to learn and make non-random decisions based on reasoning. “Consciousness” shall be defined as a state of awareness capable of degrees, where a person, animal or machine might be conscious of some phenomena but not conscious of other phenomena. The range of possible awareness appears to be determined by neurophysiological capacities under the influence of environmental histories. Thus, with respect to signs (marks, symbols) or any other reproducible and observable structure or set of events, for example, a person, animal or machine may be said to be conscious with respect to such reproducible and observable structures or symbols or the like, if they are able to use same and are not incapacitated to exercise this ability. When such structure or symbol or the like occurs within suitable causal proximity, cognition results. Consciousness should be distinguished from selfconsciousness, which is an awareness of one’s own self, and the criteria for such selfconsciousness are not yet precisely enough defined to be used in a reliable manner here in our treatise. We therefore need to develop a definition ourselves, sufficient to explain processes of objective state reductions and the like within one closed system, rather than giving room for argument about such definition in a general colloquial information-environment. “Reasoning” we want to divide into three categories: “analogical”, “credulous” and “skeptical”. Analogical reasoning is an inference that transfers information from one problem, situation, observed phenomenon or abstract information package to another that is relevantly similar. It occurs when two things or kinds of things are compared and the inference is drawn that, because they share certain properties in common, they probably also share other properties. The weight of an analogy tends to depend on the extent of the comparison and the relevance of the reference properties to the corresponding attribute. Reasoning by analogy tends to be fallacious when there are more differences than similarities, there are few but crucial differences, or the existence of similar properties is assumed to be conclusive in establishing other similarities. Credulous reasoning is a feature of defeasible reasoning according to which a maximally consistent set of defeasible conclusions is inferred. In particular, in the case of conflicting defeasible conclusions, all of which are equally warranted, the system selects a maximally conflict-free subset of conclusions. Skeptical reasoning is also a feature of defeasible reasoning according to which

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conflicting defeasible conclusions, all of which are equally warranted, are discarded, and only non-conflicted conclusions are drawn. As we have discussed above, classical information can only be transmitted or processed at speeds slower than that of light in vacuo. Quantum information seems, in particular in regard to entanglement effects, to be instantly traveling. Nevertheless, both need a carrier, and that carrier has physical properties, so the spooky action at a distance seems not to fit into that category, because, dependent on the reference frame of an observer, same may see a future event triggering an event in the present or even in the past. Similarly, the argument of extrasensory perception or prophetic perception of future events (not such that are perceived as a result of logical reasoning of past events and to be understood as mental extrapolations into the future, but such where Divine interference or other Divine action is or was claimed) have to be taken into account as non-classical information processing or transmission, but we need to deal with them with great caution. If quantum entanglement plays a role in such phenomena, and if with that the making of a demarcation or ‫ רקיע‬is necessary to reveal and retrieve such information, we need to determine what decisive action is needed to do that. With the above definitions in mind, let us now discuss the making of such decisions. Besides purely random decisions87 without intelligent reasoning we should expect from any intelligent Creator or other observer that such decisions are made according to such intelligent reasoning. Such reasoning requires according to the above definition of intelligence a learning process. For such learning structure and information is needed in form of definitions and propositions, such as • • • • •

Well established facts; Conjectures; Proven theorems; Statements given by an authority and acceptance thereof; Expressions having the logical form of a proposition but no belief value.

Certain propositions may be “imperatives” in decision making. Intelligent behavior consists in the departure from the completely disciplined behavior of computation, but a rather slight departure, which does not give rise to random behavior or to pointless repetitive loops. Such loops are to be found in evolving systems that are not state reduced. In Kabbalah this means we have evolving or “running and returning” states during the processes of emanation (Atzilut) until the system is transferred into creation (Beriah), where it again evolves until it is transferred into formation (Yetzirah), where it evolves until it comes into Assiyah (making) to become physical. On the way all the complementary information is discarded. The evolving states or “closed loops” allow theoretically a “testing” of all possible solutions of the evolutionary equation (e.g. Schrödinger, Wheeler-DeWitt) until all boundary conditions and initial conditions for the newly to be created reduced state are determined and the state reduction can take place. This does not mean an intelligent Creator has to go through all those possibilities and make a decision after contemplation and deliberation as if He is located outside the Creation, but all conditions of such a state reduction are embedded into the system already from the beginning or evolve with the system (in this case for example our universe). We can make this fact plausible and may convince proponents of “intelligent 87

We include into this the purely accidental measurement or observation of an evolving state and with that the making of a state reduction.

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design”88 of the unlikeliness of such ad hoc decisions of the Creator or “prophetic actions” within the normal evolution of the physical world. Such action is not necessary in the “master plan of the universe”. He seems to prefer to use the laws of Nature and the evolving boundary conditions of such states to let the system find its way into a reduced stabilized state, maybe merely because of the following difficulty: A decision making process is always hampered by the decision problem, which is known as the Entscheidungsproblem. Formulated by Hilbert, the decision problem for a given formal system is the problem of providing a formal algorithm 89 to determine whether a sentence (decision) can be inferred from a given knowledge base in the system. More broadly, a decision problem takes the form of a family of problem instances, for each of which a yes or no answer is required. In the case of the decision problem for predicate logic, the instances take the form of sentences of first-order logic (Aristotelian logic), for which we want to know the answer, whether the sentence is satisfiable. The decision problem for classical first-order logic was proven to be unsolvable by Church and Turing in 1936. A routine or procedure that can be carried out in a finite sequence that in every case yields a definite answer yes or no to a question within a specific domain of inquiry cannot be found due to Gödel’s incompleteness theorem. Such a procedure can be found for a fixed class of problems in the ideal case for almost all of them, within a certain amount of uncertainty. Once such a procedure has been found, the problem is solvable and those questions are decidable. Our problem here is the necessity to form a demarcation (‫ )רקיע‬between opposites or between observable and observer to establish a stabilized system. This presents us with a formidable set of problems: • • •

When and how is the decision made to form a demarcation? What is deemed to be a decision? How is the decision being enacted?

We have to look at above mentioned effects like false vacuum inflation and what are the conditions and criteria for a decision that such inflation will take place, as well as who is the decision maker and what conditions and criteria identify such decision maker. Another question arises as to the definition of a decision as conscious, sub-conscious or un-conscious. We suppose the total system Creator and Creation together to be infinite in all respects, including a mind, but this presents us with a problem. The infinitude only allows evolving and entangled states that fluctuate. To stabilize, the system needs to become limited, and this is also true for the mind or mind-like parts of such a system. For the mind to stabilize and make a decision, infinity is rather an adverse property, for the following reason. If we allow an infinity of symbols there would be symbols differing from others to an arbitrarily small amount, meaning they would be hardly distinguishable. Such distinguishability is limited to a finite minimum value determined by the resolution capacity of the observer or detecting system and his or its capability to make a decision on such distinction, and finally on his or its capability of establishing and deciding on the place of a demarcation between the objects, 88

In this case “intelligent design” has to be understood as a totally externally controlled system that is designed at the whim of a Creator and may disregard the laws of Nature. 89 An algorithm is a well-defined sequence of steps (procedure or routine) that takes some value as input and guarantees a value as output in some finite number of steps.

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phenomena or such entities to be distinguished from each other; whether they are physical in the sense of objects or objects of information in the mind does not make a difference in this respect. Similarly, if we break up any decision process into “simple operations” which are so elementary that it is not easy to imagine them further divided, there must be a “most elementary” type of decision process. One would imagine a yes/no decision is the most elementary, but this is a mistake as this is an outcome of a decision process and not the process itself. We are not looking for the most elementary result of a decision but for the most elementary process to get such a result or the most elementary initialization of such a process. Let us, for the purpose of determination of the decision process of highest simplicity, first analyze the steps necessary to make an intelligent decision on a choice:

1. Collection of information about all (or most) possible choices. If there are infinitely many choices possible, this information will be incomplete. 2. Processing that information: • Determination of choices according to possible outcomes; • Analysis of all time-sequences as they appear to the decision maker or will appear to him, as far as this is possible; • Analysis of causes and effects and their time-sequences including possible shifts or changes of the reference systems involved. 3. Determination whether all processes anticipated in 2 are invariant under changes of coordinates or other changes of the decision maker during the process, as far as possible. If any infinities or elliptic elements occur inside such anticipated process, boundary conditions need to be introduced by choice and so on. The latter decision processes are incomplete. 4. Categorization of the results of 2 and 3 into: • Possible and impossible choices; • All cause/effect pairs or trees into time-sequences; • Choices of convenience (e.g. timings etc.). 5. Determination of space-time coordinates of the decision to be made. 6. Execution of the choice by action. This constitutes a generalized example for a decision that implies reasoning. Of course there exist decisions that are completely without reason and totally random, which constitutes the other extreme of a decision. The main question about how most of such decision processes are executed revolves around three possible kinds of reasons to base such decisions or decision chains on: • • •

Pure randomness which may be weighted by probability distributions; Based on some logic or entirely logical; Authoritarian which can be logical and rational to illogical and irrational;

The nature of the intent of such decision plays always a role in such decision processes. Only the intent together with the chosen deed constitutes a classifiable decision, but there exist also un-classifiable decisions, e.g. the initiation of a deed without intent. A system which is undecided or partially undecided obeys (partially) Schrödinger’s evolutionary equation, the collapse of the wavefunction or the transactional obtaining of the

77

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desired communicable information is achieved by the decisive action in making a ‫רקיע‬, and in the classical limit, by shifting same into infinity towards the “undesired” (defining) opposite of the then “measured”, “observed” or “willed” observable or action 90. In all cases, the undesired information or action and with that the outcome of such action is discarded. Depending on where in the decision making process information is discarded, sub-decisions are made irrevocably, inevitably leading to choices preventing any revision of the decision process. If with that vital information is discarded towards the beginning of the process, the outcome of such process may lead to logically sound but despite that erroneous choices and irrational actions. An example for this is the more instinctual behavior of uneducated or immature humans towards others, and in particular others alien to them, at the beginning of their interaction. They contend to worry exceedingly about the categories into which they fit themselves or other people and often associate their opinions with not necessarily representative (typical) members of such categories or with hearsay. Without any rudimentary statistical analysis in their minds, they end up in some cases with generalizations leading to prejudices early in their decision process determining how to interact. In extreme cases fatal decisions such as for example the commitment of violence or murder become acceptable. Others who are more educated and control them might use this condition to start hostilities such as war or genocide to remove obstacles or alleged obstacles out of their “path to more power and resources”. The instinct to control others, and thereby to control resources for personal uses and breeding, is probably inherent to humans. Naturally this instinct inclines the more powerful and not necessarily more educated individuals or “categories” of individuals to shape “laws” to their own advantages which they then rationalize as “justice”. They then try to “sell” their package of values to their neighbors by using peaceful or violent persuasion. This can occur on grounds of decision making on the basis of “G-d given law” or man made philosophies and legal concepts. In case of selfish power play and, to a certain extent, behavior induced by survival-instinct, the controlling category or categories abhor any questioning and are of consequence anti-intellectual (conservative), while adamantly claiming the “spiritual authority” or “iron logic” of their desires, choices and/or decisions. This happens, in particular at times of drastic changes in a society or circumstances of that society. For example technological changes or revolutionary scientific insights inside that society or external changes affecting such society might lead the controlling category or categories to believe their interests or themselves being threatened. Even if the controlling category or categories have genuinely “good” intentions not only for themselves but also for the non-controlling members of that society, they may fear a destabilization of that society or parts thereof. Be such threat imagined or real, they will arrive at decisions leading to hamper the development or use of the innovation or even sabotage the part of education enabling individuals to partake actively or passively in that innovation. This effect is amplified exponentially, the earlier in the decision process irreversible choices are made, because with each choice the complementary information belonging to the complementary choice is discarded with that. If that happens in education, societies may be forced to discard information vital for their development and they may end up disadvantaged within a national or global context.

90

This decisive action can be referred to as“redemption” from the undesired.

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In the most primitive forms of societies or assemblies of subjects91, the subject that “loves” another has come to recognize that other subject or object as a source of gain, whereas the subject that “hates” another recognizes that other subject or object as a block to its own objectives. These objectives can range from pure survival to any higher “motivation”. An example in nature for this is the immune system of a human which is necessary to reject sickness, while it is detrimental for organ transplantations. In atomic physics we see a proton attracting an electron “to make a zivug” to form a hydrogen atom; in the nucleus an additional neutron is regarded as no threat and it can merge with the nucleus, but if a proton is approaching it gets repelled unless it forces its way in by having enough energy. Then the nucleus is forced to change its identity. There are countless examples for such “love-hate” decision making in nature from primitive ones like the relationship of elementary particles over chemical or biological attractions or repulsions (rejections) up to human or societal relationships, but the underlying principles of “potential gain or loss” are valid in all such relationships. In Kabbalah zivugim underlie also attraction and repulsion rules and are mostly denoted as front to front, front to back and back to back relationships. For the preservation of identities or of well functioning systems Nature has provided such systems with the ability to “decide” on defense mechanisms which are higher developed the more complex such a system may be, such as an immune system or societal and intellectual or philosophical defense mechanisms. For example in developed human society conservatism or the delayed or slowed down dispensation of intellectual innovation is necessary to preserve the stability of the leadership for the time being until that innovation is no threat for that leadership and its education or knowledge level is on par with that of the innovators. In case of a stagnating education or knowledge progression of the leadership relative to the rest of the population either the survival of that leadership is threatened or the population splits into at least two groups, if the total power levels of the respective groups are held equal. If the power level is higher on a lower educated or less intelligent leadership, conflict arises in the quest of the establishment and the innovators to win followers. Violent establishments or innovators shift the conflict resolution into throughout irrational confrontations of physical or legal powers. They may then end up with a growing and better educated population in case of the more intelligent group “winning” the conflict, or with a stagnating or in the worst case completely paralyzed uneducated population leading to a complete breakdown of the system92. The introduction of “morality” or “ethics” based on certain philosophies as a regulator ameliorating the harsh natural laws of societies tries to avoid pure predatorleadership, as we will see later and claims to be called “civilization”. The system of the seven Noachic and the 613 Jewish mitzvoth and the corresponding Halachic systems are very good examples of legal foundations of such civilizations. For example the Jewish mitzvah of “loving your fellow as you love yourself” is a classical case of an amelioration of the harsh natural laws of society. In regard to our example “society” which can consist of highly developed biological entities like humans down to very primitive assemblies of particles assembling in atoms, molecules, crystals or genetically coded entities, we have with growing complexity of such system the growing need of more and more intelligent decision making processes. With such growing complexity the number of incomplete subsets of the decision process grows, causality gets 91

Subject is here defined as an entity that can exert an action onto another entity that may change or affect for example its survival or its identity. 92 A case where this happened not long ago is Cambodia under the menacing “rule” of the Khmer Rouge.

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relativated as soon as the decision maker’s reference system or viewpoint can change during the process and statistical properties of the decision making process become dominant. This is describable within the same concepts as they are valid and used in statistical physics or quantum theory. Statistical physics in the classical limit describes large assemblies of physical objects with all uncertainties involved, while quantum theory describes small numbers or single objects, taking uncertainties related to complementary properties of such objects into account. In all these cases, in the macroscopic and the microscopic limits of physics, information is discarded or “lost” with making the irreversible decision to observe a certain property or set of properties of the object(s) concerned. Similarly, information and its objects, e.g. bits, decision operations and choices with their resulting actions within an information processing or decision process underlie statistical and quantum laws like for instance uncertainty relations, the 2nd law of thermodynamics93, orders of time and causalities. Violations of orders of time and causality are possible under the same conditions as we have seen in our examples in physics94. To make a decision, we need to gather information about all possibilities how to reach the desired outcome of that decision. The number of those possibilities is determined by the inputs of information available to the decision maker. Again, the number of such inputs is always finite, while their values can include infinities or singularities. In order to reduce the necessary inputs to the decision making process to a minimum not to violate scientific methodology95, we need to discuss first the situation of choice / no choice systems. Then we need to define dimensions of valuing criteria of making choices and see whether and how they depend on the will of the decision maker. This means in clear language, we need to see whether those choices depend on any causes and are having the observed actions as effects. We also have to check whether the alleged causes are statistical patterns of associations that are characteristic of causal organizations, patterns that can be given meaningful interpretation96 only in terms of causal directionality. Graph theory provides a formidable method to distinguish between causal and purely chance events or phenomena. In the deterministic extreme, where all variables are expressed in finest detail and the Markov condition97 certainly holds, causality prevails with a probability of almost 1, while acausal or non-deterministic phenomena appear incomplete and the Markov 93

For instance, in information theory one treats measures of uncertainties with information-entropy, joint entropy and conditional entropy (equivocation). 94 We deem it necessary here to remind the reader of the physicality of any information as same needs a carrier to exist, even if we call some information or entity “spiritual”, as we will explain later in detail. 95 This principle of scientific methodology of disposing of all redundant information that is not necessary to describe a phenomenon is called Occam’s razor. 96 The problem of meaning, sometimes also referred to as the problem of representation or the problem of content is among the central issues confronting cognitive science. Since different signs (symbols, words, sentences or mathematical expressions) can have the same meaning, the meaning of a sign cannot be properly identified with its linguistic or mathematical formulation. In the case of defined signs there exist equivalence classes of signs that have the same meaning, but that two or more signs have the same meaning does not explain what it means for any of them to have any meaning at all. Among the various theories of meaning that have been proposed, the language-of-thought hypothesis maintains that every human being has an innate mental language, where learning an ordinary language simply involves pairing up the words in that ordinary language with innate concepts in the language of thought. We will discuss this issue in relation to the kabbalistic view of the importance of letters and words in the creation process and what role they play as carriers of information in our and the “higher” realms or worlds. 97 Each variable is independent of all its non-descendants, conditional on its “parents”.

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condition will be violated. With the added condition of stability 98, events or phenomena (distributions) have unique minimal causal structure as long as there are no hidden variables. When nature decides to “hide” some variables, the observed distribution (effect, phenomenon) needs no longer be stable relative to the observable set, i.e. we are no longer guaranteed that among the minimal latent structures compatible with the observed distribution, there exists one with a directed acyclic graph structure. This does not mean that through the acyclic structure there is necessarily defined an “arrow of time” in the phenomenon that “defines” the hierarchy of causality. There exist causal structures which are caused in a non-temporal way, arising the concept of “statistical time”. Its definition is as follows: Given an empirical distribution P, a statistical time of P is any ordering of the variables that agrees with at least one minimal causal structure consistent with P. It is further conjectured that in most natural phenomena the physical time coincides with at least one statistical time. According to these definitions and our previously described gedankenexperiments on the relativity of causality it is possible to make the statistical time run opposite to the physical time, which means the variables are independent from each other conditional on their future values rather than their past values; and this can be done by a simple coordinate transformation. This suggests that the consistent agreement between physical and statistical times is a byproduct of the human choice of linguistic primitives and not a feature of physical reality. For example if X and Y stand for the positions of two interacting particles at time t, with X’t the position of their center of gravity and Y’t their relative distance, then describing the particle’s motion in the (X, Y) versus (X’, Y’) coordinate system is a matter of choice. This choice is not entirely symmetric. It prefers coordinate systems in which the forward perturbations are orthogonal to each other, rather than the corresponding backward disturbances. This preference is merely grounded on the “taste” of the describing individual which is influenced by his or her daily life experience of a forward arrow of time that is perceived in the macroscopic world despite the often camouflaged reality. This preference could represent survival pressure to “predict” future events to facilitate evolution of phenomena. Under the assumption of model minimality (and/or stability) there are patterns of statistical dependencies that can uncover causal relationships. These relationships cannot be attributed to hidden causes unless we violate one of the basic principles of scientific methodology, the semantical version of Occam’s razor. Unfortunately statistical analysis is in itself somewhat constraint in reliability. If we ask the question how reliable are programs tackling these problems, we can only answer they are as good as human perception, but without the subjectivity inherent to such perception. For example distributions with tens of variables require fewer than 5,000 samples to recover their structure including the (correct) time direction. In quantum systems like in our experiments above, where the information exchange is only one or a few bits, such statistical analysis does only make sense if the same experiment is carried out many times over to ascertain the graphs of interference and non-interference, and 98

A system is stable, if all independencies are remaining invariant to parameter changes.

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then this has to be done again over and over to ascertain the noise levels of the total measurement. Only then a causality assessment like the one described above can be done, but then we might already have reached the classical limit of that phenomenon, i.e. we pushed the demarcation (‫ )רקיע‬between observable and observer infinitely near to the observer. In such an analysis the cause (particle emission) and effect (detection) will show forward causality always, because the erasure process takes place after detection. It erased same and with that caused the restoration of the interference pattern, but that takes place definitely after emission by the source. Hence, overall causality is not violated but just “camouflaged” by the “undoing” of the first information exchange and replacing it with its complementary one. This reminds us of reversible computation, the quantum eraser and our gedankenexperiments on causality discussed above. It is believed that inferred causation can be of help to uncover hidden causalities and reversed arrows of statistical time in relation to conventional time. Physical time and its direction as well as causal relationships are vital for decision-making. In complex decision procedures including infinite procedures the minimalization procedure for the supply of sufficient inputs into the process makes the problem a finite one. The concept of reversed causal relationships can be of use in the making of choices, because in these cases “future” events are the causes of “known” events. On the other hand, our discussion above shows, how complicated decision processes are and how many uncertainties are dependent on complementary observables and they themselves are again subject to errors. In statistical or quantum systems, the “spontaneous” making of a decision to choose for instance to collapse the wavefunction or break an entanglement by objective state reduction or self-observation of the system depends on statistical and not deterministic rules. The probability distribution function for our Uranium-238 nucleus mentioned above to decay can be determined deterministically, but the time when it will do decay if alone is non-deterministic, with or without hidden variables and with or without the external interference of a willed action99. Why such statistical behavior of nature is vital for the survival of the universe may not seem obvious at first glance. Similar to the camouflaged causality relationships that are uncovered by statistical data-mining rather than deterministic continuous analytic “reasoning” a non-deterministic behavior of nature allows for example Uranium-238 nuclei not to decay all at the same time. They decay with a half-life of 109 years despite it is very unlikely that they took that long to be produced during the creation process that took for the nucleosynthesis about 3 minutes. So one can say, they all were created roughly at the same time, to decay statistically over 10 9 years. To shed light on this phenomenon and other similar ones concerning the behavior of information in general, and in particular in the form of decisions or choices to “spontaneously” break a symmetry or reduce a state or stabilize an undetermined evolutionary state of a system, it is good to recall the ubiquitous 2 nd law of thermodynamics that, in the classical limit that presented us with an asymmetry of time. Up to now we have dwelt on the extreme of complex decision making processes. Let us now explore the other end of complexity, simplicity. As it is written in Etz Chaim “in his simple and smooth will, the desire arose to create …” a most simple will should be able to be defined. “Smooth” in this case suggests to be isotropic and homogeneous for symmetry 99

This willed action is limited to the initialization of an objective state reduction which took place at the time of the formation of the nucleus by fixing the probability distribution function for its decay. This decay depends on the gravitational and other self-energies of the nucleus and is determined at the time of the emergence of the interaction laws of its nucleons, i.e. at the time of the symmetry reduction to the period of nucleo-synthesis during the creation process of the universe.

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reasons discussed above, “simple” refers to no properties, but desire seems to be out of place for an entity without properties, names, locations or time of existence, simply being defined as One. Desire here is a generalized will to make a decision about starting creation. The desire may be an urge that can be “instinctive” or purely physical. We have to consider the possibility that this desire can be a forced decision with practically no real choice. Alternatively, we can consider again a dichotomy of infinitely many choices and one choice only, similar to our point/sphere system. Taking into consideration the initial condition of One superseding absolute nothing, we can postulate but not prove the point representing that oneness. Alternatively we can assume one empty set as a starting point, which we associated with the number zero. One is according to that view defined as an empty set nested into another empty set which together represent a two-dimensional object. The one dimension of this object is the space where the number one is located. In contrast to that a singular point does not need any space to be located in, and hence, it is a zero-dimensional object, but it is countable as one object. By this countability there is already a distinction made between one and the point. The set of natural numbers at the beginning consists only of one element, but we have already the 2nd distinction made, so there are three objects countable, and with that n objects so that the whole set of \{0} is created. One point in infinity is also the only one unique object that does not need any auxiliary structure to exist, and it is a geometrical entity. As shown above, it is in the state of being unobserved identical (fluctuating) with an infinite sphere with fluctuating dimensionality between zero and infinity. The dependence of its dimensionality towards its volume has also been shown above. The meanings of its dimensions are also still “grand unified” as a fluctuating undefined state of affairs. What is now the desire to create? The decision to be made leads to the choice “to be or not to be”. As we have seen in all our previous discussions, a demarcation or ‫ רקיע‬has to be made to stabilize the undefined state into a defined one. The necessary decision needs inputs. Where do they come from if there is only one system as our undefined point/sphere system available and nothing else? – The answer is self-evidently “from this singular system itself”. What inputs are available inside this system? – The only information available is point, sphere, and dimensions100 with only potential names, infinity, one, and zero. We saw above how from these ingredients space-time inflated from a false vacuum that had been caught up in irregularities of the fluctuations of the still unnamed dimensions. We said earlier, the emergence of time, even a statistical time, is essential for any observation in the sense that communicable information can be produced. Something like time started to exist according to the Ari z”l when the spheres were filled with light, one after the other, the first manifestation of dynamics in that model. At the onset of inflation we needed a false vacuum trapping nearly all the energy of the Big Bang or at least an energy high enough to produce a universe as we observe it today. The initiator for such a false vacuum is an irregularity or instability. We can live with that as a still evolutionary process where no will and no observation are needed to come up with this effect, but what makes the inflation stop? – In the Torah we learn about the Creator saying “‫”די‬, enough, and the world stopped expanding. How did he say “‫ ”די‬in the language of Physics, and where in the process? With that He made the object of Creation finite in at least one dimension which is the running down of the energy density to the ground state of the true vacuum which is definitely finite. 100

These dimensions are still not counted or numbered, but they latently represent the natural number system in form of spheres of 0 to n dimensions nested into each other like empty sets nested into each other, as we have seen above.

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The energy densities in the false vacuum state before inflation are very high for at least one reason: the time-coordinate together with the space coordinates were squashed into a tiny space and hence, the energy uncertainty reaches very high values. This energy density could not be lowered as rapidly as it would be required. In the state of grand unification of the Standard Model of particle physics a false vacuum arises naturally. Those theories contain scalar fields like for example the Higgs field that is supposed to give mass to the matter separating from radiation later. It is typical of Higgs fields that the energy density is minimal not when the field vanishes, but instead at some non-zero value of the field. If the energy density is zero we speak of a true vacuum. It depends on the slope of the potential energy density versus the field magnitude of the scalar field, how long it takes for the energy density to be lowered. The peculiar properties of the false vacuum come from its large negative pressure. According to general relativity there is a gravitational effect that is very important: pressures like this create gravitational fields, where positive pressures create attractive fields and negative pressures repulsive fields. These are the driving forces behind inflation. A fluctuation of tiny order of magnitude then starts the inflation as described above and expands space-time by factors of the order of 1075 or more. There is no upper limit for that factor, but as soon as the false vacuum decays, the energy locked into it is released. During inflation, the energy density of space-time remains constant as does the gravitational selfenergy density that compensates for the energy increase. The total energy of the system can be very small and by the action of gravitation the conservation laws of Physics are not violated. Besides that, the flatness and the homogeneity of the universe can be explained by this theory as well as the ‫די‬, the stopping of the inflation process as we learn it in Kabbalah. The slope of the energy decay to zero energy density determines the time of ‫די‬, but that there is such stopping at all is determined by the laws of Physics which, we need to remind ourselves are not self-evident and their quantitative properties like for instance the value of the fine structure constant (1/137) are not derivable by any theory. This seems to justify the suggestion of the Torah that there is a saying of the Creator to stop the process. As we will see in the following investigation, there is a surprisingly simple way to deduce the numerical value of the fine structure constant and other fundamental constants of physics from a geometry resembling the concentric assembly of sfirot, if we assume the validity of quantum mechanics at the very onset of Creation. The mathematical model proposed strongly suggests fractal properties and zitterbewegung (leading to Brownian motion) as well as dispersion relations of Fourier and Laplace integrals (leading to mathematical uncertainty relations), ingredients of the foundations of quantum mechanics and the measurement problem with the EPR paradox. Again, as in our example of the Uranium-238 nucleus, gravitation plays the role of the initiator in stabilizing an evolutionary undefined state. Our explanations can quantify the process very nicely, but the time when such interaction leads to the stabilization, can only be determined statistically, and hence, the outcome of ‫ די‬is statistical. The same is valid for the conclusion of such processes. Gravitation is directly observed in conjunction with mass. Our scalar field, in this case the Higgs field, plays a crucial role in manifesting a material universe where in the end of the process light and matter are decoupled from each other. Gravitation, in this case in conjunction with a Higgs field, enables the space-defining inflation of a matterfilled universe that stabilizes by symmetry reductions due to cooling 101. The matter distribution changes allow time to get defined in that universe as well. It may be noted that during this phase of the universe same is completely filled with a hot soup of primordial 101

The cooling is due to expansion and “evaporation” of firstly very dense primordial matter or energy.

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matter from which by symmetry reduction all known matter, light and free space, or better vacuum, emerge. This same gravitation makes again objective state reductions and breaks the entangled undefined state of the universe. Be reminded that gravitational energy is negative. To understand the mechanism proposed by Peter Higgs on a suggestion by Philip Anderson, which gives mass to all elementary particles, we need to discuss this and other mechanisms of gravitational interaction with matter. The problem in using a spontaneous symmetry breaking model in physics is that it predicts a massless scalar particle, which is the quantum excitation along the direction of the energy minimum or true vacuum. There is no potential energy cost to move around in the minimum region, so the energy of such particle is pure kinetic energy, which implies that its mass is zero, but no massless scalar particles were ever detected. It was Peter Higgs’s insight that when one combined a gauge theory with spontaneous symmetry breaking, the two problems solve themselves very elegantly: the massless mode102 of the Higgs combines with the vector boson to form a massive vector boson. The massive scalar bosons are called Higgs bosons and still have to be found experimentally103. Before the symmetry breaking all elementary particles except the Higgs bosons themselves are massless. However, when the scalar field spontaneously slides from the maximum to the minimum energy104, elementary particles acquire mass. The origin of the masses can be interpreted as a result of the interactions of the particles with the “Higgs Ocean”. How can we understand objective state reductions as the means of the Creator to make a demarcation or ‫ רקיע‬using gravitational energy that is negative? In the Zohar we find after Parashat Trumah the Sifra Detzniuta, the book of that which is concealed. In Physics, negative energies are normally concealed for us. We now want to look at both viewpoints. Negative energy denotes a negative existence that can “swallow” positive energy or existence to annihilate it to zero105. This does obviously not happen in nature except in the case of a black hole. The negative energy rather manifests itself as an attractive field for positive masses, while negative masses cannot be observed throughout the observable universe. In Physics a black hole will only be represented by its gravitational field, its mass is not observable since it is beyond its event horizon, and it can swallow any energy coming near it and crosses this event horizon. It emits Hawking radiation and nothing else besides its gravitational field. The consequences of the above mentioned swapping of space and timelike coordinates in a black hole suggests a re-coupling of mass to the gravitational energy to be not distinguishable from each other and being located in the singularity of the black hole. In Sifra Detzniuta we read about five chapters [chambers] which are comprised in a Great Hall and fill the whole Earth. Said Rabbi Yehuda: “If they are so comprehensive, they are better than all!” – Said Rabbi Shimon: “Verily, it is so for him who enters and comes out; and it is not (‫ )לא‬for him who enters the Not (‫ )לא‬and comes out.” Rabbi Shimon Bar Yochai 102

This massless mode can also be found in the early state of the universe, when it needs gravity to expand our universe and create massive matter. 103 At the time of the writing of this treatise the ATLAS experimental setup at the LHC in Geneva nears its completion. It will finally verify or falsify the existence of the Higgs bosons. 104 This is similar to the process where the universe’s space-time slides down from the state of a false vacuum to a true vacuum, acquiring more volume. 105 Zero point energy is not zero due to the information lost in the process.

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explains now about a person who knows wheat grain but no wheat flower products. He tastes for the first time such products and comes to the conclusion that since he knows the essence of these products he ate he is the master of them. “And because of this disposition he knew as Not (‫ )לא‬the delicacies of the world, and they were lost to him. It is likewise for him who seizes the general principle of wisdom, and knows as Not (‫ )לא‬all the pleasing delicacies that derive from the general principle.” We can understand this as a valid principle also in the laws of Physics. The negative energy of gravitation is the essence of the geometry of space-time as we have seen above. In the Zohar this is allude to by the “lamp of darkness” that the Creator “carved out of the supernal luminescence”. It spurns inflation and the production of massive objects due to the geometry of the created space-time, but it does not constitute the Creator or Creation itself. It is only a derivative of the Creator or, if we want to say so, a tool of his. This is the reason that in Parashat Beshalach an assignment of a negative existence to the Creator Himself is regarded as a grave sin. The negative energy of the gravitational field only makes it possible to avoid negative mass. For example anti-particles have positive mass so that when they annihilate with corresponding particles, energy is released in form of radiation which manifests itself as other particles or light. This constitutes positive energy at all times. Sifra Detzniuta goes on to explain: “The book of that which is concealed is the book of the balancing in weight. Until Not (‫ )לא‬existed as weight, Not existed as seeing face to face, and the primordial Kings died, as their crowns were not found, and the Earth was nullified, until the Head (‫ )ראש‬desired by all desires, formed and communicated the garments of splendor. That weight arises from the place that is not Him. Those who exist as Not are weighed in ‫יה‬106. In His body exists the weight. Not unites and Not begins. In ‫ יה‬have they ascended, and in ‫ יה‬do they ascend, who Not are, and are, and will be.” The term “weight” is an allusion to the single combination of all the sfirot, while “weights” are individual sfirot. “Face to face” is the condition whereby ‫ ז"א‬is turned towards ‫א"א‬, so no creation is manifest. The Primordial Kings are the un-manifest sfirot in the worlds at the state of ‫א‬107, which are witnessing states108 of ‫א"א‬. The term “crowns” here alludes to the world of Atzilut as explained in Sefer Yetzirah 3:7, 8 and 9. We can justify the term “crown” (‫ )כתר‬as denoting Atzilut as no other states of Creation existed at the stage of the first Tzimtzum. ‫ ראש‬is here another name for the supernal sfirah of ‫כתר‬, while the “garments of splendor” denote the manifest sfirot as they emanated (Atzilut) in the second Tzimtzum. ‫ יה‬indicates the action described in the world of Beriah, where the ‫ י‬corresponds to Atzilut (emanation) and the ‫ ה‬to Beriah (creation). From this we can see that the Not, if we define it as gravitational energy which is negative, existed before mass emanated which we can define as the weight mentioned here, until the Head desired the garments of splendor as the manifest ten sfirot which are here said to be weights. These weights can also be interpreted as the naturally occurring elementar particles, if they are identified with the letters of the Hebrew alphabet which connect the sfirot in the Etz Chaim. It is said that he formed and communicated them (see Sefer Yetzirah 1:1), and it is mentioned that the weight (mass) arises from the place that is not Him. This we have to Cf. ‫ דרוש מטי ולא מטי‬,‫ספר עץ חיים‬ This refers to the state of creation where the first ‫ רקיע‬was coming into existence, but no manifestation of a physical world existed, as explained above in our treatise about the first Tzimtzum. 108 We could also say observer states. 106 107

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understand as mass arising via some symmetry breaking from the realm of the physical worlds Beriah, Yetzirah and Assiyah during their formation after the second Tzimtzum and not as some property of the Creator. The Creator being not massive reminds us again of His non-corporeality. Now we know that neither the Not as gravitational energy nor the mass itself or the combination of both have anything to do with any negative or positive existence of the Creator Himself who is still simply One without any other description of His. Negative gravitational energy emerges only during inflation, as we have seen above, and masses are positive. The understanding of the Primordial Kings as un-manifest sfirot parallels the elementary particles before the symmetry breaking while the manifest sfirot parallel the massive existence of them. The un-manifest sfirot (witnessing states) then can be understood as the observers that act on ‫ כתר‬that “decays” to let the ‫ צינור‬with the Infinite Light pass through to manifest them. This can be interpreted as a self-observation of the then existing Total Existence or as its emerging self-consciousness, represented as the ‫ ראש‬desiring to create. In Etz Chaim this is referred to as the “most simple will”, and the above question about the “desire” of such a simple system is answered by our interpretation of the selfobservation process as self-consciousness that enables the system to have a desire. This selfobservation then also stabilizes the geometry of the Total Existence, at least in the part that contains any worlds or universes. Without an at least most simple form of self-consciousness of that Total Existence It is not manifest in an observable manner, but only in an evolving state, as is the part of It we call Creation. For reducing an entangled or evolutionary state an interacting field like gravitation is enough to serve as an objective observer109. The state vector of an observer is taken to reflect the properties of a memory register or an information carrier 110 capable of storing information, and the values recorded by such storing device are somehow connected to its “subjective” experience111. So far we have defined the function of the non-manifest sfirot and in particular that of supernal ‫ כתר‬as a latent demarcation between the expelled Infinite Light and the fluctuating vacuum, where the state reduction stabilizing the Total Existence is made by the non-manifest sfirot. As soon as they become manifest being filled with light which is also the onset of a time-like coordinate, the real creation (‫ )בריאה‬following this emanation begins with ‫ חכמה‬or wisdom. On this level the differentiation between individuals or opposites does not exist 112. Hence, from this level down to Malchut, we can regard this subsystem as one unit making said objective state reduction, alluded to by “opening” the Crown for the ‫ צינור‬with the light. We can therefore say that on this level there is no ‫ רקיע‬differentiating the dimensions of all the worlds, but there is the Crown ‫ כתר‬differentiating between the outer expelled Infinite Light and the vacuum designated for the creation of the worlds. For example on the level of ‫חכמה‬ there is no differentiation of past and future or good and evil. Information-theoretically this 109

Cf. Osnaghi, S. “The entangled roots of objective knowledge”, 2006 UFBa-report, Universidade Federal da Bahia, Instituto de Física, Campus Universitario de Ondina, Salvador – BA, Brazil. 110 We will discuss this fact later as a way to explain the functionality of a “soul” as an information carrier not contradicting the laws of Nature. For now the reader shall be reminded that vacuum can be such carrier, as also shown in Etz Chaim and in the writings of the Ramchal in their discussion of the non-manifest sfirot described there as a reshimo. 111 In this case it would be the first subjective self-experience of the Total Existence. 112 Cf. for example ‫ מטי ולא מטי‬,‫ספר עץ חיים‬.

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implies the perception of a multifurcated future and a multifurcated past, which means it would constitute the perception of a network of events rather than one history. This can mathematically be constructed as a configuration space, where whole histories can be represented by a line or a point on the geodesics of that space. Experimentally this can be demonstrated by the quantum erasure experiment we have discussed above. Following that, only when a demarcation is made irreversibly in form of the production of communicable information together with the discarding of information complementary to it, any stable and manifest Creation can exist. We refer here again to the term ‫ חקק‬used in Sefer Yetzirah to describe Creation. Also here it is vital for the created objects or phenomena to exist in stability that information or “material” from the preceding evolving state of existence is discarded. Taking this into consideration, the demarcations or ‫ רקיעים‬between the sfirot definitely represent symmetry or dimensional reductions or both. On the level of ‫בינה‬113 or understanding we have the antithesis of ‫חכמה‬. There ideas are separated and all demarcations (‫ )רקיעים‬are defined. Understanding is equivalent with the name ‫ אלהים‬which denotes a plurality of forces of creation while the Tetragrammaton denotes unity of these forces. It can be understood in the way that ‫ הויה‬represents the creating forces of the Total Existence in an evolving state, while ‫ אלהים‬represents them in a reduced and manifest state. A parallel in the laws of Physics is the separation of forces in the symmetry breakings during the cooling of the universe. The paths of wisdom are only separated from the level of understanding downwards, meaning that ‫ בינה‬separates what evolved in ‫חכמה‬. Above we have spoken about the raising of the central point within the vacuum to ‫ בינה‬which represents the creation of the first ‫ רקיע‬separating all the distinct structures of the sfirot system and all that is in them in the state of reshimo. Hence, we can say that understanding is the great separator within the structure of Creation114. In Etz Chaim, the interacting partzufim of Abba and Imma are examples for creation processes involving Wisdom and Understanding. Such interaction is explained in Kabbalah by a zivug, similar to that of sexual interaction of male and female culminating in the creation of offspring. Only if ‫ חכמה‬and ‫ בינה‬are used together, a tangible information or physical object or phenomenon can be produced; meaning only with state reductions and discarding of complementary information any stable creation can be effected. In Sefer Yetzirah we several times come across the term ‫ חקק‬or engrave in the context of the creation process. Derived from this root are ‫ חוק‬and ‫חוקה‬, rule and decree. Those rules and laws serve to remove some freedom of action. Symmetry breakings and wavefunction collapses do exactly that and a parallel in Information Theory suggests itself: Creation means state reduction, where always part of the information available is discarded. ‫ מחק‬means to erase, ‫ לקח‬to remove; this reminds of the “lamp of darkness” mentioned in the Zohar that represents a negative existence or negative energy, so to speak gravitational self-energy of the system under creation, but after inflation. It is used to remove from the vacuum rather than to add. The creation of mass in the form of the Higgs process, for example, then compensates for the negative energy and the energy balance of the total system remains zero or at least very small as required for the onset of inflation. By the same token, gravity seems It has the root ‫בין‬, between. On the level of wisdom all neshamot are united while on the level of understanding the neshamot become individuals. 114 ‫ בינה = אימא‬,‫חכמה = אבא‬. 113

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‫ספר‬

‫בס"ד‬

to act as the means of the Total Existence to observe Itself115, creating things and discarding the “unwanted” like negative mass or anti-mass 116 into Rindler space where the evolution of time means always a physical displacement of the discarded away from the chosen or observed. This happens by forming a ‫ רקיע‬between the world-space and Rindler space in form of the event horizon of the speed of light in vacuo separating between the discarded and the created or between the anti-worlds and the worlds. ‫ כתר‬is referred to as ‫רצון‬, will: It is outside and above all other mental and physical processes. The impulse of Creation went downward through the sfirot, then returning to the infinite. Only then Creation could take place, which is a clear indication for inflation taking place before the Big Bang. The “three books” of Sefer Yetzirah 1:1 which are “creating” are the three divisions of creation defined as universe, year and soul or space, time and spirit (information on a carrier like the vacuum). Before Creation there is Emanation, according to Proverbs 4:7 “the beginning is the Wisdom”. Above that we have the Crown representing the evolutionary process until it became the demarcation between the Infinite Light and the created space-time which at this stage only needs to be as tiny as the Planck scale. With the introduction of the light into the vacated space with the reshimo of the sfirot system from Keter to Malchut inflation followed by the Big Bang began, creating ‫תהו ובהו‬. This defines ‫ חכמה‬as the beginning of Creation and represents the grand unification or even the Planck epoch of the Big Bang as we will discuss later in detail when we look at the Physics of the process of Creation. Now we first want to discuss information-theoretical aspects. The supernal ‫חכמה‬ serves as the first information carrier inside the vacuum containing all the sfirot created. The supernal ‫ בינה‬then orders what comes out of memory (‫ )חכמה‬which is a completely nonverbal bit-map that has to be decoded and by that verbalized117. The verbalized form of memory then gets processed by the brain (‫ בינה‬+ ‫ )מוחין = חכמה‬of the still primordial worlds which are partially stabilized into ‫ דעת‬or knowledge which can be accessed by the use of speech or writing (language including mathematics) to give qualifying, quantifying and interaction-defining information118 about the Creation to take place, this process itself being part of that Creation, but this happened only on the level of Yetzirah and some of it in Beriah. In Atzilut nothing was patterned or regularized, only emanated. That regularities of knowledge or experience reflect the structure of an underlying reality is an assumption by human prejudice, the truth rather being the ‫ דעת‬itself reflecting that structure. There is no reason to postulate a process of state reduction or decision making on this primitive level. This implies that the whole argumentation about such a process is just the way we as observers process information available to us and not a reflection of the “total reality” involved that causes our observation. The existence of a well-established network of “objective” facts is presupposed by any physical model of the measurement or system stabilization “process” itself. Another interesting fact is, the construal of the state vector is guided by the need of the observer to establish stable correlations between facts and to 115

It can observe itself or interact otherwise with itself and so be able to break entanglement or evolutionary states of existence. 116 Rindler-space we will discuss later in our chapter for suggested research. 117 This happens as the sayings of the Creator to create as written in the Torah and as the mathematical structure representing that same Creation. 118 Cf. ‫ ספר ספר וספור‬in Sefer Yetzirah 1:1.

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anticipate efficiently the outcomes of his manipulations rather than being constrained by the purpose of providing a faithful representation of a pre-structured reality; and in particular this fact gives the Creator the liberty not to pre-plan every detail of His Creation but let it evolve in permanent interaction with Him119. As we have discussed earlier, objective state reduction represents such permanent interaction with the Creator being the Total Existence. Therefore quantum entanglement and with that any evolving state of the universe ought to be understood as reflecting not the structure of a putative reality underlying the phenomena, but rather the conditions of invariance which allow reproducibility and predictability of that interaction. Such conditions of invariance can only be recognized, if the symmetries entailed by them are broken or the evolving state is reduced (separation before recognition). This separation is a necessary but not always sufficient condition for recognition 120, alluded to in the Torah by the saying “and G-d saw that it was good”. This “seeing” figuratively shows a separation of Creator and Creation. Such separation is of course not to be understood as total, because the Creator being infinite and the for us observable aspect of the created object being finite at least in dimensionality may in the non-observable aspect of such created object still be entangled with the Creator, making this aspect unobservable unless the entanglement would be broken. As an example for such unobservable part of a created object we can refer to the life force or soul of such object which cannot be directly and physically observed, except for the actions it may cause. To illustrate this, let us assume the mind is part of the soul and the information content of that mind is in an evolving state wherever it may be located. The mind is linked to the brain which is the physical carrier and processor of information. Only the information that becomes state reduced and with that communicable is observable in contrast to evolving information on that carrier. Information of that mind on any other carrier121, e.g. the vacuum as we alleged as a possibility before, is not accessible at all. The nature of such carrier may be “physical” only in the realm of dimensions different from our observable world, as alleged in for example Otzrot Chaim. Inside the realm of those dimensions the behavior of information and its carrier may well be equivalent to information on a physical carrier in our observable realm. After this attempt to link “spirituality” with “physical reality” or better to show their equivalence, we want to come back to a still not sufficiently discussed matter: what governed and governs the “decisions” and “stabilizations” in creatio ex nihilo? We want to resort again to information theory. The entanglement or evolution of quantum states, their breaking and the resulting paradoxes remind us of a much simpler example: reversible and irreversible computation. Information is physical and not an abstract entity. It is inevitably tied to physical degrees of freedom through the properties of the information carrier like charge, spin, a mark on paper etc. That ties information to the laws of Physics and ties it to the parts available in the physical universe122. Reversible computation allows symmetrical operation of computation without the loss of information or energy, if the system is a closed system. As soon as an “end-result” is desired, this information needs to be made communicable and therefore state-reduced. Then the system cannot be considered closed anymore. 119

Cf. Sefer Tanya by R’ Shneur Zalman of Liadi and other literature supporting this viewpoint of Physics. For example in ‫ מטי ולא מטי‬we can see the entangled vessels by seeing a spectrum of light, but we do not recognize the shape of the single vessels. 121 We refer here to the kabbalistic descriptions of the parts of the soul which are defined there as not residing in any part of the body (e.g. Chayah and Yechidah). 122 With that we conjecture that all Creation comprised within the supernal Crown such as Adam Kadmon and the four worlds obey the laws of Physics, and that includes our minds as well. We will discuss this in detail later. 120

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Let us now look at a possible proof of the validity of the above assertion that all information underlies the laws of Physics. In the case of non-reversible computation part or all of the initial information before computing is lost and some of it is transformed into new information. If we consider an erasure of information in a closed system like mapping a state of information from 1-space into 0-space, the conservation laws dictate that in such a conservative system phase space cannot be compressed, and hence, the reduction in information must be compensated for by an expansion into other non-informational degrees of freedom of the computing system, such as the development of heat. Such development of heat by information erasure is definitely observable and measurable as explained by Landauer123 and references therein. In reversible computation we can restore the erased state by decompressing the information bearing degree of freedom. Due to possible diffusion in the compressed (erased) state, such reversibility is limited by time, but in case of such information recovery the entropy of the system will increase in both the compression and decompression cases, which is in agreement with the 2nd law of thermodynamics. In such cases of energy-to-information conversion, and of course in the reverse cases any decisive computation process generates an increase in entropy124. To lower such entropy one has to put energy into the system. This energy dependence is in accordance with physical law. The other argument in favor of information being physical is the necessity of a carrier of information for the purpose of storing or processing. Displaying or reading of such information is always connected with a physical carrier. Concluding this argument we can state that any information-theoretically concise action requires the laws of Physics to be carried out or observed in any possible way. Hence, any observation or observing entity including its mind or soul needs to obey physical law as it is valid in the respective dimensional domain it may be located, and so any transformation, storage or creation of information needs to be defined as a physical process and not a purely abstract one. Furthermore, any physical process, being dynamic, needs the existence of at least a statistical time or a time-like coordinate in configuration space. The same is true for any process concerning information, without exception. This is to be understood as a refutation of the common interpretation of "‫ "סדר זמן‬as “no time” in Atzilut and Adam Kadmon; it has to be understood as statistical time. If we accept the above assertion that any information and its whatsoever way of processing is a physical set of events, then we need to accept that mathematical structure and objects also are manifest as such only as information and are with that physical. This, in turn, allows us to say all mathematical concepts connected with the creation process are physical entities and processes. They also underlie physical law and can be transformed into physically manifest objects as we will see in the following discussion. For example space-time as a geometrical structure may be curved and with that producing gravity, but it is itself considered a mathematical structure.

123

Landauer, R. “Irreversibility and Heat Generation in the Computing Process”, IBM J. Res. Develop. Vol. 44 No. ½ Jan./Mar. 2000. 124 Shannon, C.E. “A Mathematical Theory of Communication”, The Bell System Technical Journal, Vol. 27, pp. 379-423, 623-656, July, October, 1948, and references therein.

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Time seems to be a mental rather than physical dimension, but also here we can experimentally see its physicality: it is influenced by energy. Special and general relativity show us very nicely how physical it is. Any information exchange and any information extraction (measurement or observation) is an exchange of energy, as we have seen in the case of the discarding of information, and the exchanged energy needs to either be in a reference frame where an observer can distinguish between the states he observes or in case of simultaneity of that exchange the observer must move. In any case we need a time-like dimension to realize that. 5. Consequences of objective state reduction and information theory for the onset of creatio ex nihilo: At the onset of inflation we need at least a “seed” space-time with some energy that cannot be released. A particularly interesting scenario definitely is the creation of space and time itself from “One (absolute nothing)”. Alan Guth125 writes in the preprint of his talk: “If the universe can be eternal into the future, is it possible that it is also eternal into the past? 126 Here I will describe a recent theorem which shows, under plausible assumptions, that the answer is no.” He explains that the averaged Hubble constant will be incompleting the blue-shifted expansion into the past if greater than zero. He concludes, the universe, even after (infinitely) many cycles would need a boundary condition for the past. In plain language, it needs a beginning, a small bubble where energy cannot be released immediately for the initialization of inflation as a cause for the Big Bang. Our question now is: How can such a bubble be created and what initial conditions are sufficient to create it and only it? Let us look at our point in infinity at the beginning of Creation again. Which mechanism allows that point to grow into a small bubble as required by inflation theory as an onset of inflation? – We need: • • •

•

Space-time Energy Outside boundary (the question in Physics has to be asked: a boundary to what? – In Kabbalah this issue has been elegantly resolved by placing the Infinite Light outside that boundary) Gravitational drive of energy decay into space-time, meaning that gravitation needs to be emerging from the Planck state127.

We have:

125

MIT-CTP #3811 … herewith implying that there is no beginning of time. 127 If Einstein’s proposal of gravitation being purely an effect of the geometry of space-time is right without any constraints or additional requirements, the amount of gravitational energy should be calculable. The quantum behavior of space-time volumes of the order of magnitude of the Planck state, however, prevents us from thinking that simply. A viable theory of quantum gravity still has to be developed, so we can only suggest directions of research at this point of time. 126

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• •

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‫בס"ד‬

One (absolute nothing) represented by a point in infinity The question whether we can assume the validity of the laws of Physics at the onset of Creation or do we need to induce them? – At this point of time we can qualitatively show the validity of these laws, but quantitatively we have difficulties to explain why for instance Planck’s constant has the particular value it actually has.

We assume that the laws of Mathematics hold always, even in the absence of mathematical structure, in a very constraint manner, so that objects like a point in infinity are allowed. The initial condition is a point in infinity which represents an infinite sphere as described above. Time for a fluctuation is not needed, because the two states of the point are a dichotomy, they are equivalent and one cannot distinguish between them. We have seen that the erasure of information produces heat in a closed system. The system in question is definitely closed, because there is nothing besides it. If we erase the oneness of the point and lose the dichotomy of the infinite sphere we lose information and gain energy. This would be in accordance with the engraving process described in Sefer Yetzirah as ‫ חקק‬and its derivatives. A hint to that is given in Etz Chaim through the “simple and smooth will” that gave rise to the first Tzimtzum with the expulsion of light and its separation from the space around the middle point. How do we do such a thing in Physics? We were speaking about the fluctuations of the point/sphere system above, which includes the fluctuation of the dimensionality of that system between zero and infinity. We also learned that at radius one the surface and the volume of that sphere has a maximum at seven dimensions and tends to zero above about 20 dimensions. Let us assume the system fluctuates in its dimensionality in a way that allows noise in such fluctuation. Even at a minimal mismatch of one of the dimensions relative to the others of 10-33 cm or 10-43 seconds which are the orders of magnitude of the Planck scale minimally needed to start inflation, the inflation factor would have been about 1059, which agrees with current inflationary models128, accounts for the 1090 particles in the universe and would not violate Heisenberg’s uncertainty principle. If we take the fluctuations in the background radiation of about 10-5 into account as such noise, we could imagine the following scenario: All researchers agree that the nature of reality changes qualitatively in this domain, which would suggest a noise level of 10-48 seconds or 10-38 cm. Time and space cease to be an appropriate concept on this scale129. In a process often likened to radioactive decay, our classical universe that emerges at the Big Bang at time 10-33 s is represented as somehow springing out of timelessness or nothing. The latter we can discard as we have proved before; we have at least our point in infinity. The state of the point as a point is timeless, because the definition of time or its choice by fluctuating “asynchronously” or “noisy” to space is not made yet as is a state reduction that would stabilize the system and by “forgetting” the unneeded information or structure would supply energy to the system. The exact time that ends the fluctuation is not known. In a general grand unification including gravity and everything that ever can be created, thought of or even things we are totally unaware that they may exist, no symmetry reduction is made, it is an evolving state without an arrow of time, because in that state everything is reversible and entropy does not grow. The only physical explanation for any symmetry reduction and with that an onset of a certain dynamics can be sought in such a statistically behaving system only in its noise or some spontaneously arising 128

These models conservatively estimate the exponent of the inflation factor as about 60 to 70. These orders of magnitude are not anymore accessible experimentally, and it is doubtful, they ever will be. 129

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instability. An observable or even theoretically conjecturable cause for the system to reduce there is none. The question how long such a state existed and on what time scale it decayed is meaningless; there is no time that allows a “how long?” and there is with that no time scale for decay either. At this point and due to the poor state of our scientific knowledge about these criteria of the onset of Creation and the first state reduction we do not want to speculate, but we suggest that a point defect in a superfluid may be a good start to simulate our point in infinity, with two constraints: the system will not fluctuate dimensionally and the superfluid mimics a vacuum. Most physicists have a deeply rooted notion of causality: explanations for the present must be sought in the past. This approach will be seriously flawed if the very concept of the past is suspect. If quantum cosmology before inflation really is timeless, our notion of causality may have to be changed radically. If the Wheeler-de Witt equation is like the stationary Schrödinger equation, then the point where time is born, plays an important role, but is not the locus at which some all-decisive die of our worlds is cast. We know that our universe is not totally symmetric, we know the noise to signal ratio of the background radiation, and we know with that about the asymmetry of the configuration space starting in a point and ending in infinity. The Wheeler-de Witt equation130 now has to bed itself down onto the landscape of that configuration space. What happens in quantum theory cannot be totally unrelated to the corresponding classical theory. Sitting in the midst of things, we feel carried forward in time, an arrow that points from nothing to something. A scientific theory of the universe and the higher worlds in which structure is created as a first principle should be possible. Kabbalah suggests this very strongly as does Vaughan’s famous poem “The World”131: I saw Eternity the other night Like a great ring of endless light, All calm as it was bright; And round beneath it, Time, in hours, days, years, Driven by the spheres, Like a vast shadow moved, in which the world And all her train were hurled.

The question is: how does this structure emerge from the separation of the all-manifesting light and the point in infinity, and how do they separate? – We shall now try to conjecture an idea that might be a route of research to solve this question. Let us look first at the possibility of a noisy point with a fluctuation of the dimensions of the order of magnitude of 10-38 cm, at least for the spatial dimensions. Be reminded that the unit of length here is only a simile, since the purposes of the dimensions are not yet defined, they are completely interchangeable. Let us assume that at least one dimension’s synchrony with the others fluctuates by this value, all others fluctuate less. According to Heisenberg’s uncertainty principle, the orthogonal dimension to length or position is momentum. This dimension should then fluctuate accordingly with a phase shift of π/2. Since momentum contains time in form of a pointing vector, we can assume a momentum fluctuation propagating as a “space-wave” away from the central point or infinite sphere, outwards and inwards, respectively. This would create in the finite number of dimensions a standing wave between the center point and the infinite sphere, its wavelength depending on how many 130 131

This equation is similar to Schrödinger’s equation describing the evolving state of the universe. Note the similarity to the Kabbalistic view of the world.

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dimensions are relevant for it. The system then locks in at the Planck scale and creates a space-time of Planckian dimensions, and then the whole thing inflates, because the energy equivalent to the Planck mass is too high to be contained in such a small space as the Planck space-time. With that gravity is emerging and enables the system to inflate and then stop. A detailed proposal for a mathematical model containing a global structure that makes it possible to for example find in it the fundamental interaction constants is shown below. The presence of momentum implies the presence of energy and with that temperature, which explains the thermal state of the Big Bang. The energy density of this small space is very high, so it also should be very hot. This high energy density should be enough to form a false vacuum and initiate inflation. The separation of the point from the light could then be understood as the process of separation of space-dimension and momentum-dimension creating the wave between the limits of propagation, so that the imprint of that wave forms a reshimo in form of false vacuum in its maxima and normal vacuum in its minima. Between those space can inflate in the appropriate dimensions and contain in a similar way sub-waves (harmonics) defining subsets of sfirot. Expanding this picture to infinite radius gives exactly the kabbalistic point of view, while it would also explain the still open time-span of 10 -35 seconds after the beginning of structure to the onset of inflation 132. The Planck time of 10-43 seconds is here assumed to be the smallest possible increment of time realizable in a physical universe. Its noise value of five orders of magnitude less is supposed to hold only during the transition from mathematical structure to physical structure. How do we then explain the second Tzimtzum? – The system needed to open the demarcation between the expelled light as explained above, to become self-observant or selfconscious133. This self-conscious structure in its totality with the inner (point) and outer (supernal Crown) light and its demarcations defining the configuration space of the creation of the worlds and the central point as a stable physical system in the sense defined above, including all information on its proper carrier, and including all its history in past and future we shall call the Total Existence – our Creator who is One. If He would not comprise all His Creation and would not be one with it, the Oneness theorem of the Torah that is a positive commandment, would be gravely violated. The above reasons also explain why the Creator has no name, and all the names alluding to Him are in truth only variables denoting certain aspects of His manifestations. These should not be regarded as the objects of worship, G-d forbid, but as symbols reminding us of our paths in the worship of a nameless, dimensionless, only incompletely describable infinite being, the One Absolute Total Existence. Now let us look at the energy density and entropy of the proposed system in its form of what we want to call a Planckian bubble from the information theoretical point of view of the kabbalistic version of Creation. If we erase only one bit, namely the sphere separating the light of the ‫ כתר‬from the initial ‫י‬, the energy density will be kT ln 2 . 1032 / cm3. The entropy, on the contrary, would be extremely low, about k ln 2. From this we can deduce the minimum size of the bubble. We have to take into account that with the mathematical equivalence of 132

The onset of the Big Bang was at 10-33 seconds. Lee Smolin in his book “The Life of the Cosmos” describes a self-creating universe, likening its growth to the largely unplanned development of cities. Quantum cosmology does give almost g-d-like power to structures to bring themselves into being. 133

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the point and the sphere the stable system can be only extracted by an objective state reduction, which is divided into the two primary Tzimtzumim, by simultaneous erasure of half the ambiguous information which is minimally one single bit per dimension. The gravitational energy for n dimensions will be minimum –kT n ln 2/volume. If we assume that the fluctuating point is erased after forming the first ‫רקיע‬, leaving the infinite but limited structure of the imprinted vacuum with a center point in the middle, positive energy density needs to balance the negative energy density in the process, so the inflation of space can begin. In this conjecture we assume again the physicality of any information such as the oneness of the “absolute nothing” we begin with, meaning the point/sphere system has to be regarded as a mathematical structure representing primordial space-time in infinitely many dimensions. The constraints of volume, as we have seen above, limit the possibility of dimensionality to a finite number that can make physical sense and carry information. Then the question arises: What is the carrier of information “One”, if there is no space, no time and no other object? – The answer is inevitable: The only geometrical object fitting into no environment is a point; it is “almost nothing”, but not quite as we have seen, and it is the carrier of the information “One”, but that does not make it physical. Only its property to represent a fluctuating or evolving mathematical structure that can comprise anything allows under certain criteria to assign physicality to it. Let us try to do this. In general relativity we learned that curvature of space-time defines gravity. If now our space-time in the still evolving state is a small bubble, the curvature is very high. This would mean a center of gravity in its middle. If it fluctuates without noise and concentrically, nothing will happen, but if it fluctuates as we have explained above, this center of gravity will move inside spacetime and cause a distortion. Taking into account the conditions of gravitational state reduction as outlined above, such uncertainty in the position of the center of gravity in the system causes the Killing vector to be ill-defined and causes a decay of the system similar to our Uranium nucleus. This creates a state reduction of at least two objects within the system or one object and the system. If we argue along the lines of Chaim Vital and the Ari, this may be the expulsion of the light and the onset of time. In the last chapter we shall propose research in this direction and also specify directions for the formulation of some new theory. The equivalence of the erased point at the effective state reduction should give the minimum quantization of energy. This fraction should be fundamental, if Boltzmann’s constant is correct. There is though a problem with the definition of temperature within an evolving totally undefined system, and this might be the reason that we can have fractional quantization, but a discussion of this would go beyond the scope of this book. It remains the question whether we can freely assume the validity of the laws of Physics or do we need to induce them from the phenomenology (like the 2nd law of thermodynamics follows the inception of momentum and then matter distribution)? – This is a very difficult question, because it is not clear how many elliptical argumentations lurk there underneath the nice theoretical carpet, and where the experimental signposts stop being and leave us alone to logical evaluation of a possible and plausible scenario. Yet, there is Planck’s quantum h that we just checked whether it holds for the one point being erased. Hence, a minimum amount of energy should prevail in the system and with that a minimum amount of time. The creation of energy implies the creation of time and vice versa, due to Heisenberg’s uncertainty principle. If, due to the geometry of the system, time is squashed together with space into a point, the uncertainty of energy becomes very high. Hence, it does not matter which “caused” the other, but they emerge together and with that space, time and energy imply momentum

96

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and with that the onset of dynamics. With that all uncertainty relations in all dimensions were created, but how they were quantified still remains a mystery. We need to recall that all our observational data are maximally only half of the originally available information in the evolving system. This implies that all theoretical explanations of the most fundamental constants of nature remain subject to human guesswork, if such complementary information cannot be retrieved from observation. Following the history of the universe back in time presents us with the formidable problem that at each symmetry reduction information was lost, irretrievably. Hence, we have to use iterative methods in going forward and backward in our theory, so to speak running and returning. In case of the one point in infinity we have to do with a “one-particle” system which is unique in the history of the universe, and because of that all complementary information that may have lead to a quantification of the most fundamental constant(s) of the laws of Nature was lost forever with the first state reduction in the history of the universe. An emergence of a universe from a space-time in point-like form is unique and cannot be repeated or simulated in any experiment, because the state of “absolute nothing” is not possible to produce for the following reasons: Our universe exists and with that an absolute nothing is not producible in any way, and since we can only perform experiments inside our universe, the minimum structure possible where such an experiment could be performed is the physical vacuum. Inside our universe there is no possibility of absolute zero energy or temperature for reasons of quantization as we can see it manifested in e.g. the Casimir effect or the Aharonov-Bohm effect. This means that we would have to go outside our universe to a place without any structure which again is impossible, because such place would only exist relative to our universe within the Total Existence and with that possess coordinates within it. This makes the situation where we have a dichotomy of point and sphere unrepeatable and unique. The only possibility we have is to simulate such a scenario in a condensed matter system mimicking the behavior of our universe. How this is done, and how such a system can be mimicked, we will see later in the above mentioned attempt to show a mathematical structure that could resemble physical reality and deliver the interaction constants.

Interlude:

Can Mathematical Structure and Physical Reality be the Same Thing? – An attempt to find the fine structure constant and other fundamental constants in such a structure Abstract We try to demonstrate a simple mathematical structure’s properties as an observable physical reality or toy universe. Commencing from properties of an n-dimensional Euclidean structure we develop the motion of a point within that structure into a means to determine one or more interaction constants for this point in its geometrical environment. We discuss the implications of dimensionality and try to find a reasonable minimum amount of interpretation to let the

97

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mathematical structure resemble an observable physical reality without “plugging in” constants. Instead, we only “plug in” some elementary concepts of physics we try to keep to a minimum. We discuss in what way the mathematical structure could be conceived as a physical reality and whether it could be a physical reality without any claim of completeness. In this exercise we find the fine structure constant to be the most naturally emerging constant.

1. Introduction In 2006/7, Frank Wilczek [1, 2] stated that fundamental constants in physics, like for example interaction constants are purely numerical quantities whose values cannot be derived from first principles, meaning, they are not derivable from equations describing certain physical theories, let alone real phenomena that also are not derivable from such equations without “plugging in” natural constants. He further stated that these natural constants make up the link between equations and reality, and their values cannot be determined conceptually. Arthur Eddington [3] tried for the greater part of his later life to find a geometrical principle to describe physics on the basis of the fine structure constant’s peculiar numerical value, 1/137, to no avail. Koschmieder [4] uses lattice theory to explain the masses of the particles of the Standard Model, concluding that “only” photons, neutrinos and electric charge are needed to explain the masses of all the particles. He refers to MacGregor [5, 6, 7] who shows in three papers the dependency of the masses of the particles of the Standard Model solely on the electron mass and the fine structure constant’s numerical value in natural units. Nottale et al. [8, 9] propose a model of “scale relativity” that solves the problem of the divergence of charges or coupling constants and self-energy with the fine structure constant, α = 1/137, on the electron scale. They attempt to devise a geometrical framework in which motion laws are completed by scale laws. From these scale laws they obtain standard quantum mechanics as mechanics in a nondifferentiable space-time134. In particular, in reference [8] Nottale demonstrates a derivation of the fine structure constant by “running down” the formal QED inverse coupling from the electron scale (Compton length) to the Planck scale by using its renormalization group equation135. The numerical value achieved by this procedure is pretty close to reality. A shortcoming of this approach is it yields different values for the “bare charge” or “bare coupling”. Again, he needs to refer to experimental observation to choose the “correct” or “physical” of the three possible solutions. Furthermore, specific length scales like the Compton and the Planck length have to be “plugged in” to come up with realistic values for the coupling constants he determines. Similarly, Garrett Lisi [10] needs to choose the symmetry breaking and the action by hand to achieve an otherwise compelling proposal for a “Theory of Everything” matching the Standard Model. Other approaches to derive the numerical values of coupling constants, and in particular the fine structure constant, border on numerology or other “esoteric” approaches bearing little resemblance of physical reasoning that can be derived from observational experience underlying the construct of the mathematical structures proposed.

134

They do not arrive at a discrete space-time, but rather postulate it. Such equation needs physical insight to be “derived”. A merely mathematical reasoning without reference to phenomena or physical concepts is impossible. 135

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In our approach we try to avoid any input of numerical values for interaction or coupling constants, but resort only to some fundamental concepts of elementary physics where necessary. By allowing generalized dimensionality we include the possibility of a fractal picture of space-time that seems to be, at least tentatively, justified by phenomena such as Brownian motion and zitterbewegung, the latter of the two showing true fractional dimensionality, and by quantum theory itself that proposes the Planck length and Planck time as a smallest scale. It shall, however, become clear in the course of our treatment of the underlying mathematical structure we have assumed that such phenomena are the result of the underlying mathematical structure. The introduction of additional dimensions in Kalutza-Klein theories or string theory as well as the above mentioned approaches seems to warrant two fundamental questions: 1. Is there a fundamental connection of space geometry to at least one of the coupling constants? 2. What role plays dimensionality in the sense of Hausdorff’s extended view on dimensionality and fractional dimensionality in physical interactions? We attempt to shed light onto these questions considering some properties of spaces seen as mathematical structures containing, resembling or being such physical interactions without claiming the identity of our structures with physical reality as such. We try to keep the physical reality as simple as possible to see how much “physical law” in form of properties of the underlying structure such simplistic example can produce, and how much additional input in form of mathematical structure or its properties is needed to make our structure be a realistic “toy” universe. Max Tegmark [11] proposed in 2007 a mathematical universe hypothesis stating “Our external physical reality is a mathematical structure”, based on the assumption that “There exists an external physical reality completely independent of us humans”. He argues for the equivalence of a mathematical structure and the physical reality it describes and we observe, not merely the mathematical structure describing the physical reality. Despite his effort to encode numerically elements of language defining or describing mathematical entities or (partial) structures, at least one information theoretical problem remains: one need to agree on the encoding. We do have no proof of a “natural” encoding mechanism that would be provably inevitable by emerging from the structure itself as a “by nature preferred encoding mechanism”. We hold against the quest for an absolutely mathematical nature of physical reality that human language and its content may well be translated into mathematical symbolism or “language”, but cannot be immune against a decidedly willed, random or even illogical treatment of that physical reality by humans. Furthermore, any distinctions within the structure are arguably manmade, except they would “automatically” emerge from the structure itself. Thereby the choices made what to look for inside the structure may be also arguably man-made. Besides this caution we find it enormously interesting to try to build a mathematical structure “from scratch” that describes or resembles a physical reality. We are not insisting on what is the “ultimate scratch”, but interested whether we will be able to argue in favor of an identity of mathematical structure and physical reality.

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We will try in the following to investigate a mathematical structure resembling a physical reality using a simple example for such a reality. A central question we shall try to answer is whether and how such structure can provide us with numerically acceptable unique values for, say, conditions of minimal physical (inter-) action. The choice of our example cannot be completely arbitrary and random. Hence, we try to determine from the properties of a simple structure and first principles136 whether we can find a physical (inter-) action we can observe. In section 2 we choose as a starting structure for our example Euclidean space137 in arbitrarily many dimensions. To include fractional dimensions into our discussion we construct an n-dimensional structure with n a real number. We further allege all physical reality should look the same in any arbitrarily chosen locality of that space. By the introduction of time we introduce a structure similar to Minkowski space, but we shall use complementary spaces such as momentum space as a basic structure to arrive there. In section 3 where we also try to define what movement is and how time-like coordinates arise from it. In sections 4 to 6 we construct such complementary spaces and demonstrate some properties of “position space” and “velocity space”138, taking into consideration “acceleration space”, all in particular dependent on dimensionality. We use the conditions we found in those sections to derive a possible physical interaction in section 5. In sections 6 and 7 we attempt a discussion about the physical meaning of dimensionality and a relativity of space-volume in n dimensions and try to give an interpretation of a possible dependency of observed physical interactions on dimensionality by discussing velocity or momentum densities in different dimensions for identical movements taking “acceleration space” and “jerk space” into consideration, to finally conclude in section 8 with a discussion of our findings and try to assess how much interpretation is necessary to find the physical reality in the mathematical structure. In a brief outlook we try to suggest a program for systematically exploring avenues towards the development of a TOE based on purely geometric considerations.

2. N-dimensional Euclidean space For a (geometrical) object or its motion to be described or to take place, a certain minimum volume of space is necessary even if we follow Mach’s and Leibniz’s argumentation in favor of the non-existence of absolute space and time. Mach insisted that science must deal with genuinely observable things which made him deeply suspicious of the concepts of invisible space and time. Mach’s idea suggests that the Newtonian way of thinking about the working of a universe, which is still deep-rooted, is fundamentally wrong. The Newtonian philosophy describes objects of the universe 136

We try to limit these to the definitions of position, time, velocity, acceleration and higher time derivatives as specified in section 3. 137 NOT space-time! 138 Velocity space shall be at this stage identical with momentum space as we try not to define anything like a mass yet.

100

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contained in a space-time that exists before anything else. The Machian idea takes the power from space and time and gives it to the actual contents of that space and time which is seen as a holistic interplay of space and its contents. This means the actual structure of space and time is determined by the dynamics and spatial distribution of its contents. We will see in this treatise how such space can emerge from a very simplistic dynamics139. Depending on the nature of such dynamics, complementary spaces will play an important role in demonstrating “physicality”140. In regard to scale, we do not assume any scale but define the length of elementar movement as one and the resulting time interval also as one. We want, for the moment, not too strictly adhere to Mach’s principle but allow a spherical space in n dimensions enclosing our object or its movement. To avoid more restrictive assumptions we allow highest possible symmetry of our space which is spherical symmetry. We also choose to allow arbitrarily many dimensions n (real number), and our space shall be Euclidean. We reserve the right to further generalize as we progress building our structure. It shall be understood that space with n = 0 can contain a point, n =1 a line, n = 2 a surface and n ≥ 3 a voluminous object. For the word “volume” we want to allow besides a conventional voluminous geometrical object an area of a surface and the length of a line as a volume; only a point without any motion shall have zero volume. We will see the reasons for our choices during our construction process. We further generalize dimensionality to n  [12]. Before we embark into any reasoning about (inter-)actions, we discuss the behavior of the volume of a sphere as a function of its radius and of dimensionality without suggesting or assuming a special metric or gauge invariance we normally would use to describe physics. A spherical volume element of radius one (unit radius) is described by Hamming [13]: V ( r , n) = C n r n =

(π ⋅ r 2 ) k , with n = 2k k!

Since Γ(k + 1) = k!, n will be even for integer k. Generalizing n yields a function V(r, n) that is continuous and differentiable in respect to radius and dimensionality including fractional dimensions. With

k!= Γ ( k + 1) = Γ ( n2 + 1) we get for our spherical volume element of radius r and dimensionality n

V ( r , n) = 139 140

n 2

(π ⋅ r ) Γ ( 1+ n2 ) 2

We do not, however, adhere rigorously to Mach’s principle. Cf. sections 4 to 6.

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as its volume. For unit radius this yields a dependency of the volume from dimensionality as shown in Fig. 1a, and Fig.1b shows a plot of V(r, n). V 5 4 3 2 1 5

10

15

20

n

Figure 1a

1 0.75 0.5 r 0.25 0 8 6 V

4 2 0 0

Figure 1b

2

4

6

8

10

n

As we can see, the voluminosity of our n-dimensional sphere behaves counter-intuitively. The volume reaches a maximum for unit radius and decreases to zero for large n. Furthermore, the dimension where the maximum volume occurs increases with increasing radius. In such a space we can describe the positions of points or objects relative to each other and arrive at a description of dynamical behavior of a system of objects by looking at their velocities and positions relative to each other. We agreed above that we want to enclose such an object or system of objects by a suitable sphere representing a geometric space spanned up by the “physical” action141. We will see later that for our considerations it is sufficient to simply look at the volumes of such enclosing spheres. We remind the 141

One could argue the action of a moving point to be “mathematical” as well.

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reader about such spheres being chosen for the convenience of having highest possible symmetry. Whether they can stand the test of being or resembling a physical reality, we shall see later. 3. Motion We need to agree on the following facts as philosophically necessary to describe a space emerging from a point. Let us assume that there exists a point in no environment that we let move over a length one to create a straight line that we want to consider as the radius of our n-dimensional sphere we discussed above. Our point shall have no physical or other attributes attached to it other than that of a point resting. We further agree that we can move our point from one to another position as we decide. The familiar definitions of “position”, “velocity” and “acceleration” shall hold, but we do not want to introduce definitions like “force”, “momentum” or “energy” at this stage. Any other properties of the point like “mass” or “charge” shall also be un-defined “unknown labels”. We only allow mathematical entities to exist together with our three “physical” definitions as follows: 1. Position as a vector x = (x1, x2, … , xn); 2. Velocity shall be a vector v = dx/dt; 3. Acceleration shall be a vector a = dv/dt. The time shall be denoted by t and higher time derivatives of a shall be considered for non-uniform accelerations of our point. The concept of time has to be introduced as a comparison of the motion of our point relative to a clock-mechanism which imposes a formidable problem in so far as uncertainty is concerned. For convenience, we shall regard the time as a continuum to allow differentiability and integrability, but for a realistic picture of physical reality we would have to assume, strictly speaking, a clock with infinitely high frequency142. This said we can now investigate how we can describe the movement of our point that constructs our sphere. Thereby we do not scale any lengths except that the observed movement shall end at length of radius one and the two known positions shall be at r = 0 and r = 1 at t0 and t1 respectively. The velocity of the moving point can only be determined, if one knows at least two different positions at two separate instants of time143. John Wheeler remarked in his article “Law without Law” [14]: What we call reality consists of a few iron posts of observation between which we fill in by elaborate papier-mâché construction of imagination and theory. Thus, we have to consider two separate points in space as well as 142

We do not want to indulge in fundamental discussions about the nature of time in this paper, but we point out that any definition of time should be dependent on motion, if we accept the 2nd law of thermodynamics as the origin of the arrow of time we observe classically. 143 We can, in the simplest case have a uniform velocity or a velocity reaching the value 1 after time and space interval one, if it is considered to rest at the beginning of the movement.

103

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in time as the minimum information we can obtain to determine a velocity, and hence, our assumption made above for r and t is justifiable. If one regards a static position of a point as zero dimensional, it can be at any position relative to another point at rest in any dimensionality. If we construct a velocity space in n dimensions, both points will be resting at the origin of that space. This means according to Mach’s principle that velocity space does not exist for those static points or is represented by one point. When the one point changes position moving relative to the other at some not necessarily constant velocity, the moving point will be able to construct a “velocity-sphere” in n dimensions144. In position space such movement will be represented by a line of minimum one dimension which is a co-dimension in position nspace, because the line can be existent in many dimensions. In velocity n-space a point with uniform velocity existent in many dimensions will be represented by a point in that velocity space and have a minimum co-dimension of one in position space. This implies that any movement represented by less than one co-dimension in position space is unphysical or at least physically questionable for now. We want to restrict this implication for the moment until we have discussed the meaning of fractional dimensions in the context of movement. To effect any interaction145, a minimum volume in spatial and velocity space is necessary, allowing for acceleration (change in position and velocity) at all times. From this we can conjecture that any change in velocity or any interaction needs to take place over at least one co-dimension within the respective n-spaces for position and velocity, if there are no effects present such as zitterbewegung. Hence, any motion connected to an interaction constructs a minimum volume of position and velocity space as well. The current view of Mach’s principle in the context of general relativity that one creates a problem with handling a space-time metric, in particular concerning problems of masses relating to space-time curvatures, can be weakened by our above assertion of a minimum volume of both types of spaces being required for any interaction or being constructed by that interaction. If one further accepts the equivalence of energy density and space-time curvature and the resulting assertion that all matter can be expressed by the geometrical structure of space-time, one has to accept also that dynamics should be expressible in terms of changes of that very structure which in our case is a change in radius with time. Those changes, however, are constraint naturally by the relationship between the space “hosting” dynamics, momentum space146, and that “hosting” position, spatial space. Changes of this structure are a critical issue, whether one can assume a mathematical structure to be a physical reality. Only in Mach’s sense this would be correct. 4. Some properties of position and motion

144

Again, it is and remains the choice of the observer, how many dimensions he or she chooses to construct a spherical volume element with a radius determined by the displacement of a point in position and time. 145 For any interaction (or physics) to take place, change in motion must be allowed to observe that interaction. 146 This we simplified to velocity space as we have given no mass to our point.

104

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Let us take our point and move it from position x1 to position x2. This movement can be described as Δx = x2 - x1. In Euclidean space we can connect the two positions with a straight line, and in other types of space with a geodesic line. To define another distinction, because we consider one point moving from one position to another, we need to introduce another label or coordinate, time. In n dimensions, this can be regarded as the construction of a quotient space of position change versus velocity change, fixing the time scale by implication. If the point is considered moving continuously from one position to the other, our time coordinate can be considered continuous as can its path. Since we have not agreed on a particular scale or system of units, we want to define this movement as having length one in position space and length one on the time coordinate. We remind ourselves again of Wheeler’s remark cited above, which implies that if the point moves through positions x1 and x2 at a constant velocity, this velocity can have any value. If we, however, consider the point resting in its first position and then covering unit length in unit time, the start velocity will be zero and the velocity in the second position will be one, if the point is uniformly accelerated. The mean velocity over the distance will be ½. According to our above assertion the spheres in our n-dimensional spaces will be built by giving a radius to position and velocity spheres. If the acceleration changes on the way but remains over the unit time interval at unit value, we do not know the exact relationship between position and velocity. The velocity known between the two positions is always between zero velocity and the end velocity in the accelerated case, since the point rests in its first position and reaches the second position in unit time. If we do not know whether and how the point is accelerated, the uncertainty of velocity lies between the mean value and one, in this case it will be ½, if the position and time differences are precisely known. For |Δx| = 1 we will induce an uncertainty of |Δv| = ½, so that their product becomes ½. We will show later, how this relatively sloppy estimation of uncertainty can be more rigorously derived from purely geometrical considerations as we will see below. Above we agreed that only mathematical structure in form of Euclidean space exists in form of an n-dimensional sphere constructed by the displacement of a point representing its radius. Whether we decide to move the point to a unit sphere surface with constant velocity or accelerated from rest leaves us no choice regarding the introduction of movement, meaning, if we have only a resting point that we want to move and define its displacement as our radius, we have to start at velocity zero and produce with that an acceleration. To measure the position of a point while moving, it is not necessary to bring it to a halt. Hence, we do not worry about what happens to our spherical space in its totality after the introduction of movement but decide only to look at a spherical volume element with maximum radius one within the evolving space. We can now further argue that besides acceleration introduces a velocity to a resting point, acceleration also needs to be introduced by a “jerk” j = da/dt. This would produce the following scenario: let us assume, |j| = 1, then a(t) = ∫01j dt = 1t =1, and v(t) = t2/2 with x(t) = t3/6. Vice versa, we need a mean jerk <j> of 6 to reach length one in unit time. Now we can introduce infinitely many “introductions” of the motion in question and will end up with x(t) = tn for reaching length one. Could this be a quantum jump? – We will suggest an answer later when we know more about uncertainties, but one thing is sure:

105

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for higher order jerks we get nonlinear acceleration and with that chaotic behavior of the equation of motion that applies, and even the uncertainty relations between position and acceleration or jerk behave chaotic themselves. We will see this towards the end of the paper. At this point of our construction of a mathematical structure describing accelerated motion in n-dimensional spherically symmetric space we need to define a velocity space corresponding to our position space. We need to look at the velocity change over unit length and time once more. Let us look at two simple cases we borrow from school physics: Case 1: If the acceleration is known as one, the integral of dvdt equals ½. If Δx = 1 and Δv = ½, then their product will be half, with x = v 2/2 from Fx = max = mv2/2 for starting from zero velocity and static zero position. Hence, Δx Δv = ½. A change in position of length one in a time interval of one means a velocity over that distance of one. This is only valid, if the velocity is considered constant over the time interval in question. For an accelerated motion of our point, the velocity reaches one at the end point of the interval, so that for a = 1 = const. the mean velocity = ½. Since only two positions are known for position and velocity, there is no way in telling whether the motion is accelerated or not. Hence, the velocity can lie between the two extremes of ½ and 1, and the uncertainty of v becomes ½. Case 2: If the acceleration is introduced by a “jerk” of one in a time interval of one over unit distance, then <x> = ½ and Δv = 1. Therefore, the uncertainty of position is ½ for induced acceleration and with that Δx Δv = ½. Furthermore, an uncertainty in mathematical structure of a similar type exists also in the context of complementary n-spaces. The complementary spaces can be expressed as Fourier transforms of the spaces representing lower time derivatives than themselves, so that a position space can be transformed into a velocity (momentum) space, transforming into the time domain. We have argued above that our point moves in an n-dimensional spherical volume. This volume is a function of radius and dimensionality. According to our construct of a velocity space being the Fourier transform of our spatial volume function, we argue that for n-dimensional displacement or movement from rest there exists an n-dimensional displacement or movement in velocity space. If this is the case, we need to determine minimum conditions of both volumes for enabling such movement in n dimensions. Above we have analyzed the uncertainty relation for a movement of unit length through unit time without scaling such units. We can see, similarly to our two cases above, that there is also an uncertainty of purely mathematical nature in the relation between a mathematical structure like our Euclidean n-sphere volume and its Fourier transform. For a simple real space displacement and its transformation there is a minimum uncertainty: For

∞

∧

∫

∧

| f ( x ) | 2 dx =1 normalized, the Fourier transformation f ( p ) = f (v ) is also −∞

normalized, according to Plancherel’s theorem. The dispersion about zero is 106

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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∞

D0 ( f ) = ∫ x 2 | f ( x) | 2 dx , and −∞ ∧

D0 ( f ) D0 ( f ) ≥

1 , according to [15]. 16π 2

So we can write for space and velocity a minimum mathematical uncertainty of: ∞

∞

−∞

−∞

∧

( ∫ ∆x 2 | f ( x) | 2 dx )( ∫ ∆v 2 | f (v) | 2 dv) ≥

1 , [16]. 16π 2

This value is the general mathematical uncertainty for complementary variables which we call in physics “observables”. The numerical value for such uncertainty can be determined for any structure and its transformation. One can therefore state for complementary mathematical sub-structures that if one of them is precisely known, the other is only known in a very imprecise way or not at all. Hence, it is questionable whether the complementary structure has any reality at all [17]. Anyway, we can say if both structures are known and have reality, both structures are showing a dispersion of accuracy. For that reason we may allege a slightly blurred structure. If the precisions of both position and velocity are equal, we have a noise or “blurring” of the structure of 7.957% for both of them. A fundamental question arises, how to accommodate uncertainty in our mathematical structure and how to interpret it in physical reality. If, as alleged at the beginning, the mathematical structure not only represents physical reality but is it, the introduction of dynamics in the mathematical structure creates complementary variables (observables) and with that uncertainty arises, where the uncertainty of one sub-structure determines the uncertainty of its complementary sub-structure, and hence, is observer-dependent. If we then want to quantify such uncertainty, we can do this in two ways: 1. By introducing dispersion or probability distributions and their respective functions and their relationship to each other; 2. By examining the fractional dimensional behavior of the structure and deducing probability distribution functions from them taking behaviors such as random walk or zitterbewegung into consideration. The very impossibility to assign to each position of our moving point a velocity lies in the fact that the distance the point covers to exhibit a velocity can be regarded as unit length no matter how short this distance becomes. Even by introducing differentials we end up with uncertainties being dependent on the dispersion of the function describing position. Hence, no matter how tiny we choose our distance covered by the point in an equally tiny amount of time, the product of the dispersion integrals will always be the same, meaning, the uncertainty is self-similar regarding length and time scaling. It is well known that random walk, noise, zitterbewegung and the like are exhibiting fractional dimensions. In our further investigation of the behavior of a moving point in n-dimensional space we shall analyze an n-dimensional generalized uncertainty relation.

107

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A further consideration is the role of space as a mathematical structure. We have assigned a volume to both position and momentum or velocity space, employing the conditions of uncertainty derived from purely mathematical reasoning. We further analyze the resulting product function of p or v dependent on x or r and n147. As a minimum velocity or momentum we take ½ as the minimum velocity of our point determinable by observation. We arrive at the following results: The spherical position space volume element dependent on radius and dimensionality is determined by

(π ⋅ r 2 ) 2 , V x ( r , n) = n Γ ( 1+ 2 ) n

as we have seen above. Its Fourier transform represents the velocity or momentum space volume and is determined by

V p ( p, n) = −

2π

− 12 + n2

nπ | p −1− n | Γ (1 + n) sin( ) 2 . Γ (1 + n2 )

For Vp (p, n) we have integrated over the radius and arrive at a function of momentum and dimensionality. If we imply an uncertainty principle, we can argue that before the point moved there were neither position nor velocity or momentum space volumes available. With movement we enable at least a position volume element Vx with its complementary volume Vp. Before that both were zero, so that we can speak of Vx and Vp as ΔVx and ΔVp. If we accept our above reasoning for our two cases of uncertainty for accelerated and unaccelerated motion, we arrive at a generalized uncertainty relation 2 ΔVx ΔVp = 1. This yield

2 2π

1 −n 2

−n 2

(r ) | p − 1− n | Γ (1 + n) s in n(2π ) − 1= 0, n Γ (1 + 2 ) 2

and solving for p representing momentum or velocity results in

 π 2 −n (r 2 ) 2 csc( nπ )Γ(1 + n ) 2 3 2 2 2 (1 + n )  p ( r , n) = 2 ±  Γ(1 + n)  −n

1

147

1

 −1−n  .  

Since we have no mass defined, there shall be equivalence of p and v as well as x and r.

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If we set, as outlined above, p (r, n) = ½, and we consider an interaction constant α proportional to r2, we can obtain plots for p (√α, n)148. Our solutions will be complex, so we can plot the modulus, the real part and the imaginary part of the momentum or velocity. 5. Possible interaction for a momentum or velocity larger than ½ Plotting the momentum (velocity) versus α (in our units r = α if we consider the generalized charges as one) and n renders for the first six dimensions a rather surprising result. In Fig. 2 one can clearly see the minimum mathematical uncertainty’s square-root emerging as a minimum α around the fifth dimension. This value is not far away from the numerical value of the square-root of the fine structure constant in natural units, 1 1 3 7.0 3 5 9 9 9,1 which is the elementar electric charge in the same units. Results are summarized in Table 1.

Table 1 Dimensions 0-2

4-6

148

Codimension 1.4217 1.0875 0.24 1.1061

n for pmax

Min.

0.72 0.64 0.525 4.96

0.02685

α

0.07826

In the following all plots have to be understood that p ~ v and r ~ α .

109

Fraction of α 1 2/3 1/3 1

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

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0.02

0.04

r

0.06 0.2 p 0.1 0 0

0.08 2 n

4 6

Figure 2 A search for the value of the fine structure constant’s square-root value renders a remarkable result. For the area between four and six dimensions we have solutions for p = ½ as well as in the area between zero and two dimensions. Around five dimensions the area with positive real momentum for p ≥ ½ and the interaction resembling an electric charge, spans a little more than one co-dimension. Between zero and two dimensions we obtain the same conditions of a little more than one codimension around one dimension for ⅔ of an elementar electric charge, while ⅓ of a charge appears around ½ dimension with a co-dimension of a little less than one quarter co-dimension, as can be seen in Fig. 3.

110

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0.0265 0.03 0.027 0.04 r

0.0275 r

0.028

0.02 p 0.01

0.05

p0.1 0.05

0

0 0.25

0.4 0.6

n

0.5

0.75

1 n

1.25

1.5

Figure 3

Puzzling is the emergence of a numerical value of an elementar electric charge from the conditions given above and its nearness to the value of 1/4π around the fifth dimension, while around one dimension the numerical values of fractional charges are emerging. The co-dimensionality slightly bigger than one hints to a slightly chaotic behavior of the movement of our point that we let span up our space. The question arises why no other interaction constant emerges from our geometrical structure other than the fine structure constant. A further investigation rendered the same behavior for all odd dimensions greater than five (see Fig. 4).

0.04

0.06

p0.1 0.05

0.08

0 0 10 n

20

Figure 4

111

r

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

‫בס"ד‬

Can the other known interaction constants be derived from the fine structure constant and at what conditions we have to look at in our mathematical structure? Maybe if we look at momentum density as a measure of interaction-spaces and their minimum conditions, we can reach at least an estimate where to look for other interactions. This means also gauging the time to the same scale in all dimensions including the fractional ones. 6a. Momentum or velocity densities within a spherical n-dimensional space element We found that the numerical value of the fine structure constant can be determined from geometrical considerations only, if one makes the simple assumption of constant acceleration, but its value still emerges in a very unexpected way, at least superficially. The value does not appear as any local minimum of α (n), but at a co-dimensional range between about 4.5 to 5.5 dimensions. The exact value of Δn being slightly larger than one may suggest an overlaying minimal zitterbewegung for such (inter-) action which would be very interesting to investigate further. Additionally we want to argue that the boundary condition of pmin. = ½ over a constant acceleration within unit distance and time is a legitimate one in the sense of Wilczek’s condition of “minimum phenomenon contribution” to our structure. It is merely a logical consequence of our observability we have constrained to two instants of time. We need to remark that the deviation for pmin. at 5 dimensions from ½ is +0.01020489005 for the exact value of the fine structure constant, and the deviation of xmin. from one is -0.0728. This yields an overall error of the uncertainty at 5 dimensions of 0.16975%. This error’s contribution to the deviation of the co-dimensionality is negligible. Surprising, however, is the fine structure constant’s emergence dressed as the elementar electric charge an n-dimensional spherical space element, while all other constants do not appear. This may suggest a dominance of the fine structure constant over all other known interaction constants so that 1. either all other interaction constants are dependent on it or 2. the other interaction constants are independent from the geometry of space. In particular, the other 1/r2 –dependent constant, the gravitational constant, seems in this context not to be affected by the application of an uncertainty relation to Euclidean space at all. We therefore suggest exploring whether the induction of acceleration in form of higher derivatives of spatial motion may be related to the emergence of different interaction constants in different dimensions or whether momentum or velocity densities in different dimensions could be related to a length of motion similar to an uncertainty principle. If we assume for the latter case pmin. = ½ over unit length motion, we should be able to find a minimum interaction dependent on momentum or velocity density in different dimensionalities of our spherical space element. Since the volume changes with dimensionality and the distance in form of the radius not, we should be able to find some relationship like that.

112

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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‫ספר‬

To test our hypothesis we shall construct a momentum (velocity) density space we will relate to a length of motion. We determine the function for the volume of a momentum density space based on a Euclidean spherical volume element in n dimensions. It is 1

 π 2 −n (r 2 ) 2 csc( nπ )Γ(1 + n ) 2  −1−n 2 2 ±  . p ( r , n) = 2   Γ(1 + n)   Assuming the same conditions as above, we can set the momentum ½. We assume further the proportionality of interaction constants to powers of r such as the fine structure constant and the gravitational constant being proportional to the square of the radius. We further assume generalized charges to be one and let the point bearing that set of unit charges move from its position at rest to the surface of our n-dimensional spherical volume element. The momentum density will therefore vary between zero at the center and one at the surface of the sphere. Here it is assumed that the velocity of the point changes linearly from zero to one. Hence, p ∝ r (t ) , while r and p are complementary observables underlying the same conditions as we have established above for the finding of the fine structure constant. −n

1

3 2 (1 + n )

To determine whether the other interaction constants somehow depend on the fine structure constant we try to find the smallest volume required for an interaction that we norm to one in all dimensions. This allows determining the radius of the smallest sphere in n dimensions enabling an interaction resulting in a movement over unit length and time. A smallest sphere is in this case (n-1)-dimensional as we have discussed earlier. According to [18] the radius R of the smallest sphere in n dimensions enclosing an object with diameter one is given by R=

n , 2( n +1)

which averages over the dimensions in question to about ½ (we only try here to get a rough estimate). With p 2 2αq 2 / r = r2 r2

we can see for p = ½ that α = r5/8. This shows the dependence of the fine structure constant on five dimensions and that we need to divide our momentum volume by the real volume multiplied with its square root to norm five dimensions to the fine structure constant. If the other interaction constants really depend on the fine structure constant, at least dimensionally, we should find them by applying our generalized uncertainty relation.

113

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Let us first look at unit momentum density. We obtain from p(r, n) = ½ and dividing by the volume of a smallest sphere with radius ½ with the condition mentioned above  (π / 4) 2     Γ(1 + n2 )    n

α ( n) =

5

2

  1+ 3 1+ n  nπ   2 (1+ n )  π −0.5+n Γ(1 + n) sin   2   2  2 2   Γ(1 + n2 )   

       

−1 / n

.

A semi-logarithmic plot over the inverse radius dependent on dimensionality obtained from the above conditions is shown in Fig. 5. Here log r = log √α. log r

5

10

15

20

25

n

-5

-10

-15

-20

Figure 5

A numerical value of about 10 for the strong interaction is obtained between zero and two dimensions, around n = 1. The electromagnetic interaction follows between four and six dimensions around n = 5, followed by the numerical value for weak interaction between eight and ten dimensions around n = 9. The numerical value for the square root of the gravitational interaction related to the fine structure constant emerges around n = 21 which is the sixth dimension with purely real solutions for momentum. It appears from these results that in this structure only odd dimensions and their surroundings yield “ground state velocity” or momentum, because they have real solutions. It seems that first of all the fine structure constant is the dominating constant that exists in all dimensions as a result of the uncertainty of the complementarity of momentum and position space. Only in regard to momentum densities (Poynting vector) on a constant momentum density surface in n dimensions it seems to appear “dressed” in different strengths of interaction dependent on n. Hence, it can be that we can observe dimensions higher than 4 as “labels” like electric charge or mass on an elementar particle. The dominance of the fine structure constant suggests Lorentz invariance, so that vmax. = 1 = c. This implies for p > ½ the introduction of an additional term that could be mass and/or 114

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zitterbewegung. For now, we leave this and any relativistic implications to speculation to be investigated in a later publication.

6b. Conditions for acceleration inducing velocity and acceleration induced by a jerk In our results above we can clearly see that the interaction constants are never found in a way that they occur at integer values for n with p = ½. We alleged a superposition of zitterbewegung to explain this behavior. We find, by the same token, the numerical value of e.g. the fine structure constant in a region where the co-dimension is slightly greater than one. One could argue, why should a strictly one dimensional interaction not be possible and our point have the velocity ½ with co-dimension one at the experimental numerical value of the constant? – Zitterbewegung might be the answer, but how can we show any supporting evidence for such a possibility in our mathematical structure that is purely geometric? The geometries of velocity and position spaces give enough volume for such an effect, but we could also allow a different type of motion added instead of the zitterbewegung, e.g. some regular vibration or the like. As we will see below, this bears the difficulty that a(r, n) is not a continuous function and with that a continuous vibration is not provided with enough space. It will be a chaotic vibration. A more extensive analysis of the chaoticity of such a vibrating moving point (or string) is beyond the scope of this paper, but will be treated elsewhere. We stated above that position and velocity are complementary observables, and we therefore treat acceleration and jerk analogously as Fourier transforms of velocity and acceleration respectively. Thus we can conjecture position, velocity, and acceleration and jerk to be complementary to each other. Velocity is complementary to position, acceleration is complementary to velocity and position, and jerk is complementary to acceleration, velocity and position, so that uncertainty relations between all of their pair wise combinations can be established. To obtain expressions for the volumes of acceleration and jerk we Fourier transform Vp to Va and Va to Vj as follows:

Va = −

1 × Γ (1 + n2 )

 −1+ n2 n  nπ π | a | Γ ( − n ) Γ ( 1 + n ) sin    2 

(

)

(

)

  nπ   nπ − 2n cos  + i − 1 + (−1) − 2 n sign(a) sin  1 + (−1)   2   2

115

      

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

1

Vj =

[

× π

2Γ (1 + n2 ) − 3+ n 2

×

 nπ | j −1− n | Γ (− n)Γ (1 + n) 2 sin  2

)

(

‫בס"ד‬

‫ספר‬

)

(

(

)

  nπ   nπ −2n −2n cos sin  1 + (−1)  + i − 1 + (−1)   2   2

)

(

  nπ   nπ 2n ×  i − 1 + (−1) 2 n cos  sign( j ) + 1 + (−1) sin  2   2 

]

   

0.08

r0.082

0.084

1´10 5´10

0

Figure 6

20

a

0 1.5

1

0.5

21

n

For a qualitative discussion of the results we first present a plot of Vx Va = ½ (Figure 6), where 1/2 denotes the uncertainty. We obtain at n ≤ ⅔ (upper dimension of ⅓ of the electric charge) a large acceleration space of a ≈ 1021. For n ≥ ⅔ and a > 0 we obtain a relatively random distribution of real solution “patches” for the acceleration. We can clearly see that in the region occupied by ⅓ charge, below ½ dimensions there is no space for acceleration, while at n > ½ there is a strongly chaotic behavior of the function a(r, n), reaching acceleration values of over 1037 within unit distance.

116

   × 

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

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0.08

r 0.082

0.084

0.03 0.02 p 0.01 0 4.5

5

4.75

5.5

5.25

n

0.08

r 0.082

0.084

20000 15000 a 10000 5000 0 4.5

4.75

5

5.25

5.5

n

Figure 7

If we then look further at the conditions our acceleration minima (a = ½) show in the same dimensionality, and if we notice the “patched” allowed paths of our point having an acceleration, we see that our point needs slight dimensional changes to cover its path. These changes look random like a “dimensional percolation” rather than a straight path, and thus we can expect zitterbewegung that will for larger r cover two dimensions and resemble Brownian motion. This type of motion is suggested by the properties of the available space constructed by our moving point. The acceleration plots show a constraint to constant acceleration only between n = even + ½, while around odd dimensions the acceleration space allows (or even suggests) strong chaotic accelerations and with that zitterbewegung. In Figure 7 the overlap regions of the constant acceleration regions in a(r, n) with the regions of p ≥ ½ in p(r, n) are very small and occur very closely around the experimental numerical values of the interaction constants (error ~1.8%). In the other regions where zitterbewegung dominates, an additional velocity or momentum component needs to be added to our half momentum. It

117

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫בס"ד‬

‫ספר‬

is remarkable that the interaction constant is determined by constant acceleration and not by the minimum r ~ α of the momentum (velocity) p(r, n) ≥ ½, where the acceleration a(r, n) shows chaotic behavior. Vj shows as well chaotic behavior and is dimensionally discontinuous. A short discussion of one possible scenario referring to the initiation of acceleration by a jerk function alone or by a jerk initiated by a snap may direct to some fundamental ideas about motion and interaction. What does the geometry of the spherical n-dimensional space element tell us about interactions, minimum time intervals and minimum lengths? – An instant of time, for example, cannot be determined at a ground state with zero energy. Time would spread to infinity. According to Machian ideas time as a result of motion of points without further properties is therefore not determinable without the knowledge of two positions. If we do not know the energy and angular momentum of a Newtonian system, we need at least three instants of time to reconstruct the space-time where Newton’s laws are fulfilled. In a Machian system, however, two instants of time suffice, and the two configurations can be “best matched” to recover the information [20]. This still does not give us an absolute minimum time or space interval, but we know that Δx and Δt cannot be zero for two distinguishable configurations, and hence, space-time itself underlies uncertainty principles. The quantization itself is determined by the products of the respective complementary space-volume functions and their dispersion relations, as we have seen above. Furthermore, any interaction is also dependent on space volume functions. We will now discuss the scenario of a uniform jerk of strength 6 over unit time and what it does to our point. Therefore we determine the product volume of position and acceleration under those conditions and get 1

a ( r , n) =

πn n  Γ1 +  2 

−2 n

×

 nπ   nπ   nπ  × [ −2π n ( r 2 ) 2 cos  Γ( −n)Γ(1 + n) sin  − 2 ( −1) −2 n π n ( r 2 ) 2 cos    Γ( −n)Γ(1 + n)  2   2   2  n

n

2

2

−1

 nπ   nπ   nπ  n sin  + 2iπ n (r 2 ) 2 Γ( −n)Γ(1 + n) sin  − 2i ( −1) −2 n π n ( r 2 ) 2 Γ( −n) sin     Γ(1 + n)] 2 2 2       n

n

For the real part of a (r, n) we can plot 100 dimensions where the dimensions 1, 5, 9, … possess real solutions only. This is shown in Fig. 8. We subtracted 6 from the acceleration so that only values equal or bigger than 6 are shown in our plot. We can clearly see the region where a ≥ 6 which is necessary to transport our point over unit length in unit time will limit the smallest length for each dimension below which the acceleration will be higher than 6. Analyzing rmin.(n) we find a minimum at 40 dimensions of the order of magnitude of one. The lowest dimensions resembling unit length with 10 to 20% zitterbewegung we found to be 20 to 24 which is the region where we find the square root of the gravitational interaction constant as shown above. In our

118

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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system of units this minimum length is very close to the Planck length. The same order of magnitude acceleration that allows the transportation of the point to v = c = 1 we find in the appropriate dimensions of electroweak interaction at the Compton length scale. Below those lengths the acceleration would lead to superluminal speeds reversing the charge-parity-time product or violating Lorentz invariance. It seems to follow that for each interaction type there is a minimum length set by the limit of maximum velocity c. 1.2 1.4 r 1.6 1.8

2 1 0.75 0.5 a 0

0.25 20

40

60

80

n

0 100

Figure 8

Klinkhamer [21] argues for a fundamental length scale not necessarily equal to the Planck scale that is related to a non-vanishing vacuum energy density or cosmological constant. If there is no direct presence of matter or non-gravitational fields this fundamental length can be different from the Planck length. He further alleges that a subPlanckian space-time structure determines certain effective parameters for the physics over distances of the order of the Planck length or larger. Seiberg [22] states that gravitational interactions cause a black hole at r < lPlanck. From the calculations of section 5 we saw that from five dimensions onwards the momentum becomes larger than ½ at a length scale of the order of the electric charge’s numerical value. This lies within the Planck length as well as all the other fundamental constants’ numerical values found in section 6a. The exception is the strong interaction, but it lies well within the Compton scale and well within the region where a ≥ 6. We may speculate that we can regard the physics within the Planck length as a sort of reservoir for interactions. According to Seiberg’s statement we may regard the domains below the critical lengths found for different dimensions as a formation length for different “charges” characteristic for the fundamental interactions. If we take the black hole idea for gravitation seriously, we might as well generalize this for all other interactions and propose a scenario where length-like dimensions swap into time-like

119

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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‫בס"ד‬

dimensions. There then remains for all interactions only one spatial dimension the point can move on. This region can be described as a mirror image of negative dimensions, where we can regard the negative dimensions as time-like. Probing this, we found that in negative dimensional space the acceleration reaches an average of 6 over a time interval of about one in -21 to -25 dimensions which corresponds to 20 to 24 dimensions in positive dimensional space. The point acquires zero acceleration at t = 1. This means after such time interval we have force free movement along one spatial dimension. After this time the acceleration within these dimensions reaches values below 6 so that it can be transposed into positive space. With that happening sequentially through all relevant dimensions, the point may acquire all its properties as a particle on its way to the Compton scale. As we will see, this includes also spin. Since the induction of acceleration is jerk, we need to determine what orders of magnitude jerk are available to transport the point into n-dimensional space and which preferred interaction governs which dimension. It seems that if the jerk j = 6 (in Fig. 9 j = 0 is equivalent to j = 6) over minimum a length of one continuously, the dimensional maximum for that condition lies just below 10 dimensions, suggesting dominant electroweak and strong interactions, leaving gravitation untouched. As we can see from Fig. 9, gravity shows only a tenth of the length of a jerk present in the first ten dimensions. Additionally the strength of the jerk becomes weaker with increasing dimension. This clearly means a delay for the point to reach over the Planck length in the gravitational dimension.

0.25

0.5 r

0.75

1 1 0.75 0.5 j

5

15

10

0.25 0

20

n

Figure 9

We can interpret this further in the sense that the strong and electroweak forces thermalize long before gravity comes into the play outside the Planck length. This means the gravitational energy would remain within the Planck scale until the electromagnetic part of our point reaches the Compton scale and acquires mass as its gravitational part leaves the Planck scale. Speculating further, the not yet thermalized gravitational degrees 120

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‫בס"ד‬

‫ספר‬

of freedom remain inside a very small volume for a longer time than the degrees of freedom of the standard model forces. They cannot leave this volume element inside the Planck scale, but have to overcome a volume inflation of a factor of 4×1023 from r = 0.1 to r = 1. Since we talk about negative energy here, and this process takes about 10 20 Planck time units until the other forces reach the Compton length and gravity comes out of the region where the energy (acceleration) space is larger than necessary to accelerate our point’s gravitational degrees of freedom to c, but the jerk to do that is not strong enough to achieve this, our spatial volume around the gravitational degrees of freedom stays small (1.5) against the spatial volume around the standard model degrees of freedom (2×10240) at the Compton scale. The geometry became with that: three real dimensions with their surroundings spanning up a six dimensional spheroid wrapped into another six dimensional spheroid with hardly any volume, but a high negative energy density. This could be further interpreted as a possible cause for inflation. To test this interpretation our “one point moving” scenario to make up an n-dimensional sphere needs to be modified to an energy density model similar to existing inflationary models, but this is beyond the scope of this paper. To go further to a snap as the cause for our point to move and span up a space does not fundamentally change the above scenario very much. We think, however, it may be worthwhile to examine the issue of inflation further in a different paper. From Fig. 5 we can list the numerical values of the fundamental interaction constants in Table 2. Dimensional range Interaction Numerical value √α Purely real dimensions

0-4 strong 3.16 0
4-8 Electromag. 1/√137.036 4
8 - 12 weak 8.3×10-4 8
12 - 16 spin 1.3×10-10 12
16 - 20 spin 5×10-16 16
20 - 24 gravitation 4.18×10-23 20
Table 2

Besides the four fundamental forces we found around the dimensions 13 and 17 orders of magnitude for interactions that could resemble the Lorentz invariance violating spin dependent interaction constants predicted by Arkani-Hamed et al. [23]. Insofar as spin is concerned, we have not yet made attempts to find conditions for the induction of spin in this structure besides the numerical values as we became aware of Arkani-Hamed’s work during the compilation of this paper. We included the numerical values of his predictions, because we find it highly interesting that they appear seemingly “at the right spots”.

7. Some suggestions on the question of dimensionality

121

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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It seems disturbing that charge and its fractions appear within the realm of six dimensions at places that are anything else but straight forward integer dimensions. The fact that the smallest fraction of ⅓ appears explicitly around half a dimension and has a co-dimension of little less than about a quarter suggest that the existence of a “point charge” is questionable in any dynamic system. Since any interaction constant needs motion or dynamics to be able to be determined, by experiment or by mathematical technique, the terms “complementarity” and “uncertainty” become a key feature of both mathematical and physical reality. For the dimensionality of a moving point to be determined, we need to consider that we need one dimension to enable movement of a point which has zero dimensions as such, if at rest. The minimum value of the uncertainty between position and momentum is ½. Hence, we can conjecture that a “point particle” in the conventional picture needs to be replaced by a point-like geometrical object of a dimension between 0.4 and 0.66 dimensions. Remarkable here is the asymmetry around ½ dimensions. The exact meaning of ½ dimensions is not very clear, but may be derived from the meaning of 1.5 dimensions, as we will see. If this point would move without uncertainty in position, it would create at least a second point which creates a line between the point’s positions before and after movement. If now some noise or zitterbewegung is added to its movement due to uncertainty, the total co-dimension becomes greater than one. If the point stays in its position with uncertainty and thus exhibits dimensionality of smaller than one and greater than zero, a quarter co-dimension may be explained by its uncertainties in velocity (momentum), position (radius) and dimensionality. We have used a product of momentum difference and difference in position to determine the dimensions where the interaction radius corresponds to the experimentally determined charge. Hence, the uncertainty in position needs to correspond to an uncertainty in dimension as well. In this picture, a point’s dimensionality between zero and one dimension denotes its readiness to move at the minimum average speed of ½.149 A further interesting issue is that because of the fractional dimensions involved in our determination of minimal interaction constants, we need to consider defects in the space structure which automatically will lead to defects in the time structure. Rowlands [24] points out some very interesting aspects on continuity and divisibility of space and time. In the conventional perception time seems to be infinitely divisible. At least two arguments may be considered against such an allegation. First, there arises the very well known paradox of Zeno of Elea, and second, if we would try to infinitely divide time we would need to construct a periodic motion of infinite frequency which means infinite energy would be needed to drive such motion. Space, on the other hand, gives no rise to the allegation that it is not infinitely divisible as such, but this becomes a fundamental issue if such space contains dynamic systems or, in the Machian sense, is dynamically evolving due to the dynamics of its contents. In the definitions of velocity, acceleration, jerk or snap, time is the independent variable, and space is the dependent variable. As we have seen above, interactions are taking place where irregularities like zitterbewegung are involved and acceleration in regards to the radius of our toy universe becomes noisier the smaller our structure is. According to Seiberg’s allegation mentioned above, we swapped 149

Our calculations above rely often on mean values, because of the imposed constraints in observability. We remind the reader that we look at our length and time interval defined as one as the smallest discernable distance which is not scaled.

122

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

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space-like coordinates into time-like ones and tacitly accepted this also happening to fractional dimensions. If we accept this, we have to accept defects in time and allow fractal time. In such case it is essential to discuss the effect of defects in time on the physics that is happening around such defect. If we allow fractional dimensions for space, our situation is somehow clear and the consequences for experimental predictions are known, but if we allow a deviation from the one-dimensionality of time, those consequences are not entirely clear. If we, however, define the arrow of time or the flux of time as a consequence of the thermodynamic behavior of the distribution of matter in space, a fractal time dimension becomes thinkable. This may result in a discontinuous and heterogeneous flux of time. In Kobelev’s papers [25] the fractality of time produces preferred coordinate systems, but we think this can be remedied by leaving the overall dimension of time an integer, meaning the fractality is localized. One possible solution to this dilemma is to consider an initial jerk or snap for an input of energy, but then we consider our toy universe as open to inputs from objects of negative dimensionality which could be regarded as reservoir spaces or sinks making the observable universe a dissipative system. We have such objects in the form of black and white holes or naked singularities available in our universe. The contents of such objects may reside inside the singularities, and could be interpreted as residing in negative dimensions, if one accepts the notion that negative dimensional space is contained in a singularity. Both positive and negative dimensional spaces together may then be regarded as a conservative system with an average integer time. An interesting feature of fractal space-time is its time asymmetry that is restored to symmetry if the fractal and non-differentiable features are taken out of this picture. This speculative discussion reveals a very essential question: Is the presence of zitterbewegung a necessary requirement for time asymmetry? – If the answer is yes, this has far reaching consequences for how we need to look at the physics of our universe. Fractality and non-differentiability of time-related spaces that we represented as Fourier transforms can become a very simple explanation for time-asymmetry, uncertainty and similar features of the structure describing physics of the universe, but building such structure still requires observation and interpretation. Otherwise we have no right to assume that we see the emergence of for example the fine structure constant from the geometry of an emerging spherical n-dimensional space, and we have to assume Einstein’s relativity principles as valid. Another point that we want to put our attention to in future work is the influence of the acceleration function a (r, n) and the jerk and snap function on the behavior of strings. In particular the acceleration’s irregular surface may cause some interesting chaotic behavior when applied to strings. 8. Conclusions and outlook We have demonstrated the dependence of a purely mathematical uncertainty on dimensionality. From geometrical considerations we have arrived at numerical values for

123

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minimum space for movement and movement densities in n dimensions. We have not scaled our results to any physical size; nevertheless the results are somehow intriguing, if we scale to natural units. We have done this implicitly by scaling to one. We want to conclude with a discussion what the dimensional treatment of a moving point in n dimensions reveals and what it does not. The moving point’s velocity or momentum can only be determined by two positions in space-time. If the movement is accelerated, one does not know what exactly happens between these two positions, mathematically and experimentally. We determined an emergence of the numerical value of the fine structure constant at co-dimension ≈1.1 around 5 dimensions in our representation. This reveals that the point needs at least one dimension to move plus some dispersion of that movement. To cover around one codimension between zero and two space dimensions we need at least ⅔ of that value of the fine structure constant. Between the same dimensions momentum density considerations revealed numerical values in the range of the strong interaction at mZ [2], where fractional electrical charges occur as charges of quarks. This should be further investigated but lies beyond the scope of this paper. Furthermore we have to ask the question whether time is determinable with absolute exactness. The answer is no, because time is measured by clocks, and clocks have the intrinsic property of periodic movement to which we compare a position in space-time. Hence, space-time has to be “rough” and only differentiable in a “blurred” picture. If this is taken into account, our spherical position space element needs to have a rough surface as well which amplifies the effects observed on our allegedly smooth model. Because of the minimum momentum and uncertainty considerations, it can be alleged, a resting point fulfilling both cannot exist. Hence, we cannot speak of a zero-dimensional object, if any interaction and with that any physics is concerned, also because any interaction requires motion or at least motion-like behavior of said object as below one dimension. Quantum mechanically, we would need a ground state of zero momentum (energy) for the realization of a resting point. For p = ½ this cannot be realized, unless we expand our sphere to infinite radius in zero dimensions. What this means is not entirely clear and shall be treated elsewhere. For now, we only want to suggest some speculative ideas which might be interesting for considerations such as the growth of a mathematical structure from nothingness that could represent or even be a physical reality. Before we do that, we want to give an interpretation of dimensionality in position and velocity space. In our representation the movement at p = ½ alongside a particular dimension gets a real value only at odd dimensions while even dimensions are asymptotically approached. Between zero and two dimensions the case seems to be clear cut how to interpret what is allowed to happen to a movement of a point on a twodimensional surface, while in higher dimensions we see a certain analogy, but is it a necessary or sufficient (or both) condition to generate an electric charge by a point in moving same within e.g. 4.5 and 5.5 dimensions at a little more than p = ½? -- What our analysis does not show is how exactly this object or its movement looks like when it makes up that charge. We only know that a slight zitterbewegung is involved besides a straight and smooth movement. It also does not show us why such charge necessarily

124

G. Maimon, S. Makmel, P. Ben Avraham, ‫רקיעים‬

‫ספר‬

‫בס"ד‬

should be quantized. The only plausibility is to look for standing waves in a resonator (space?), or just take multiples of unit intervals in position space and relate them to a set of dimensions as we have done with momentum density volumes. For that set of dimensions we take the largest radius equivalent to an interaction constant minimum as a measure for our volume element and extrapolate to the other dimensions. We conclude that we found an interesting way to construct a mathematical structure around a very simple “phenomenon”, a moving point producing a unit n-sphere by its motion. By minimal input of phenomenology we succeeded to reliably find the numerical value for the fine structure constant in natural units, which also seems to be the most fundamental constant as it can be found without resorting to calculate momentum densities. Using the simple concept of position and some of its time derivatives we arrived at a (less reliable) way to determine numerical values of other interaction constants. A remarkable and somewhat surprising property of our “evolving toy universe” is the behavior of its shape when Fourier transformed into complementary spaces. By simple conceptual assumptions of limitations of observability it rendered at least the fine structure constant reliably and showed conditions for chaotic movement like zitterbewegung being included in that fine structure constant. This may lead to new ideas for the formulation of a TOE taking such simple conditions into consideration. We think we have shown a simplistic but viable example for a relatively naïve mathematical structure and minimal conceptual input, what richness lies in the structure’s (spherical space’s) transformations, if interpreted. Without such interpretation there is no way of recognizing such structure as a (simplified) physical reality, and such interpretation has to be made by an observer. So, we come back to Wheeler’s signposts and the space between them: only if all the space between them can be filled with certainty, we can say we have a mathematical universe that is determinable without an observer and his or her participation. The very scalability of r = 1 in our model and the independence of the fine structure constant from this scaling shows at least in this model no reason for a Planck or Compton scale as they appear to us in meters, seconds and other arbitrary units. The nature of time and our conclusion of the inevitable “roughness” of space-time, however fine that may be, it will be a finite value dependent on the means of the observer, forces us to assume mean values for position or for time derivatives of position. Uncertainty is mathematically ubiquitous even without quantum mechanics; it exists for complementary spaces and definitely for classical wave mechanics as well. Besides the unfinished items “beyond the scope of this paper” mentioned above we want to suggest a few things worth looking at in the context of this little model that rendered α = 1/137 so surprisingly: A paper by David Hestenes [19] tries an interpretation of quantum mechanics by zitterbewegung. Extending our little toy universe towards such an idea would be interesting. Another idea is the generalization of charges to Noether charges representing symmetries could help to understand symmetry breakings in a dimensional context. An action minimalization and such symmetry breaking could be helpful as a “conceptual” plug-in for Lisi’s TOE attempt.

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Last not least we ask whether the constraint of minimum two space-time points in the primary structure of position space to determine any complementary spaces with all its uncertainties is a must for observer participation or not. Finally, we can answer the question in the title as follows: mathematical structure and physical reality can well be the same thing, but will that structure ever be complete? – We doubt it, without observer participation in form of at least interpretation, not to speak of measurements, and encoding it into something we call “insight”, it may well be the same thing and even complete, but we will not recognize it for lack of completeness in our human way of using mathematics as a language. Some fill-ins between Wheeler’s signposts will always remain papier-mâché as long as mathematics is incomplete, at least for a TOE (this expression is also subject to a definition agreed upon by individuals by consensus – a compromise). Last not least we need to remark that all distinctions like Tegmark’s “reality independent of us humans” are man-made separations dependent solely on the man-made decision where to draw the line. In a real GUT or TOE those lines must be moveable at random, because all needs to be one, otherwise it cannot be a GUT or TOE. References: [1] [2] [3] [4] [5] [6] [7] [8] [9]

[10] [11] [12] [13] [14] [15] [16] [17]

F. Wilczek, Fundamental Constants, ArXiv: 0708.4361v1 [hep-ph] 31 Aug 2007 M. Tegmark, A. Aguirre, M. Rees, F. Wilczek, Dimensionless Constants and other Dark Matter, ArXiv: Astro-ph/0511774v3 11 Jan 2006 A.S. Eddington, Fundamental Theory, Cambridge University Press, Cambridge 1946 E.L. Koschmieder, Theory of Elementar Particles, ArXiv: 0804.4848 [physics, gen-ph] 15 May 2008 M. MacGregor, A “Muon Mass Tree” with α-quantized Lepton, Quark and Hadron Masses, ArXiv: 0607233 [gen-ph] 20 July 2006 M. MacGregor, Electron Generation of Leptons and Hadrons with Reciprocal α-quantized Lifetimes and Masses, ArXiv: 0506033 [gen-ph] 25 May 2005 M. MacGregor, The experimental lifetime α-quantization of the 36 metastable elementary particles, ArXiv: 0806.1216 [gen-ph] 1 June 2008 L. Nottale, Scale Relativity, Fractal Space Time, and Quantum Mechanics, in Chaos, Solitons and Fractals 4, 361-388, Pergamon Press 1994 L. Nottale, The Theory of Scale Relativity: Non-differentiable Geometry and Fractal Space-Time, Computing Anticipatory Systems, CASYS 03 – Sixth Int. Conf. (Liège, Belgium, 11 – 16 Aug. 2003), Daniel M. Dubois (ed.), American Institute of Physics Conference Proceedings, 718, 68 – 95 (2004) A. Garrett Lisi, An Exceptionally Simple Theory of Everything, ArXiv: 0711.0770 [hep-th] 6 Nov 2007 Max Tegmark, The Mathematical Universe, subm. to Found. Phys., ArXiv: 0704.0646v2 [gr-qc] 8 Oct 2007 F. Hausdorff, Dimension und äuβeres Maβ, Mathematische Annalen, 157 – 179, 1918 R.W. Hamming, Learning to Learn, Session 9, n-dimensional Space, Naval Postgraduate School, U.S. Navy, Feb. 2008. J.A. Wheeler, Law without Law, in J.A. Wheeler and W.H. Zurek, Quantum Theory and Measurement, Princeton University Press, Princeton, N.J. 1983, p. 182 -216 M. Pinsky, Introduction to Fourier Analysis and Wavelets, Brook/Crole 2002 E. Stein, R. Shakarchi, Fourier Analysis – an Introduction, Princeton University Press, Princeton, N.J., 2003 A. Einstein, P. Podolski, N. Rosen, Phys. Rev. 47, 777 – 780, 1935

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[18] [19] [20] [21] [22] [23] [24] [25]

‫ספר‬

‫בס"ד‬

H. Jung, Ueber die kleinste Kugel, die eine räumliche Figur einschliesst, Journal für die reine und angewandte Mathematik 123, 241 – 257, 1901 D. Hestenes, The Zitterbewegung Interpretation of Quantum Mechanics, Found. Phys. 20, No. 10, 1990, 1213 – 1232 J. Barbour, The End of Time, Weidenfeld and Nicholson, London 1999. F.R. Klinkhamer, Fundamental length scale of quantum space time foam, JETP Lett. 86, 73 (2007), ArXiv [gr-qc] 0703009v5. N. Seiberg, 23rd Solvay Conference in Physics, Dec. 2005, ArXiv [hep-th] 0601234v1, 31 Jan 2006. N. Arkani-Hamed et al., Universal dynamics of spontaneous Lorentz violation and a new spindependent inverse square law of force, ArXiv 0407034v3, 2004. P. Rowlands, A foundational approach to physics, ArXiv [physics] 0106054, 19 Jun 2001. L.Ya. Kobelev, Physical consequences of moving faster than light in empty space, ArXiv [gr-qc] 0001043v1, 15 Jan 2000. L.Ya. Kobelev, Can a particle’s velocity exceed the speed of light in empty space?, ArXiv [gr-qc] 0001042v1, 15 Jan 2000.

After this interlude we need to remind ourselves, John Wheeler asked the question in a bit different way: “Are billions upon billions of acts of observer-participancy the foundation of everything?” He also remarks: “What we call reality consists of an elaborate papier-mâché construction of imagination and theory fitted in between a few iron posts of observation.” Einstein, Tolman and Podolski proved150 there is a problem in knowing the exact past in the same way as knowing the exact future due to constraints imposed by quantum mechanics that arise from a limitation of the knowledge that can be obtained by measurement of momentum. They conclude that “the principles of quantum mechanics must involve an uncertainty in the description of past events which is analogous to the uncertainty in the prediction of future events. It is also to be noted that although it is possible to measure the momentum of a particle and follow this with a measurement of position, this will not give sufficient information for a complete reconstruction of its past path, since it has been shown that there can be no method for measuring the momentum of a particle without changing its value. Finally, it is of special interest to emphasize the remarkable conclusion that the principles of quantum mechanics would actually impose limitations on the localization in time of a macroscopic phenomenon such as the opening and closing of a shutter.” We see a general, unavoidable principle of uncertainty, relativity, incomplete information flow and ambiguosity throughout our attempts to determine a way to explain what happened right at the beginning of Creation. The initial condition of no space-time existing, the dichotomy of a point in infinity and an infinite sphere can explain the “popping into existence” of a certain amount of energy and time only if we assume as valid the laws of Physics we know back to the event of an objective state reduction before inflation and the Big Bang. This has to do directly with the indeterminism and statistical character of Nature described and proven by Einstein, Tolman and Podolski. A lot of attempts have been made to “objectivate” the process of quantum state reduction to stabilize an evolving physical system, which represents the essence of the measurement problem in Physics in general. The essence of quantum mechanics represents probabilities for the occurrence of events in a given arrangement. In order to be complete, it must also be able to represent the individual events themselves. Therefore it should be supplemented with a judicious and comprehensive 150

Einstein, A., Tolman, R.C., Podolski, B., “Knowledge of past and future in quantum mechanics”, Phys. Rev., 37, 780-81 (1931).

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definition of measurement or state reduction which allows one to express objectivity. This first of all needs a definition of objectivity as such. Objectivity should be expressed as independent verifiability in concrete physical terms. The basic postulate defining an event and guaranteeing its objectivity is that it can be observed or read in at least two independent, mutually non-interfering ways with necessarily agreeing results151. In case of our one point of origin problem at the onset of creatio ex nihilo this objectivity is simply not given as we will see now. The first Tzimtzum are not really objective in this sense. We shall further see that this objectivity does not exist for any one particle experiment. Objectivity is the opposite of subjectivity which is the way any individual sees an event happening. Subjectivity is the default state of any observation because of the principle of relativity, as we have seen above. Any observer will have his own reference system and with that his own world line within the event horizon he is in, and that precludes any observation of any event from being strictly objective in the sense of the definition given for objectivity. For one-particle experiments such objectivity is fundamentally unattainable for the reason of each and any observation in the sense of the quantum mechanical definition that such observation is only complete if communicable information is produced. Any of the quantum erasure experiments show that if and only if such communicable information is erased, complementary information can be recovered with the constraint that such recovery is never simultaneous with the registration of the original event. Hence, both observations have always different space-time coordinates. On grounds of this argumentation we can conjecture that objectivity is in all cases constraint by an uncertainty dictated by the necessity for at least two non-interfering and un-entangled bits to be produced for a measurement to be objective. These two bits can never have the same space-time coordinates as two points can never have completely identical coordinates in any space whatsoever without being one point all together. The distance of these two bits in space-time determines the uncertainty of the objectivity achieved. In plain language this means, since we constructed the definition of objectivity by the necessity of two independent subjective observations of the “same” event, objectivity always is incomplete and never absolute. We can understand this in the same way as a measurement always has an error and with that is subjective in regard to its private world coordinates, any objectivity can only be understood as a reduction of the uncertainty of such world coordinates by a second measurement by which at least a second communicable registration of the same event takes place. This is, however, not realizable for one-particle experiments such as quantum erasure and the similar. One and the same event can only be measured twice if once erased, and hence, it is not the same event anymore. At least one space-time coordinate-value of the second registration needs to differ by at least an infinitesimally small amount from the first. In any physical system the recognition of such a difference is dependent on the resolution of the measurement device. Likewise in a mathematical model of the system this one coordinate-value needs to differ by at least an infinitesimally small amount δ which inter alia determines the uncertainty of the objectivity.

151

Simonius, M., “Measurement in Quantum Mechanics: From Probabilities to Objective Events”, Helvetica Physica Acta 66 (1993) 721, and references therein.

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‫ספר‬

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Let us now look a bit more carefully at our infinite sphere which in two dimensions is represented by a circle with infinite radius. Consider two antipodal points on a circle with finite radius. Two lines extending outward from any point on such circle meet in its respective antipodal point. If we extend the radius of the circle to infinity, the lines extending from such a point approach a straight line as the curvature of the circle approaches zero. In the limit of infinity of the radius the lines through the antipodal points become parallel, but still they meet in the respective other antipodal point in infinity. Hence, we can conjecture that the point in infinity is equivalent to an infinite circle or sphere and to two parallel lines or planes infinitely far apart from each other. Now consider a radius-line of a finite circle extending from its center point to one of the antipodal points and a second line extending from its center point at an angle φ to the radius and let us construct a tangent of the circle through that antipodal point. The radius intersects the circle and the tangent in the same point while the line at an angle φ to that radius intersects the circle and the tangent in two different points, and the latter at an angle θ. The distance between these two points tends to zero in the limit of infinity of the radius, while the angles θ and φ remain constant. It is obvious that a reconstruction of the center point from two neighboring points of the circular curve by intersecting two lines intersecting the curve rectangularly will yield that center point in case of a finite and in case of an infinite radius. If we, however, try to reconstruct the center point of the infinite circle by using the tangent and the angle θ, we will, despite of the distance of the two intersecting points tending to zero, arrive at a contradiction. This represents the indeterminacy of the locus of the neighboring point, pushing it infinitely far from the tangential point of the curve rendering the distance of the circular curve from the tangent as infinitely large. We can conclude that in the limit of infinity it is uncertain whether objects are curved or straight and, despite the knowledge of a certain large surface area, it is uncertain where the center point can be found. We can say, in this limit the center point becomes disjoint into infinity from the surface of the object and from the point in infinity. The very nature of information, being physical, and mathematics being a language expressing such information and its processing and even its creation, transmission and reading, demands also for mathematical structure and objects uncertainty. This uncertainty arises, as we have seen, from limit operations and as soon as infinities are involved in any argumentation. Hence, indeterminism and paradoxical situations in any theories or descriptions are ubiquitous, as is incompleteness. The locus of the center point in our universe is indeterminable in space and in time. As we have discussed above, our space-time is a four dimensional space lying on a spherical surface, which is represented by the de Sitter space-time. It is a Lorentzian four-sphere of imaginary radius, giving intrinsic metric signature (+, -, -, -) in Minkowski five-space. If we suppress two spatial dimensions, we arrive at a hyperboloid with an of course disjoint singular center point which was the origin of all. Kabbalah agrees to this in Sefer Yetzirah 1:7: ‫עשר ספירות בלי מה נעוץ סופן בתחלתן בסופן כשלהבת קשורה בגחלת שאדון יחיד ואין‬ ‫לו שני ולפני אחד מה אתה סופר‬:

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‫בס"ד‬

Ten sfirot of nothingness, their end is embedded in their beginning and their beginning in their end, like a flame in a burning coal, for the master is singular, he has no second, and before One, what do you count? The singular (‫ )יחיד‬master is after stabilization of His Creation disjoint from all the spaces populated by the worlds and the sfirot. Since G-d is absolutely One, he can also not be called the Cause, as this would imply an effect as a “second”. Hence, we have to regard also the Cause as a creation of the Holy One Blessed be He ((‫קדוש ברוך הוא‬, and this creation needs to be acausal, simply because before the concept of cause is created as a byproduct of time, there is no cause for the cause, it just emerges as time emerges at the onset of dynamics. In His unlimited sense, infinite dimensionally and with the highest possible symmetry as expressed in the language of Mathematics, He needs neither space nor time; in His projected sense onto the Worlds and with the Infinite Light He encompasses all152. The construction of the ‫ צינור‬is also clear now. It is according to the above analysis of our mathematical structure resembled by the reciprocal space of the space spanned up by our concentric spheres, namely momentum space. If we represent such reciprocal space geometrically correct, it will have in three dimensions the form of a Mexican hat open at its top. Principally, Etz Chaim and other kabbalistic literature describe the space where movement and dynamics are described as the ‫צינור‬, while the sfirot are the spaces of static locations. The center point which becomes disjoint from the sphere system describes by its movement during the fluctuation of the outermost sphere a straight line into the reshimo system of the spheres as described by the Ari z”l. The uncertainty and the properties of the reciprocal space or momentum space described above give it a thickness. According to the Zohar, Etz Chaim and Sefer HaBahir the Infinite Light does not exist between the innermost sfirah and the center point as well as the ‫ רקיעים‬between the sfirot do not contain it. The allusion of the light being set aside, as we have discussed at the beginning of this treatise, suggests the separation from the Creator rather than a creation of light. The same is true for the ‫ רקיע‬or “firmament/demarcation”. This can also be construed by the fact that the Torah, ‫'בראשית א‬, does only mention ‫ ויהי‬for “let there be” and ‫ ויבדל‬or ‫ מבדיל‬for “separate” or “distinguish/demarcate” and not ‫ ויעש‬for “made” like for all that was put into action actually after the creation process. This shows that the (upper and lower) waters as well as light and darkness or land and sea did not have to be put into action, just distinguished. They existed before days could be measured by any spiritual or physical being other than the Creator Himself. The treatment of space and time as well as of any information inside other dimensions than physical space and time and their categorization through observational and registrational activity, and their processing through the mind or other means always obey the laws of Nature which were created and set into place by the Creator, no matter whether they are known or unbeknown to us. We learned before that all dimensions, with a few exceptions, defined by opposites are infinite and their limit has no end. An exception to this is time which has a beginning and another one is mass which can only be positive, they have no opposites. Both constitute half-dimensions according to the definition of dimension that 152

Please note the two aspects of the Creator which always will remain a dichotomy of His existence in an ever evolving state, because the Total Existence is and will always be a closed system without anything besides it.

130

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follows. Opposites can be appropriately visualized by an infinite line connecting these. Immediately there comes up the question about the demarcation or ‫ רקיע‬of for example light and darkness or good and evil, and how can be determined where on that line the demarcation intersects. Since this line is infinitely long so that its end points are in infinity, the middle is dependent on the observer. Again, as in quantum mechanics, the existence of the demarcation is important, not its exact position. There is no absolute position on an infinitely long line without origin; otherwise it would be a half-line. Hence, we can conjecture the position of the demarcation is decided upon by the entity which makes the demarcation. Depending on dimensionality of such a demarcation and on the appropriate uncertainty to be determined by that same entity it also has a width. Sifra Detzniuta 1:5 states: “The will of all wills that is revealed with the prayers of those below.” This will of all wills corresponds to the forehead of Adam Kadmon downwards through that of Arich and Zeir Anpin to the actual partzufim of all Jews descending from Jacob, Rachel and Leah, depending on the level of decision making and on the world(s) involved. In such a way the will revealed by prayers of those below becomes physically understandable as making demarcations on dimensions involved in those prayers. Conceptually this is also true for decisions made on halachot made by those below on the given 613 mitzvoth and their dimensions, which is the reason why the Creator gave the power to make those decisions to the Earthly Court. This we will discuss in detail later when we analyze such decision making by an example from the Gemara. One of the most important consequences of the above discussion about creatio ex nihilo is that such creation is effected and only becoming possible by the removal of idealizations of pure geometry or of parts of freedom of action by symmetry and state reductions rather than by adding something to the structure at the onset of Creation. As we have seen above, such uncertainties are given together with the fractal dimensional behavior of dynamic processes in position space and its complementary spaces. Energy production is achieved by taking away information or structure, precisely according to the specification of such taking away by Sefer Yetzirah: The action of ‫ חקק‬constitutes a top-down construction from the infinite. To illustrate this proposal of Kabbalah we can conjecture the following: In the always evolving state of the Infinite Total Existence there exists latently all ever possible information, structures, and thoughts and, in short, absolutely everything. Through state reductions of parts of this everything and the discarding of information that results in its transformation into energy or “light” these parts of the formerly evolving “everything” become manifest and stabilized observable entities. This approach supports the attribute of the Creator as “Almig-ty” and is supported by Etz Chaim as we have discussed above. The obvious question should arise now after we advocated the principle of taking away or reduction rather than using the magic hat-trick of creatio ex nihilo, where does anything come from, if we have nothing at the beginning? – Answer: It is coming from the dichotomy of absolutely nothing and One, with One being All. We can argue like this, because in the same way as we conjectured the fluctuation of the point into an n-dimensional sphere system, we can conjecture that these fluctuations may contain anything that might ever be created in an evolving state waiting for state reductions and symmetry breakings as the tool for manifestations of Creation.

131

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6. Information and quantum theoretical treatment of the question of consciousness or self-consciousness of systems: Up to now we have seen in our analysis of Creation, at least in the scientific argumentation that uncertainty and incompleteness are unavoidable in such a creation process. We want to further argue that such an uncertain, statistical and relativistic system is to be preferred to a rigid deterministic system of infinite precision. The best example to explain this is the processing and storage of information in computer science. There we use statistics for the recovery of data and to stabilize computer systems and, of course, quantum computer systems. The statistical nature of data systems such as computers and the human brain justify to approach the functionality of a thinking process in such brain or if we want to talk about consciousness the functionality of same with quantum theory. It is widely accepted that consciousness or mental activity is in some way correlated to the behavior of the material brain. Since Quantum Theory is the most fundamental theory of matter that is currently available, it is legitimate to ask whether Quantum Theory and with that also Information Theory could help us to understand consciousness. May the reader be reminded that information being physical needs a carrier and that such carrier can be space. To be communicable, such information needs to be imprinted on a carrier that is readable by the entity it is destined for. Evolving information is not accessible or observable. The original motivation in the early 20th century for relating quantum theory to consciousness was essentially philosophical. It is fairly plausible that conscious free decisions or Free Will are problematic in a perfectly deterministic world, so quantum randomness might indeed open up novel possibilities to explain free will. On the other hand, however, randomness is problematic for volition. Quantum theory introduced an element of randomness standing out against the previous deterministic worldview, in which randomness, if it occurred at all, simply indicated our ignorance of a more detailed description as for example in statistical physics. In sharp contrast to such epistemic randomness, quantum randomness in processes such as spontaneous emission of light, radioactive decay, or other examples of state reduction is considered a fundamental feature of nature, independent of our ignorance or knowledge. To be precise, this feature refers to individual quantum events, whereas the behavior of ensembles of such events is statistically determined, so that the indeterminism of individual quantum events is constrained by statistical laws. As we have seen above, this is connected with the placement of the ‫ רקיע‬between the states expected to measure. Individual events have a chance to happen or not while large numbers of events underlie the rules of classical statistics, and hence the ‫ רקיע‬shifts into infinity away from the events desired to measure. Other features of quantum theory which were found attractive in discussing issues of consciousness were the concepts of complementarity and entanglement. Pioneers of quantum physics such as Planck, Bohr, Schrödinger, Pauli and others emphasized the various possible roles of quantum theory in reconsidering the old conflict between physical determinism and conscious free will. Variants of the dichotomy between mind and matter range from their fundamental distinction at a primordial level of description to the emergence of conscious mind from the brain as an extremely sophisticated and highly developed material system. One important aspect of all discussions about the relation between mind and matter is the distinction between descriptive and explanatory approaches. Correlation is a descriptive term with empirical relevance, while causation is an explanatory term associated with theoretical attempts to understand

132

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‫ספר‬

‫בס"ד‬

correlations. This we have seen extensively in our discussion of causality and statistical causality. For example in statistical causality the correlations of two systems can result from a common cause in their history rather than from a direct causal interaction. An example for this is quantum entanglement, where the entanglement stems from let us say a common source of the particles. In physical systems causal relations typically represent interactions. For the mind-matter problem, the situation seems to be more difficult, because space-time itself or the vacuum can be carriers of information153 so that it seems to us as if there is a difference between mental and physical processes. In our opinion, the physicality of information only concerns its existence, processing and rendering as such, and not the information content at all154. That is rather to be described by mathematical means, bearing in mind that mathematics itself is a language and information is normally processed by mathematical operations. This has to take place on a physical carrier, but the main question is how the information processing is organized in a brain as a processing physical carrier. As an analog for that the principle of a computer with all its limitations and despite its different architecture might be a good start to understand the difference between information content and its carrier or processing system. A computer can contain information as its carrier but has next to no influence on the content of such information, content denoting what the information in question may mean for the computer user. Such information content is independent of the carrier while its processing is dependent on it. The content is fed into the system from outside or, in some very limited cases may be programmed into the architecture of the carrier. In case of e.g. a human being most of the information content in the brain is acquired from outside through the sensory system, while all information content governing the body and its organs is genetically encoded. How far acquired information becomes genetically encoded including all mechanisms necessary therefore is only sparsely known at the time of the writing of this book. Adaptation of organisms to the environment for example and the possibility of encoding such mechanisms leading to such adaptations into the genetic make-up of biological entities are today very sparsely researched. In the genetic code of an animal or a plant many sequences are “white spots on the map” or called garbage code. This does not mean they have no function. Their function is simply not known to us for the moment, but surely further research will reveal the purpose of such code. For that reason research into this direction should not be subject to ideologically colored dismissals and political arguments. Evolution and adaptive behavior of organisms are far too little researched for either advocacy or dismissal in our quest to theoretize about the development of life. Its Physics and the Physics of consciousness is far too little known to embark into such battles. The existing knowledge in the field of consciousness consists primarily of empirical correlations between material and mental states. These correlations are descriptive, not explanatory as they are not causally conditioned. So far it is only known that certain parts of the brain are activated during particular mental activities, but an explanation why certain areas of the brain are correlated with certain mental activities is far from mature at the time of writing this treatise. The main problem still is to define a mental state in rigorous terms, such as material states are defined. Hence, the definition of what is consciousness precisely is not clear at all. Psychology and neurophysiology have no clear and rigorous definitions of these terms, as one can see for example with the definition of a mental state. The day to day 153

The physical vacuum contains structure as can be seen from the Casimir effect which will be discussed later. The information carried by the vacuum is of quantum nature. 154 The question is, who imprints such information content on a brain and how is it done?

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definition ranges from “mentally unstable” to “mentally stable”, meaning the mental activity of the former is distorted while the latter is not. This refers to social behavior patterns rather than states of the brain related to a certain activity. Compared to a physical state of a particle or an informational state of a bit which is described by either some quantum numbers or simply by zero or one, a mental state rather refers to a mostly complicated bit-map of information. In our previous discussion we tried to define a most primitive state of selfconsciousness by inferring a will or “intentional consciousness”. To understand will or intentional consciousness we need to define and explain “will” and “intention”. An intention is a thought pre-mediating an action, for example making a choice and carrying it out. This pre-mediating thought, be it rational or irrational, underlies an at least partially algorithmic process initiating a decision as explained above, when we spoke about decision making. In a reductionist approach a neural network can be regarded as having an intention to for example find an event or a pattern of events after it was taught to recognize such an event or pattern. This can be achieved by a pure software application using a computer as a carrier of information. It can be said, the neural network, if activated, intends to find the learned pattern, but can it be deemed conscious of that pattern? – We think within the limitations yes, if it is switched on it is conscious of the pattern and may recognize it, if it is switched off it is unconscious in the sense of our definition here. A living organism may be conscious of food, but if unconscious, it will not recognize the food. In our search for a most primitive sort of consciousness we have to accept such a definition which is supported by the fact that a particle detector system that produces communicable information to effect a state reduction permanently is rudimentarily conscious but not self-conscious. The second definition needed is that of “will”. Will is connected with desire, and hence, our neural network could be deemed willing to find the pattern it is programmed to find. One could now argue that will and intention do not apply to pre-programmed machines, however intelligent155 they are. On the other hand, we tried to explain the mechanism of the onset of creation with its first state reduction involving the discarding of information and transforming it into energy by the “simple and smooth will” of the Creator as described in Etz Chaim. According to Kabbalah and Physics, there exists an extreme reductionist definition of will: the forgetting of at least one bit of information to create energy and time. It is remarkable that in Kabbalah this will (‫ )רצון‬is not described as an intention (‫)כוונה‬, which is fully in accordance with modern science. To shed a little bit more light onto the conundrum of consciousness or, if one likes to call it the physics of consciousness, let us go back to information, causality and time, having quantum theory and relativity in mind. Quantum information is deemed to be able to travel forward and backward in time, which is surprisingly helpful for us to see what the implications of a particular quantum entanglement are that are otherwise not so obvious. The reverse time channel of a quantum information link presents the quantum amplitudes as complex conjugates of the forward in time channel’s amplitudes. In decision making we have seen that the cause of a choice may be an event in the future, an anticipated event, the probability of which to occur in reality is sought to be influenced by the maker of the choice. In our mind, the signal from the anticipated event travels back to the present and lets us make a decision for a choice of action. In Physics, we 155

Intelligence here is regarded as defined above as a measure for the ability to learn.

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can suppose that an EPR pair of spin ½ particles is created from a spin 0 source. In the production of the particle pair we allow the rotation of the spin of one of the particles by a magnetic field with the result that the other particle will have opposite spin without having been in a magnetic field, if the particles are entangled. Any process that produces an EPR entangled pair has the past-propagating quantum information in one channel reflected back into the future to become the future-propagating quantum information in the other channel. There is no difference whether one regards the one or the other channel as past-propagating or future-propagating; they are fully interchangeable. Such time reversal requires the complex conjugation of the amplitudes and hence, there is an orientation reversal between the Riemann spheres of the respective entangled particles. For photons produced in parametric down-conversion it is also not possible to extract two entangled photons with the same polarization, but only opposite polarization. Another feature of entanglement is that according to the standard quantum mechanical procedures of unitary evolution, entanglements will have a tendency to spread throughout the universe so that one can hardly find any un-entangled states. This is practically not the case, as we can see in various experiments where we can regard the quantum states as un-entangled. State reduction is the only mechanism capable of cutting through an entanglement, either by observation or by another “objective state reduction” as proposed above for our Uranium nucleus, where we considered the gravitational self-energy of the evolutionary system doing the cutting. The space-time curvature at the locus of an entangled or evolutionary state is unstable and a superposition of the resulting states after the cutting. This instability ill-defines the Killing vector ∂/∂t which leads to the collapse of the wavefunction in a time-frame dictated by the curvatures in question. The Schrödinger operator ∂/∂t in such a situation corresponds to the action of the Killing vector representing the time displacement of stationarity of the spacetimes associated with the respective states making up the superposed or entangled state. The Killing vectors for these respective states are always different from each other as they represent time symmetries of different space-times, because of the principle of general covariance of the principle of relativity. The deviation of the Killing vectors of the respective states making up the superposed, evolutionary or entangled state means an uncertainty in the identification of the respective Schrödinger operators which corresponds to the gravitational self-energy of the difference between the mass distributions of the states making up the superposed state. This self-energy determines the statistical mean of the decay time of the superposition or entanglement. If, for a single point-particle, one would define the states as position states, the gravitational self-energy uncertainty would reach infinity. This is valid only if the point particle is idealized as a mathematical point that is infinitely small. As soon as we allow some small size due to noise, this uncertainty acquires a large but finite value. In view of objective state reduction and entanglement as well as proposed extra dimensions of the Kalutza-Klein type the question arises whether such reduction can be interpreted as a production of communicable information which would mean the discarding of some of the information available in non-communicable form in the superposed or fluctuating state. The non-communicability of pure quantum information related to superposed or entangled states would explain its non-constrainedness by the usual spatio-temporal causality of relativity. It cannot be used to transmit information directly, but it can be used together with a classical signal to achieve effects beyond the capabilities of classical signaling. The basic concept of quantum information or its processing, quantum computation, is that classical information in form of bit states of 0 or 1 could be quantum superpositions of both 0 and 1, known as qubits. Such qubits interact in the computing process by non-local entanglement (instantaneously),

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eventually being observed and reducing into definite states as the solution. The advantage of quantum information is, it can be teleported and its computation can be done highly parallel and densely coded because of the vastness of the Hilbert space of quantum states which is exponentially larger than the classical space. By disentangling the states and with that reducing them into classical states, the information becomes communicable and half of the evolutionary information is discarded. In spontaneous objective state reduction terms this means, half of singly carried out computations are yielding an incorrect or no useful output. Only if the process is repeatedly done or in a parallel mode, the outcome of the computation can be statistically tuned to an almost surely correct output. Some research suggests that the brain requires quantum computing for perception. While a perception algorithm working bottom up from the identification of contours could achieve a result in polynomial time, it would not achieve a unique solution. This means that the brain has to work top down through familiar perception samples on memory as a search engine trawling through all the possible things it might be perceiving156. Classical computers cannot solve such problems in polynomial time while quantum computing allows exactly this. In a quantum computing system the readout process would be initiated by outside influence in form of an operator and hence, such computing system cannot be called conscious. A conscious system should make such readout at its own will, in other words spontaneously. Such spontaneous action can be induced by an objective state reduction as proposed in the form of a gravitational state reduction which is effectively dependent on the curvatures of the space-times of the quantum state carriers involved in the process. How this could be interpreted as a very simple form of will we shall try to conjecture now. Let us return to the definition of will (‫ )רצון‬in Kabbalah. It is associated with the Crown ( ‫ )כתר‬which is outside and above all other mental processes, removed from every imaginable mental concept, because it is a very simple impulse, so to say spontaneous, in opposition to intent (‫ )כוונה‬which requires the formulation of a procedure leading to an action. This can for example be the result of a decision making process as outlined above. If we accept that will is a spontaneous action with minimal or no differentiation, we can identify it with an objective action which belongs to the level of the hardware of an information system. Being spontaneous in the physical sense it underlies the statistics of quantum state reduction, if a quantum information system is concerned. Then this objective action or will can be induced by gravitational effects and other means like e.g. observation. Since the gravitational proposal is dependent on the superposed state itself introducing this gravitational state reduction, it can be conjectured that the superposed state is self-willing. If we accept will as the most primitive form of intent, we can say it is self-conscious in the most reductionist way, because its own properties in form of the space-time curvatures of its constituent entangled states determine its disentanglement. A proposal for such a view of consciousness has been brought forward by Penrose and Hameroff157, but experimental verification is still subject of ongoing research. Gravitationally induced collapse of the wavefunction, however, has very strong theoretical evidence based on experimental data. We will for this purpose propose an This reminds strongly on the top-down approach of the principle of ‫ חקק‬during Creation and Formation. 157 Penrose, R., “On Gravity’s Role in Quantum State Reduction”, General Relativity and Gravitation, 28, No. 5, 1996; “Quantum Computation, Entanglement and State Reduction”, Phil. Trans. R. Soc. Lond. A (1998) 356, 1927-1939. Hagan, S., Hameroff, S., Tuszyński, J., (2002) “Quantum Computation in Brain Microtubules? Decoherence and Biological Feasibility”, Phys. Rev. E, 65, 061901. 156

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experiment for the verification of gravitationally induced state reduction in our outlook on ongoing and future research. The forward and backward travel of quantum information in time has a parallel in decision making. Information theoretically we can see that the flow and causality of information can be happening in both directions, where classical information flow backwards in time is constrained to statistical and not physical time. This is the orthogonal case to quantum information that can travel backwards in physical time. Let us see whether we can use this orthogonality to formulate a sensible connection between quantum and classical information via uncertainty relations similar to those in quantum theory. Will seems to be closely related to spontaneous actions or emanations that then, again spontaneously, lead to creations and formations as described above. Concerning the mind and the soul with its different levels, quantum information may play the main role in shaping and exercising will (at least in its most simple form) and maybe also in the shaping of intentions and thoughts that are not explicable physically. Objective state reductions are very good candidates for being the cause158 of what we perceive or explain as will. If we consider the principle of engraving (‫ )חקק‬we learned about in Sefer Yetzirah and all that we learned about the evolutionary state of the unobserved and with that non-reduced worlds (Schrödinger or Wheeler-de Witt equation describing this state), we can conjecture that all information processing choices (choices of algorithms or reductions) may in the primordial stage be made by such spontaneous objective state reductions in the following manner: All possible information processing algorithms or non-algorithms are latently available in the evolving state of the Total Existence. By state reductions due to a simplest possible will, spontaneously and statistically first symmetry breakings occur, losing complementary information and gaining energy. By the same token, information is destroyed at dimensional reduction processes. In case of infinitely many dimensions it is possible to reduce only a finite number of them and leave the rest untouched in the evolving state until the next part of that still infinite content is reduced. In drawing a line (‫ )רקיע‬between the reduced and henceforth stable and the still evolving unstable or fluctuating states we construct a distinction within the Total Existence without touching its requirement to be and remain One. This needs to be understood as the demarcation between reduced and unreduced states in the assembly of all worlds. Within the system “Total Existence” itself such reductions are reversible at will, so to say, unless reduced forever by self-observation in form of production of communicable information. In case of non-communicable information such reduction would be reversible as seen in the delayed choice quantum erasure experiment. This ‫רקיע‬ between the reduced and evolving phases of the Total Existence will then appear as if the evolving part exerts “will” and “intentions” onto the reduced part by enriching it by new reduced material or information159. The “line drawn” between the evolving and the reduced part of the Total Existence can for example be the ‫ רקיע‬between the Infinite Light and ‫ כתר‬of Adam Kadmon. Atzilut could be a transfer station for unreduced “packets” emanating that get state reduced informationally in

158

Cause here has to be understood in its extended sense, namely including statistical causality which is sometimes regarded as acausal. 159 This is not to be understood as matter, but as a rather general term denoting anything mental, spiritual or matter-related.

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Beriah, still leaving a material ‫ תהו ובהו‬in Yetzirah which gets ordered and formed into what we perceive in Assiyah physically and informationally. Now that we have a primitive notion of will we can proceed to see whether we can produce an insight what may be the most primitive notion of intent. This intent is needed to define a most simple form of (self-)consciousness for the purpose of creation and the further conscious interaction with that at least partially conscious creation. We can here only try to come up with a proposal as there is no clear professional definition of consciousness available at the time of the writing of this treatise. Above we said, will can be the most primitive form of intent. This explains that intent in a more elaborate form is sufficient but not necessary to explain all above mentioned state reductions leading to creation. The form of consciousness in the primordial state of Creation must have been that of a will in its most simple form rather than intending self-consciousness of the Total Existence. A more elaborate form of intention can then be seen in the course of the ever continuing creation process, for example in the emergence and development of organic and biological entities up to the development of humans. Conclusively we can assign a self-willing or self-conscious behavior to any symmetry or state reducing system, if we allow the Ari z”l’s definition of will and if we allow objective state reduction. This simple will developed throughout the system of the Total Existence in a manner we want to propose later in our outlook for further research. We have seen that such will presents itself in form of spontaneous actions to us as observers, because a will itself cannot be observed or measured before the action caused by it is carried out. Hence, the state of pure will is always in an evolutionary state which is spontaneously reduced into an action or stabilization of an evolving system, thereby losing information contained in said system that exerts the will. We further can conclude that any process that has lead to a stabilized creation, no matter which of the worlds in Kabbalah or Physics we speak about depends on such simple will and occurs to us as a spontaneous effect due to the above mentioned reasons. Therefore we need to accept the statistical nature of such spontaneous effects as well as the uncertainties inherent to any physically or mathematically manifested form of creation whatever that may be and however it may be perceived by us. We need to accept that the will of the Creator and Sustainer is for us not deterministic and idealized in its appearance within the laws of nature, as we have seen for the most fundamental process in creation, the placement of ‫ רקיעים‬as system stabilizers. The emphasis lies in their existence and not in their exact location in any space-time. According to the Babylonian Talmud160 they also possess a thickness and house different creations in a non-revealed form, in modern terms, in an evolutionary state. The function of the ‫ רקיע‬storing souls, in particular neshamot, is especially interesting, as a demarcation is the location of the stored information making up our spiritual costume. We will discuss this issue further in the following chapter. This thickness as well as the roughness of the vessels as described in the first gate of Etz Chaim as scattering the backflow of light shows also that a demarcation in general is not an infinitely thin idealized object but a physically extended subspace of the higher worlds. It provides space in the appropriate dimensions and suggests with that a thickness of any demarcation in the sense we used that word in our discussions above. Certainly, such an “oversized” thickness is to be understood as a parable for the intrinsic nature of Creation, its 160

Chagigah 13a: “… and the thickness of a ‫ רקיע‬is a five hundred year journey…”

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uncertainties and statistical and relativistic behavior, which make it robust and stable. By the same token we can conjecture that the only and only one absolute truth is the existence of the one Creator, because He incorporates all existence, whether positive or negative. Hence, a relativistic or uncertain view of His Existence is not possible. In the following we will try to explain truth and its implications within Creation in the framework of Information Theory and Physics.

7. What is truth under strictly logical considerations? Here we will try to find out the logical view of the Torah in comparison to Aristotelian, Descartian and Kantian logic showing the implications of what we learned so far. It is rather interesting, how idealizations inherent to Aristotelian logic have influenced the thinking of Torah scholars despite of their often vehement opposition against Aristo’s philosophy. The problems caused by Aristotelian logic include the misuse of “properties” as well as failure to match idealized theories to empirically determined facts. Such logic is using categories and the rule of the excluded middle to the extent to classify empirical data into idealized extremes like “good” or “evil” instead of weighing observations and accepting error margins like we learn it in the Talmud. We need to remind ourselves that separations of categories are made by ourselves on grounds of personal decisions for particular purposes, at all times. As an example we might treat Aristo’s “sitting man” and “standing man” as different objects of observation or as a set of different states of the same object, entirely at our will or sometimes also with our intention. It is important to note here that we make the decision where to place the demarcation or ‫ רקיע‬between the two objects or between the two states of the one object. We may iterate to obtain as much accuracy as we need, but we may never obtain completion or certainty in an idealized form. In reality, such absolutist objectives are an illusion for humans. As an opposite view to Aristotelian or Kantian philosophy we will refer to the works of the Rambam who advocates the “golden middle”. Aristo formalized the categorical thinking that has evolved into a dogma in western society and with that in Jewish society as well. As a dogma it has been useful for the analysis of the world we live in, but it also, by its very nature of making categories rigid once defined, has tended to inhibit creative and realistic thinking. By supposing the definitions of words as absolutely precise without error or uncertainty margins, Aristotelian logic became a thought in words where the words rule the thinking. This is the cardinal error in this philosophy, namely setting Binah before Chochmah. In Kabbalah we learn that Chochmah supersedes Binah as unclassifying and pure thought or perception. Classifications are only introduced in Binah which is the third step in Jewish thinking and not the first. Furthermore the Aristotelian world picture separates the definitions of things or concepts from the thinking individual before that individual can let such things or concepts evolve in his mind in, if we want to say so, an entangled state. This would allow thoughts and perceptions to ripen until stabilized by categorization and verbalization. Since in verbalized thinking (level of Binah) one makes a choice each time one uses a word forming a category to which only the individual who performs that particular thought has access and by effecting a choice loses at least half of the

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originally available information, the probability of language induced confusion of thought processes rises the earlier in such process thoughts or perceptions are verbalized and with that stabilized. Categorizations in any thinking or other information processing routine have to be regarded as state reductions of such information, and with this are dependent on the establishment of demarcations (‫ )רקיעים‬that are arbitrary and completely dependent on the observer, at all times. Hence, any state reductions in thinking processes are connected, whether Aristotle likes it or not, with unavoidable uncertainties. This is one of the reasons the kabbalistic thinking process talks of a running and returning between Chochmah and Binah before producing any Daat. This process reminds of what we call in psychology iterative thinking, and in Physics and Mathematics we use iterative methods to increase the precision of a measurement, computation or mathematical result. Nevertheless, thinking and communicating without language is impossible and not constructive for any material being. The Creator or Total Existence is, in opposition to that, globally161 unchanging and simple as a whole and is varied by no conceptions of things or by any other forms. Although the custom of human language presumes to speak of the Creator in the same way as of creatures by calling Him provident or merciful for example, nevertheless nothing in Him should be, or can be, understood as distinct from Him. Therefore any question about perception, intention or will is irrelevant so far as the Creator is concerned. Any attributes of the Creator or His creations are inventions of observers who are finite parts of His creations. Words or “properties” are, by their usage and near natural or physical reality, categories chosen by individuals. The words are not identical with the reality at which individuals point when they use these words. Reality does not split when we choose our words or use of categories; categories only help the describer or observer to communicate his relationships with reality. It is a false assumption to ascribe the power of a demarcation (‫ )רקיע‬to the choice of words which are communicable, but have nothing to do with communicable information produced by a state reduction. They are only the translation of the communicable signal produced by such state reduction and with that a secondary effect of that communicable signal. Hence, language is only a tool for communication and categories are a sectioning of reality to make it easier for a human to understand reality better. This does, however, not mean that reality itself is sectioned off by the mere use of language or categories, unless an interaction with or observation of that reality is effected before the use of words describing same reality. Reality remains interconnected universally, meaning in an evolutionary state, despite the usage of words, and we who use these words are universally connected to that reality; we are part of it and so are the words we create, but they do not change reality per se. Words or language based descriptions of reality are mere models of reality with all uncertainties and error margins, if such descriptions are empirically derived or deduced from observed phenomena. On the other hand, theoretical approaches to describe reality induce from descriptions normally deduced from observational data theories predicting new phenomena. In the natural sciences this approach works rather well and in many cases such predictions are confirmed by experiment, so to say measured reality, later on. Aristotle, however, imagined that science could be placed on fundamental axioms. In mathematics this is true to a certain extent, but in the natural sciences, as our understanding 161

Globally is here to be understood as the opposite of locally.

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has progressed, iterative corrections of theories by observation or empirical data is the more appropriate way of gaining success in the description of our universe. That is, all ideas of our view of nature are subject to constant revision as new data are gathered, and previously axiomatic assumptions are subject to constant adaptation to empirical observational data, meaning effective axioms are subject to such adaptation to reality by iterative processes of thinking. Dogmatic and rigid adherence to “immutable laws” has made space for empirical advances. Kant’s categorical imperative was brought onto very shaky grounds by this obviously successful method of statistical and iterative modeling of the “truth”. Systematic progress only develops when descriptions that reasonably reflect reality are established. Hence, Aristotelian axiomatic systems of thinking introduce errors that are fundamental deviations of an uncertain and statistical reality from an idealized rigid theory, and because of that a “theory of everything” based on Aristotle is doomed to failure as is any axiomatic system of thinking that does not allow any iterative adaptation of its axiomatic. We have to remind ourselves that language is a mere tool for communication, and so is mathematics. Mathematical structure, however, has more to it as we have already seen above. The properties of physical space for instance can be understood as such as a mathematical structure which is manifested physically, while the mathematical description of it is only describing that physical manifestation. It is not manipulating it in any way that could change its properties. This can only be achieved by the interaction of the structures proper themselves. The use of language, therefore, has to be seen as a way of communicating observed “reality” allowing the processing of such information by the mind which is not constrained by the structure of such language in carrying out a thinking process, unless, G-d forbid, it has lost the ability of non-verbal thinking162. For example, prophetic visions or other mental perceptions concerning “unknown intellectual territory” and their primary processing are non-verbal and mostly without any pictorial mental imagination or perception. The verbal simile is constructed only on communication to another individual or group. This is one of the reasons that prophetic writings or kabbalistic texts always use the language and knowledge base of their contemporaries, while sometimes the real information in such texts can only be recognized and understood much later. Verbal thinking alone constrains the process of observation and classification of new phenomena, if the non-verbal thinking ability has degenerated so that such new phenomena are “pressed” into the existing scheme of categorization of an immutable dogma. Systematic progress only develops when descriptions that “reasonably” reflect reality are established bearing in mind the relativity of the perceptions of different observers and bearing in mind that every observer perceives any event in a different reference system. The maximum agreement achievable in a group of observers is the set of identical perceptions of properties of an event or phenomenon or sets of those inside a given context agreed upon by said observers. The formulation of that set of identical perceptions in any form of language is then again agreed upon by an iterative process and called “truth”. Identities are mostly agreed upon and not absolute because of their incompleteness. Such truth is always a product of a process of a chain of contemplation, discussion, agreement and decision making culminating in a set of choices inside a given context and entails the discarding of all complementary information before a formulation of the truth in 162

This would mean to place Binah consciousness over Chochmah consciousness and with that a limiting of Chochmah to the dimensions of Binah which are less than those of Chochmah.

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question is produced. This formulation can be seen in the same way as a product of a state reduction of an evolving iterative process which is finalized by an agreement which information has to be discarded. Said agreement constitutes the establishment of a demarcation (‫ )רקיע‬between discarded and retained information producing the “truth” as a reduced state of the formerly evolving or evolutionary state of the full content of information before the agreement was reached. Bearing that in mind, we need to accept the inevitable inaccuracy of all language use or description of so called truths which constitute the elements of sets of information forming theories, laws and philosophies or religions. The objects and their interactions described in such theories, laws and philosophies or religions are just what groups of individuals decide upon to be “objects”. Objects in this sense do not exist in their own right in the world. In reality all is One. It just happens to be convenient and useful for humans to separate out and focus upon parts of that unified reality. May the reader please note that nature itself has demonstrated such focusing upon parts by what we call in Physics “spontaneous symmetry breaking”. When a human being decides to refer to some section of reality in order to examine it or to communicate about it with another human being, it is not possible for either human being to ever understand exactly what the other human being is focusing upon. It is not even possible to delineate or define anything completely in the sense of any absolute frame of reference, because such frame of reference does not exist in the perceivable reality of any human being. The best that may be hoped for as truth is a good approximation of it163. It seems now that the most ancient quest of humanity to find the “ultimate truth” is thwarted and a dream destroyed, but this will only be the case if we insist on absolute and rigid standards in an ever evolving dynamic world of constant flux. We may proceed, however, by not worrying too much about the inevitable inaccuracy of all language including mathematics and information theory, and hence, physics, thus accepting a relaxation of rigor. That is, by accepting sufficient similarity as a replacement for any ambition to some unattainable total accuracy or equality. By the same token, we have to accept the incompleteness of information due to the loss of complementary information, and we have to accept that this loss of information is substantial. For example even the idea of a good or evil person or other object of observation in an absolute and rigid framework of thinking is not fully definable. What it really means is that the “evil” or “good” person is acting in a way that conflicts with, or alternatively, serves the interests of the defining subject, its ego or sense of aesthetics. There are no absolute standards written neither in the laws of nature nor in any G-d given set of rules. As an example, in Halacha the definition of cooking on Shabbat uses as a standard to define cooking the temperature of 40 degrees Celsius as sufficient to process food into the cooked state. The question arises, why not 39 or 41 degrees? – The answer is 40 degrees was agreed upon by Jewish legal authorities by legal decision making processes. Before the Celsius scale was invented or even before that the thermometer, it was surely much more difficult to decide on a threshold value for cooking. Does this mean that people before the ruling of 40 degrees Celsius sinned if they kept food warm at let’s say 43 degrees on Shabbat? – Surely not, but if people do so today knowing the “exact” temperature according to a thermometer in their possession, they surely are liable of a sin. What if the thermometer scale is moved relative to its pointer so it displays a systematic error and the user is not aware of it? – He will only sin 163

We remind the reader again on the incompleteness theorem of Gödel.

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after he becomes aware of it and continues to use the thermometer. For further discussions about Jewish law we refer the reader to the Talmud and leave it to his decision whether he thinks he can find any objectively absolute measures for what is “right” or “wrong”. According to Jewish law the observance of mitzvoth is to be judged by a court with human judges who according to the G-d given guidelines of written and oral law, and in the context of local circumstances, make a decision if so requested by someone. Hence, we make our own cultural rules according to our power, our comfort and our tastes, and, last not least, according to our own power of understanding, also in case of our acceptance of G-d given laws. We refer the reader to our discussion of objectivity and relativity above, and we refer again to our discussions of observation and its influence on the perceived “truths”, erasure of same and replacement through another in quantum erasure experiments. So, extreme caution is at place to presume the existence of “absolute truth”. The only absolute truth that exists or should exist in our model of the worlds we “know” is that there is One Absolute Total Existence or if we want to say so, Creator and origin, no other. Anything else we think of is part of that Creator and if separated out by ourselves, subject to the laws of nature as discussed so far and with that subject to uncertainties, in particular and best known to us, our physical and mental worlds, whatever those may be. We may always increase our precision in knowing them, but we can never be infinitely (or absolutely) precise. There is great fear among people that analysis will lead to a removal of “concepts of perfection”, because those fearful of such removal have difficulties to accept the reality that insecurity is inherent in uncertainties. As we have seen, uncertainty and statistical or stochastic behavior of our world makes it robust and allows repair and improvement, ‫תיקון‬. In Kabbalah we learn that such ‫ תיקון‬is the purpose of man in the context of Creation, through the performance of mitzvoth, inter alia that of constant learning to enhance our understanding and knowledge about our surroundings or worlds we live in. One of the aspects of such understanding is to accept experimentally verified facts so long until proven otherwise by another experiment or reasoning subsequently agreed upon, where the acceptance of such verification is and always will be subject to iterative thinking and discussion processes. Such processes are by nature incomplete and should be, not without reason, subjected to Occam’s razor, at least if scientific method is applied. Conclusively, any truth besides the Total Existence we are part of has to be treated within its context and relative to it and other contexts. So far, the view of science with a few allusions to what we learn in Torah. Now, what has the Torah to say about truth, and in particular the truth about the Creator, is there any significant difference? – To attempt an answer, let us quote the Rambam (Moreh Nevuchim 1:26): You, no doubt, know the Talmudic saying which includes in itself all the various kinds of interpretation connected with our subject. It runs thus: “The Torah speaks according to the language of man”, that is to say, expressions which can easily be comprehended and understood by all, are applied to the Creator. Hence, the description of G-d by attributes implying corporeality, in order to express His existence, because the multitude of people do not easily conceive existence unless in connection with a body, and that which is not a body or connected with a body has for them no existence. Whatever we regard as a state of perfection, is likewise attributed to G-d, as expressing that He is perfect in every respect, and that no imperfection or deficiency whatever is found in Him. But there is not attributed to G-d anything which the multitude consider a defect or want; thus He is never represented as eating, drinking, sleeping,

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being ill, using violence, and the like. Whatever, on the other hand, is commonly regarded as a state of perfection is attributed to Him, although it is only a state of perfection in relation to ourselves; for in relation to G-d, what we consider to be a state of perfection is in truth the highest degree of imperfection. If, however, men were to think that those human perfections were absent in G-d, they would consider Him as imperfect.

He clearly states that any description regarding perfection is only in relation to ourselves which is a clear indication of the relativity of what we perceive as the truth. A further limiting factor alluded to by the Rambam is the capability of the majority of people to imagine the “real truth”, whatever that is. Since whoever adheres to Jewish values accepts the truth value of the Torah as the highest possible, needs to understand this truth to the utmost of his capabilities, the Torah uses a language maximizing the number of people able to understand it. To achieve this, the Torah avoids attributes of want of the Creator not to arouse doubts in the common population that He is perfect, inter alia in the sense of comprising any existence whatsoever. This becomes clear from the last sentence of our citation. However, the written Torah never states explicitly the use of metaphors or parables inside its text. It needs the interpretation of a competent sage if it wants to be understood in depth. Its laws are interwoven with historical narratives which have to be distinguished from the content of the mitzvoth conveyed by it, but we call the entire Torah the law of G-d. Does history conveyed in the Torah in not always chronological sequence become law or has the sequence of history as conveyed by the text to be regarded as law and absolute truth? – Certainly not, as we are taught by all our sages. Even at the literal level it allows leeway for interpretation as we can see when we read different commentaries. This definitely has to do with an intrinsic property of all Creation as we can perceive it: uncertainty. Such uncertainty is not a blanket allowance for random sloppiness, however, but obeys at least one rule we know from Physics and Information Theory: the uncertainties are concerning complementary sets of information which implies automatically the incompleteness of information we are able to gather from study. We need to accept this like the fact that we never will be able to understand and let alone to describe the Creator completely. Does this constitute a lack of truth and a disappointment? – Definitely not, if we understand that the only absolute reference frame is that of the Creator, and with that unknowable and not observable by us. We can only fathom relative truths, with good reason: we can iterate the relative truths by learning and discussion. We can asymptotically approach the one truth but will never reach it. Infinitely many steps will be required to reach to it, at least on our own power. Only a revelation from the side of the Creator can do that by explaining the entire truth from His frame of reference. How this is possible and how He will do that and when, that remains speculation as long as it comes from a source that speaks the language of man. The treatment of such revelation is not subject of this treatise and needs to be discussed elsewhere. Let us come back to our example of corporeal attributes such as the face of the Creator. If we accept the text of the Torah as absolute truth, Exodus 23 speaking about the face and the back of the Creator, we are tempted to assign a face and a back in the literal sense to the Creator. So does the text of the Torah not convey such truth, G-d forbid? – The Rambam explains in Moreh Nevuchim 1:21 as follows: Moses sought to attain to a certain perception which is called “the perception of the Divine Face”, a term occurring in the phrase “My face cannot be seen”, but G-d vouchsafed to him a perception of a lower degree, the one called “the seeing of the Back” in the words “and you shall see My Back” (Exodus 23:23). We have mentioned this subject in our work Mishneh Torah. Accordingly, it is stated in the above mentioned passage that the Lord withheld from Moses that perception which is termed “the seeing of the Divine Face”, and substituted for it another gift, the knowledge of the acts attributed to G-d which, as I shall explain, are considered to be different and separate attributes of the Supreme. In

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asserting that G-d withheld from Moses the higher knowledge I mean to say that this knowledge was unattainable, that by its nature it was inaccessible to Moses: for man, whilst able to gain perfection by applying his reasoning faculties to the attainment of what is within the reach of his intellect, either weakens his reason or loses it altogether as soon as he ventures to seek a higher degree of knowledge as I shall elucidate in one of the chapters of this work unless he is granted a special aid from heaven…

The Rambam here clearly warns not to try to attempt to reach insights which are unattainable to man. We set that limit of ability to the limits of what is possible to attain by the laws of nature, namely the uncertainties and relativity of information attainable by experiment and reasoning taking carefully into consideration the inevitable losses of information inherent to the decisions and choices constituting such reasoning and observation. We argue that if G-d withheld information from Moses for the reasons the Rambam denotes in the above citation, we have to accept such limitation of truth. This definitely concurs with the scientific point of view we reached above. Hence, again, scientific fact and the Torah agree. Whether the limit we set here theoretically can ever be reached by mankind depends on the future development of human reasoning and scientific or philosophical method in both the study of Nature and of Torah and the development of the human attitude towards that goal. Dogmatism is of very little help in this endeavor, if not totally detrimental for the attempt of mankind to attain the highest possible truth value of its knowledge and understanding. Observations, the learning and understanding of divinely conveyed laws and other information are constraint by the inevitable decision making process and choices made in the course of trying to understand any such revelations. If the recipient of a revelation does not understand it, his interpretations he can convey to others may be false. Even if he fully understands it, which is purely hypothetical, he will render always an incomplete and uncertain interpretation, alone due to the uncertainties of language. The not understood information or the part of information that is discarded by decisions made during the interpretation process becomes meaningless. A challenge to attain this highest possible truth value or objectivity is imposed by the fact that individuals apply their internal understanding of various observations, linguistic expressions and other impressions on their mind in accord with their individual differing experiences. The widely held assumption the words one uses to convey the “communicable information” to another individual or group of individuals have some accepted definition in the sense of absolute meaning is false. These internal meanings are not understood with absolute certainty by the recipients of the conveyed information. Said understanding is at best approximate and depends also on the intrinsic precision of the language used to convey information. Mathematics has been a great help to achieve this clarity wished for, but is not accessible universally and maybe less but not totally immune to fallacies. Reason for those fallacies is the inherent uncertainty of the information gathered by the truth finding process we call observation. Even a dictionary or collection of mathematical definitions, proofs and their corollaries and lemmas cannot give authoritative answers in the sense a dogma would require them to be. This is an unattainable expectation as these can only be guides to an averaged common use of definitions. Such guides cannot and should not be expected to render absolute truths; they merely provide approximate relationships between objects of any kind and their definitions, not some static certainty of same. Definitions themselves have no static meanings; they are dynamically assigned meanings by locally varying individual inclinations.

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Dogmatism, for all the above reasons, is therefore very difficult to use as a basis for understanding the laws of Nature or the Torah. In Kabbalah, the language used and the subjects tackled are mostly based on revelations given to the prophets or mekubalim. The language of the prophets is mostly figurative and allows, as intended by the Giver of that prophetic information, room for interpretation and checks against observable reality. The Rambam writes in his introduction to Moreh Nevuchim: My primary object in this work is to explain certain words occurring in the prophetic books. Of these some are homonyms, and of their several meanings the ignorant choose the wrong ones; other terms which are employed in a figurative sense are erroneously taken by such persons in their primary signification. There are also hybrid terms, denoting things which are the same class from one point of view and of a different class from another. It is not here intended to explain all these expressions to the unlettered or to mere tyros (beginners), a previous knowledge of logic and natural philosophy being indispensable, or to those who confine their attention to the study of our holy Law, I mean the study of canonical law alone; for the true knowledge of the Torah is the special aim of this and similar works. The object of this treatise is to enlighten a religious man who has been trained to believe in the truth of our holy Law, who conscientiously fulfills his moral and religious duties, and at the same time has been successful in his philosophical studies. Human reason has attracted him to abide within its sphere, and he finds it difficult to accept as correct the teaching based on the literal interpretation of the Law, and especially that which he himself or others derived from those homonymous, metaphorical or hybrid expressions. Hence, he is lost in perplexity and anxiety. If he be guided solely by reason, and renounce his previous views which are based on those expressions, he would consider that he had rejected the fundamental principles of the Law; and even if he retains the opinions which were derived from those expressions, and if, instead of following his reason, he abandon its guidance altogether, it would still appear that his religious convictions had suffered loss and injury. For he would then be left with those errors which give rise to fear and anxiety, constant grief and great perplexity… I do not presume to think that this treatise settles every doubt in the minds of those who understand it, but I maintain that it settles the greater part of their difficulties. No intelligent man will require and expect that on introducing any subject I shall completely exhaust it or on commencing the exposition of a figure I shall fully explain all its parts. Such a course could not be followed by a teacher in viva voce exposition, much less by an author in writing a book, without becoming a target for every foolish conceited person to discharge the arrows of folly at him… We also stated (Mishneh Torah I, ii, 12, iv 10) that the expression Ma’aseh Bereshit signified Natural Science and Ma’aseh Merkavah Metaphysics…

This shows us again the Torah as well as scientific theories need leeway for interpretation due to empirically gathered new data which might augment such theories like for example Einstein’s theory of relativity augmented Newtonian physics. This does not mean Newtonian physics is entirely wrong; it only means that the underlying concept of immutable rigid space and time was not an appropriate approximation of the truth in the limit of high velocities of objects and in relation to electrodynamics, to name two examples. Newtonian mechanics or classical mechanics is still a good approximation in the classical limit where the effects of Lorentz invariance can be approximated by Galilean invariance. In appropriate limits, both theories describe the truth, but this example shows that with the empirical gathering of new data or novel thinking the approximations towards the truth can be improved. The same is valid for quantum theory and classical statistical physics as we have seen above. The Rambam’s plea for understanding incompleteness of explanations underlines the principles of understanding truth in the sense we advocate in this treatise and see it as the appropriate way of thinking along the lines of our father Avraham (Sefer Yetzirah 4:16): ‫ ארבע אבנים בונות מאה‬,‫ שלש אבנים בונות ששה בתים‬,‫שתי אבנים בונות שני בתים‬ ‫ שבע אבנים בונות חמשת‬,‫ שש אבנים בונות שבע מאות ועשרים בתים‬,‫ועשרים בתים‬ ‫ מכאן ואילך צא וחשוב מה שאין הפה יכול לדבר ואין האוזן יכלה‬,‫אלפים וארבעים בתים‬ ‫לשמוע‬:

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Two stones build 2 houses, three stones build 6 houses, four stones build 24 houses, five stones build 120 houses, six stones build 620 houses, seven stones build 5040 houses; from there go out and calculate that which the mouth cannot speak and the ear cannot hear. It is obvious that one cannot build two houses from two stones never mind 5040 houses from seven stones. Avraham Avinu is definitely telling the truth and not only the Jewish people presuppose that in their philosophy, but can we understand this on a literal level? – Let us try: The monoliths needed to provide material to build two houses could be found, but the seven monoliths to build 5040 houses would definitely constitute a problem, because they have to be bigger than the two for the two houses. The first obvious question arising is, why would Avraham teach us to look for giant monoliths of growing size for growing numbers of houses? Definitely, for any sane individual, such a request borders on the ridiculous. A closer look at the arithmetic of Avraham reveals that he is talking about factorials. The number of houses is the factorial of the number of stones. – He is clearly using figurative language to tell us a secret of the Torah, and he does this even in the sense of the second Mishnah of Tractate Chagigah: he conveys a topic the learned can understand without revealing too much, according to the standards of arithmetic of his time. Today we see immediately what he meant and understand his encouragement to explore large numbers, but for what purpose? – We propose he could have meant the exploration of the universe we live in. The reason to believe this is the following: the Hebrew alphabet has 22 letters as they are revealed in the Sefer Yetzirah. The ‫ םןץףך‬are only alluded to in this work, but not directly revealed as letters. As proof for this we propose the formation of the 231 gates of wisdom achieved by combining the 22 letters into pairs as stated in Sefer Yetzirah 2:4. The 22 letters’ permutations are 22! which amounts to about 1021 permutations or “names”. This is, as we know today, very close to the number of stars in the observable universe. A very similar figure is also found in the Talmud, Tractate Brachot 32b as well as in Sefer Raziel 18a. One truth and a great encouragement to learn Physics and Mathematics, for us at least this is a reason to understand his advice to try to understand the macroscopic universe. Thinking further we can also justify exploring the microscopic realm: divide one by the number of stars and you reach scales of length that are experimentally not yet attainable, but still away from the Planck scale. Surely, the meter was not invented yet, but 10-21 handbreadths are in the order of magnitude of modern theoretical Physics’ lower end of reliable description of experimentally verifiable effects or objects, while 10 25 handbreadths are spanning up the size of our universe describable by non-speculative theories of our time. We think Avraham Avinu’s encouragement should be followed not only regarding numbers but in general in applying the best available scientific methods and means such as observable data and experiments to iterate ourselves towards the truth, instead of adhering to principles of dogma with immutable incomplete interpretations that hinder the progress of understanding of both Science and Torah. Paradoxes or seeming contradictions between the two fields of understanding should be attempted to reveal and possibly resolve by research and constructive thinking towards unification, transforming secrets into understood knowledge. During such a process we have to bear in mind that such unification will always be incomplete, but we will be able to push the limits of our understanding further with time and newly acquired empirics, for the above mentioned reasons. Dogmatic rigidity is a characteristic of Aristotelian or Kantian logic, not of original and flexible inventive logic within the framework of Judaism as we can see on two examples in Jewish law: it is possible to use electricity for the security of the access to the Western Wall in Jerusalem on Shabbat

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without breaking Shabbat. This is a relatively young invention of Jewish technological, scientific and legal thinking, unified. A little older is the request that we should have a warm meal on Shabbat without violating the laws against cooking on Shabbat – triggered was the invention of the Cholent, another example of many of a Jewish ingenuity, caused by strict but not dogmatic interpretation of Divine Law. The principle of interpretability and uncertainty is, as we see now, superior to rigid absolutism; it makes Creation robust and able to survive even if grave mistakes or accidents happen, G-d forbid. Said principle is inherent to all Creation we can observe or will be able to observe, for all the reasons we have learned about up to now.

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3 Attempt to Answer the Initial Questions of this Treatise And Research that Could Lead to a Better Understanding of our Journey through Science and Kabbalah In this part we want to attempt to use the knowledge acquired to shed some light on the questions we posed at the beginning of this book and try to propose some, of course incomplete, answers. What we learned is that the principles of Relativity and Quantum Theory both apply as valid theories to describe Creation within a Total Existence we called the Creator, because this is the only way not to violate the law of the absolute oneness of the Creator which is the only absolute condition for creatio ex nihilo as we have made sufficiently clear above. We also need to bear in mind that without Mathematics and in particular without its subfield Information Theory many a problem in understanding the common meanings of both the scientific and the kabbalistic reporting of the processes of Creation would have been very hard to solve. On the other hand, the Rambam writes in his introductory letter to Moreh Nevuchim a seemingly discouraging passage concerning such attempts of unification: Know that also in Natural Science there are topics which are not to be fully explained. Our Sages laid down the rule “the Ma’aseh Bereshit must not be expounded in the presence of two”. If an author were to explain these principles in writing, it would be equal to expounding them to thousands of men. For this reason the prophets treat these subjects in figures, and our Sages, imitating the method of scripture, speak of them in metaphors and allegories, because there is a close affinity between these subjects and Metaphysics (Ma’aseh Merkavah), and indeed they form part of its mysteries. Do not imagine that these most difficult problems can be thoroughly understood by anyone of us. This is not the case. At times the truth shines so brilliantly that we perceive it as clear as day. Our nature and habit then draw a veil over our perception, and we return to darkness almost as dense as before.

It appears, as if this would today disadvantage any observant Jewish scientist as he would be obliged to stop teaching or discussing Physics. This is definitely not the case and we can be rest assured not to violate any commandment by discussing the Physics of Creation, because we use models and theories to do this, which the Rambam calls the use of metaphors and allegories. As we have seen above, the human mind needs the use of models to understand observations of phenomena for the simple reason that such models help to compare new experiences with memorized experiences drawing analogies, arrive at generalizations and with that at an understanding of the new phenomenon. The use of language was at the Rambam’s time the only way to explain Natural Science, there was no explicit way to mathematically model scientific phenomena and devise viable theories as we can do it today. Furthermore, a lot of models describing the universe at that time were based on guesses rather than observational fact, as we can see for example on the theory of the “celestial spheres” which, when moving against each other, make noises or “music”. This does not mean such theory was un-intellectual; it was beautiful as an explanation why the celestial bodies do not fall onto the earth, a theory preceding a proper gravitational theory and a theory of an extended ballistics. People even thought about friction between the spheres and deduced grinding noises. Maybe the Sages knew that theories like that are not really the best model of the truth as presented in Ma’aseh Bereshit but did not have a real good model to describe what they knew. Another example is the thinking and presentation of Kabbalah by the Ari and Rabbi Chaim Vital about evolving and reducing states as described in ‫מטי ולא‬ ‫מטי‬, which in our opinion is a very good resemblance of effects we see and observe today in quantum mechanical phenomena. Maybe the Sages encouraged waiting with revelations until

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a sound scientific knowledge would be acquired to have the foundation to understand Ma’aseh Bereshit properly. All speculation, but it would make sense, in hindsight however. The inclination of man to use violence to force philosophical “insights” on others and the resulting strive may also have been a reason to limit such discussions to an audience of academic standing and appropriate intellect rather than to publish and cause conflicts between the less intelligent and less educated. Today this risk has fairly diminished, but is still there in fanatic religious circles that deprive their followers of a balanced and objective education which they replace by ideology and mental or physical violence, G-d forbid. Rambam then describes the sequences of flashes of lightning as a figure to describe the different degrees of prophecy, meaning that certain parts of an unknown reality get illuminated. By interpretation one can fill the empty spaces and construct a theory which is an approximation of that reality. This method constitutes no difference to the methods of the sciences. Certainly at his time the sciences and in particular Mathematics and Physics were not aware of Relativity and Quantum Theory that form the basis of our interpretation of kabbalistic literature in this treatise. The main part of the New Kabbalah like that of the Ari z”l for example was also not known to him, nor were the principles of information theory as we know them today. Therefore he regarded as mysteries facts we can today prove experimentally, and the kabbalistic literature is available in published form. Hence, we think a fear to reveal secrets that should not be made accessible and belong to prophesy cannot apply to our field of investigation we attempt here, and it is fully acceptable to look for parallels in the sciences and in the kabbalistic literature. He writes further: The degrees in the perfection of men vary according to these distinctions. Concerning those who never beheld the light even for one day, but walk in continual darkness, it is written, “they know not, neither will they understand; they walk on in darkness” (Tehillim 82:5). Truth, in spite of all its powerful manifestations, is completely withheld from them, and the following words of scripture may be applied to them: “And now men see not the light which is bright in the skies” (Iyov 37:21). They are the multitude of ordinary men: there is no need to notice them in this treatise.

As we can see, the Rambam concedes that the majority of the population will not and will not want to understand a treatise on the level of what he calls Natural Science and Metaphysics. We agree with that even today, and the more so in the case of understanding both Kabbalah and the Sciences. For that reason we have not attempted to go beyond our professional understanding, but we allow for the person learned in one of the fields which we try to unify or at least link together, to be encouraged to learn about the other field he is not proficient in, perusing our treatise and the references therein. As a matter of fact, bear in mind that for this chapter the Rambam’s admitted limitations of the attempt to teach a new field apply: You must know that if a person who has attained a certain degree of perfection wishes to impart to others, either orally or in writing, any portion of the knowledge which he has acquired of these subjects, he is utterly unable to be as systematic and explicit as he could be in a science of which the method is well known… at one time the explanation will appear lucid, at another time, obscure: this property of the subject [of research] appears to remain the same both to the advanced scholar and to the beginner. For this reason great theological scholars gave instruction in all such matters only by means of metaphors and allegories… sometimes the whole metaphor may refer to two cognate subjects in the same branch of knowledge.

We see that the Rambam was well aware of the method of generalization of principles by what he calls metaphor or simile and we call theory. We also need to refer to the Kabbalistic writings as such similes164. For example Etz Chaim can be interpreted as a simile to the 164

No sage would expound on literal details of the secrets of the Torah to thousands by publication of books.

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Physics of the universe as well as to the structure of the human psyche or anatomy. It is important to see that general principles are conveyed by Kabbalistic literature rather than detailed descriptions of special phenomena or objects. For example, partzufim are structures of general principles with many applications. Here we shall attempt to generalize the concept of ‫ רקיע‬and by trying to answer the questions posed at the beginning of this treatise emphasizing its importance for the understanding of both the secrets of the Torah and Science, in particular Physics and Mathematics. Before the creation of space and time, what did exist, or what represents such Existence? – Both Physics and Kabbalah set the scenario of Creation into a spaceless and timeless absolute nothing as its beginning and first boundary condition, and then letting it evolve through different phases of separations into the scenario we can observe today. In Physics, the beginning is set into a point, a singularity that inflated and exploded into the Big Bang as we have discussed above. This was done by modeling General Relativity into the past, supported by observations of the background radiation and other astronomical phenomena. By arriving at a singularity in this model, one then tried to model forward in time and space from that singularity the emergence of a universe as we can observe it today, more or less successfully over the years, in an iterative process including empirical data at each time they became available. What is still missing is the process that lead from the singularity to inflation and the Big Bang. The nature of quantum gravity is still under discussion and very active ongoing research. With the help of Kabbalah we will try a proposal to a solution of this conundrum. Whether this will lead to a successful approximation of the truth only time will tell. In Kabbalah, the singularity is described in a much more subtle way than in Physics. It is part of the one Creator who is completely unknowable and with that indescribable. What, however, is known, is that the light of the Creator filled the entire existence and with this Himself, too165. This existence is described as spaceless and timeless, with neither beginning nor end. As we have discussed extensively, the beginning of Creation is seen as such light being smooth and evenly balanced, hinting to highest possible symmetry. In physical terms we could speak about the ultimate grand unification. What intrigues, however, is the expression of the Ari z”l “then He contracted Himself in the middle point which is in Him, precisely in the middle, He contracted the Light”. This contraction is seen as a result of the simplest will imaginable. This will, as the Light, is characterized by “simple” and “smooth” by the Ari z”l. From the ambiguosity of the description who or what was contracted, we can only propose the following explanation: If there is no distinction made between the Light and the Creator we can accept this as the fact of a grand unification of the Total Existence. Only with the expulsion of the Light to outside the structure of the primordial but yet undefined space around the “middle point” a distinction between the Creator/Light and Creation is brought into existence, the first ‫רקיע‬. The withdrawal of the light, as is emphasized by the Ari z”l, took place in the highest possible symmetry creating no singularities, edges or vertices. This would by the same token disallow an absolutely sharp ‫רקיע‬. A possible explanation for the avoidance of such non-differentiable objects at that stage of Creation is: if there would be a second singularity besides the one point/sphere system, those at least two singularities would have coordinates relative to each other. This would thwart the location of the point in infinity and hinder the system to be a point and sphere system. Hence, Creation as a creatio ex nihilo, as discussed here, could never have taken place. The middle 165

If we would say otherwise, His absolute oneness would be jeopardized.

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point coordinates relative to the original point in infinity of the evolving infinite dimensional sphere system are not defined. As soon as the “contraction” is done, that middle point is defined, not before. In the infinite but low-dimensional case of the sphere those coordinates lie also in infinity, but are defined as different from the original point in infinity. If the system is fluctuating in size the point moves on the radius away from the middle point of the largest possible sphere towards the original point in infinity. The same is valid for fluctuations in dimensionality if the radius is held infinite. A further, quite remarkable definition given by the Ari z”l is the emptiness of the middle point. We conjecture from that an at least infinitesimally small volume of this point after the contraction and expulsion process which enables the formerly discussed process of inflation to take place. This volume of the point is required for it to be empty, for a real mathematical point cannot contain anything but itself. In case of an n-dimensional sphere emptiness is possible as its volume is not identical to zero. How big this volume might have been for the physically relevant dimensions is an interesting question, but not easy to answer, because we have up to now no really clear idea how mathematical structure can become physical, except by the argumentation via the argument that mathematical structure is information and with that physical. A second argument is, at least for the finite dimensional space-time we live in, the space-time curvature and gravitational energy equivalent to that, as we have proposed before. Bearing this in mind, let us now look at the emergence of time and energy at the onset of Creation. Both of them are concepts not primarily measurable but only to be derived from measurable observables such as position, movement and other dynamics of a system. Likewise, space is also a concept of relative positions of observable objects inside such space. This includes the spaces of ‫ רוחניות‬and ‫ גשמיות‬equally, whose contents create those spaces for the following reason: The Austrian physicist Ernst Mach insisted that science must deal with genuinely observable things166, and this made him deeply suspicious of the concepts of invisible absolute space and time. In 1883 he suggested that it is not space but all the matter in the universe, exerting a genuine physical effect. He proposed that each body in the universe must be exerting an effect that depends on its mass and distance. Hence, the law of inertia will turn out to be a motion relative to some average of all the masses of the universe. Einstein coined this as Mach’s principle. The Machian idea takes the power from space and time and gives it to the actual contents of the universe which all move relative to each other without a rigid deterministic framework of space and time as Einstein later worked it out as general relativity which relativates the causality of space-time causing gravity or vice versa. Indeed, we even go a step further and propose the indistinguishability of matter and space geometry. We justify this by the fact that the equivalence of space-time curvature and gravitation and with that according to current physics mass does not allow us to decide which of them the cause of the other is. The gravitational interactions were not decoupled yet in the Planck state or grand unification, but gravity behaved strangely in relation to the other still unified interactions. This is the reason why the Standard Model does not include gravitational interaction. Only time will tell how gravitation can be included into the Planck state, but we will attempt to make some propositions for research based on our knowledge we extract from the secrets of the Torah, as far as this is possible. 166

We emphasize that the mind can observe abstract things as they represent content of information only. This information is physical on its carrier brain. In contrast to that, the content of the information creates a space on its own in the mathematical sense.

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One can transpose the Machian view of the universe into the spiritual worlds. In our opinion, this would make a lot of sense and allows relativity of such “information spaces”. Any information content, whatever it is, is not invisible to the mind. Therefore, according to Mach’s principle the spaces made up by sfirot, partzufim and other abstract objects acquire a “volume” defined by the dimensions applicable to such content and the amount of such content. Similarly, right at the onset of Creation coordinates and their properties were in the framework of the Planck grand unification not distinguishable. Hence, before any distinction or demarcation was effected, no dynamics as we know it today was manifest and with that no energy or time could be derived. In this state we have only acausal and atemporal fluctuations, in other words, total chaos. Only with the onset of dynamics a time can be postulated and with that same onset we can say this was the origin of time in the sense of before, now and after. This may be the reason why in quantum physics there is time symmetry in the evolving, non-reduced state. Classical time or time as such only make sense after state reduction, as we have seen in the quantum erasure and delayed choice experiments. Creatio ex nihilo in its strict sense demands the emergence of all, including time, from one origin, as we have discussed at length above. Any question what there was before the emergence of time is answered by only a boundary condition of one absolute nothing which can be said existing as One if the rigor on the word “exist” is relaxed and we allow nondynamical existence. Any further question or suggestion of eternal static existence makes no sense. Hence, the Talmud is right to state in Tractate Chagigah, 2nd Mishnah, that anyone who persists to ask further should not have been born. We conclude such question does not make any sense; there is also no observational or theoretical evidence for the necessity of such a question167. The next question we asked was why is the existence of One as the beginning of all worlds inevitable? – As we have seen above, the emergence of our universe goes back to one singularity, according to physical evidence. The same statement we find in Kabbalah, but after all our discourses in Physics and Kabbalah we think the question of inevitability should be posed on the Creation, not on the Origin or, if we want to say so, the Creator. So, is Creation as such inevitable? – Any question along those lines is difficult to answer, but let us try to reason for an answer in the affirmative. We have seen that a singularity in infinity is a fluctuating system, according to a quantum theoretical approach to the mathematical identities of infinite circles, spheres and points. The main issue we think is that only and only from one point in infinity a world can be created without any further input. Only if one singularity exists, one can say it lies in infinity and the mathematical condition of the point being an infinite sphere holds. Only with such a system and a certain measure of uncertainty as we have described it above, both mathematically and physically, creatio ex nihilo is possible. What makes it inevitable? – Any dynamics, any change, constitutes time and with that a dimension of space-time and also energy. A fluctuation between point and sphere and a fluctuation in dimensions in a random manner, not in a completely regular and deterministic 167

Even if we allow string and M theory and live in a brane world, we have still the beginning with One despite of our particular world would have emerged from a collision of branes. Ultimately, there is a beginning out of absolutely nothing; there is no way around that. Furthermore we believe that it is premature to favor string and M theory for the simple reason that in the foreseeable future there is no way to experimentally verify such theory.

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manner, makes it possible to form an irregularity in that system. Is this irregularity the reason for the separation of the ‫ צינור‬from the middle point of the system of spheres and is this the reason for the inevitability of this separation? As we can see in the illustration it is indeed inevitable, because if the radius of the inner boundary of the Infinite Light is ‫א‬n, and the radius of ‫ כתר עליון‬is ‫א‬n-1 < ‫א‬n with the system of spheres fluctuating from the original point in infinity, both spheres have that point in infinity in common and the radii of the two spheres will produce the respective middle points in different locations. Since the ‫ צינור‬starts at the sphere of ‫כתר עליון‬, it will end slightly short of reaching the middle point of the Infinite light. This can be done accordingly with all the inner sfirot that are still in a fluctuating state. The separation of the middle point from the end point of the ‫ צינור‬constitutes a demarcation or ‫ רקיע‬and the system stops fluctuation, but is not entirely stabilized in a state of reshimo. The moment the light will use the ‫ צינור‬to form the thread of light and slowly penetrate all the reshimos of all the available spheres, these will stabilize and become manifest in the realm of their respective dimensions. This all takes place in a tiny volume despite the radii of the spheres are infinite, and hence, we are allowed to make the above assumptions of how those radii behave during the fluctuation. This process is only possible, if there is an uncertainty between the sizes of the infinite radii of at least δ, rendering the gap between the end of the ‫ צינור‬and the middle point of the sphere of the infinite light going towards infinity. Physical space-time within this system is a cut of an at least 5-dimensional sphere representing in three visible dimensions a hyperboloid with its middle point disjoint from that space-time. Its surface will grow only through the evolution of time which depends on the dynamics of the contents of said space-time, as we have discussed above. As we have seen, this leads to the processes involved in inflation and the Big Bang as soon as time emerges by the emergence of dynamics. So we see that the system to be able to emerge needs noise and uncertainty. We can measure such noise of the space-time fabric as we have explained when we talked about inflation. Such noise is characteristic of any system with some uncertainty, even if such uncertainty approximates infinitesimality. Regarding time it has to be remarked that in the state of the noisy fluctuating system only a statistical time can prevail and the onset of any arrow of time needs an asymmetry or irregularity within that statistics. From such viewpoint that anything in a physical or geometrical system possesses an amount of noise even if it is infinitesimally tiny, the emergence of a material universe becomes inevitable. The status of a timeless static existence shows no dynamics except fluctuations and is limited to the amount of noise of the uncertainty of the time dimension 168, and that means in numbers an order of magnitude of 10-48 seconds. We will in foreseeable time not be able to measure such a short time, and the further we approach zero time in our theories the more uncertain they become. We think, this is meant by the Ari’s assurance of the inconceivability of the Origin or Creator, and this is one of the reasons why He has no place, no boundary and no name or description, meaning His middle point lies in infinity despite the voluminosity of Creation. Since He is in this sense not dynamic in the sense of reduced objects but in an evolving state, He underlies no arrow of continuous time. By the same token, the Total Existence’s “center of geometry” is not related to any other similar or identical system, and henceforth it has no coordinates; it lies in infinity.

168

… and of course all other dimensions also will have some noise.

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The will of the Creator, or of the primordial system of the point in infinity, how ever one wants to see the situation, is not structured in any way either. Hence, whether one regards the onset of Creation as a pure physical-mathematical process or involves Divinity, the onset of Creation or emergence of a universe was triggered by a “will” or “spontaneous event” and resumed to evolve within a very tiny amount of time. Information theoretically, this represents a go or no go decision that gets triggered by noise. What the exact value of the threshold noise for the “go” is, remains open for now. Noise is the only dynamics in the system before the spontaneous action, and since it is stochastic, no arrow of time exists. A length in time for such a state to exist before the action is therefore indeterminable and becomes meaningless169. No matter how one wants to interpret observations and theoretical explanations of such a state, if ever possible, the result is the same: a universe as we observe it and worlds of mind that we perceive, on an individual basis. The “will” in this case results in a spontaneous symmetry breaking or, in the language of our sages, in a “desire to create”; they are the same thing. Creation, for the sake of the existence of time, however, can only be inevitable, for two reasons: in Physics, because the unpredictable noise or uncertainty of Nature dictated it; in the viewpoint of Divinity, because the unpredictable “will of the Creator”170 initiated the Creation. The physics we observe tells us about the Planck state and grand unification, the Torah and Kabbalah tell us about the ineffable One; we leave it to the reader to decide, which one to choose, but remind him that the secrets of the Torah describe qualitatively the structure of all known worlds, physical and spiritual, while Physics describes the physical world qualitatively and quantitatively, slowly beginning to explore the “Physics of the Mind” which was triggered by the philosophical difficulties presented by the quantum nature of our universe and what it contains. We come now to answer the questions whether actions beyond the observable laws of Nature are possible or whether miracles or actions as a result of the will of the Creator are possible. First of all, we want to neutralize the difference between the Divinely induced and the Inevitably induced processes of creatio ex nihilo. However, whether actions beyond the observable laws of Nature are possible is a question that requires further elaboration about laws of Nature and what we call Divine Intervention 171. We remember that all space-time and any higher “worlds” can be constructed as “sitting” on a configuration space. Such configuration space contains all physical and mental creations as we have discussed above; it unifies the behavior and dynamics of all Creation in the evolutionary state. Let us now see how this works. First of all, let us see how configuration space can be interpreted as the basis of any physical or mental “world” as perceived from a human point of view. We allege that the Creator’s point of view is not fully accessible to our interpretation since we are finite and he is supposed to be infinite and encompassing all, but we will try later an approximate interpretation without the claim to be right, we just propose a clarification of such a viewpoint using a condensed matter system mimicking the situation. Configuration space is something very special in physics and mathematics, allowing anything of any theory to be placed in or as we will say from now, on it. This configuration space is the basis which all Creation rests on and at the same time the demarcation or ‫ רקיע‬within the Total Existence that we call the Creator. This demarcation divides between the observable 169

Cf. first Mishnah in Chapter 2 of Tractate Chagigah. Since the will is unfathomable by definition as we have discussed above, we perceive its result as a spontaneous event. 171 If we remember what we have learned above, the distinction between the two “extremes” is made by us, we determine where the demarcation is placed. 170

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and explicable, and the unobservable and inexplicable. To understand and accept this, we want to interject a citation from Rambam’s Moreh Nevuchim: You are no doubt aware that the Almig-ty, desiring to lead us to perfection and improve the state of society, has revealed us laws which are to regulate our actions. These laws, however, presuppose an advanced state of intellectual culture. We must first form a conception of the Existence of the Creator according to our capabilities; that is, we must have a knowledge of metaphysics. But this discipline can only be approached after the study of physics, for the science of physics borders on metaphysics, and must even precede it in the course of our studies, as is clear to all who are familiar with these questions. Therefore the Almig-ty commenced Holy Writ with the description of the Creation, that is, with Physical Science, the subject being on the one hand most weighty and important, and on the other hand our means of fully comprehending those great problems being limited… It has been treated in metaphors in order that the uneducated may comprehend it according to their faculties and the feebleness of their apprehension, while educated persons may take it in a different sense… I observed that by expounding these passages [he refers to Prophesy and some Midrashim] by means of allegorical and mystical terms, we do not explain anything, but merely substitute one thing for another of the same nature, whilst in explaining those fully our efforts would displease most people… Consider well the statement that the deeper sense of the words of the holy Law is pearls [hidden in the shell], and the literal acceptation of a figure is of no value in itself.

Any configuration space therefore is subject to change with the changing understanding and knowledge of the set of observers and their ability to formulate the shape of such configuration space in any dimensions relevant for their observational interest. We state here that the total configuration space and the totality of its geometry and other properties can never be known to any created finite being, while the notion of configuration space opens up a very comprehensive and clear way to picture everything that can possibly be created, all at once. State reductions on that space causes complementary creations to be lost, which resembles again the process of ‫ חקק‬described in Sefer Yetzirah. It also gives notions of time and history, stripping away and revealing as redundant the Newtonian superstructure. We shall now try to explain, how configuration space works in mathematics and physics, and we shall propose a possible way how to transpose this onto the kabbalistic worlds and their structures. Let us suppose there is a universe consisting of two or three points. These two or three points are forming a line or a triangle. Any change of the position of those points relative to each other forms a different line or triangle, where the dynamic change of those positions constitutes a history of that universe. The observable history of a two or three point-particle universe, when the invisible Newtonian space-time is abstracted away, is just a continuous sequence of triangles or lines. Given such a history we can let one point represent one particular configuration of triangles or lines, i.e. one point represents one line or one triangle. We then obtain a curve on the space containing all the points corresponding to all possible configurations of lines or triangles. This principle can be extended to as many parameters of any object or sets of objects in any universe or world. Hence, each world has a configuration space containing all possible configurations of the contents of that world, and any particular history of that world is a curve in that configuration space. Anything not on that curve is not state reduced and of the rest at least half is discarded. The geometry of the configuration space is given by all mathematical and physical laws corresponding to the world or universe in question. All laws depend on that geometry and vice versa, because on this level there is no causality. Let us now ask the question on what such geometry depends, and we will have to resort to “forces” that are beyond the realm of our observation, because otherwise we would exclude some properties of our observable world from its configuration space which is not allowed

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according to our definition of that configuration space: It comprises all possibilities that can happen in that world or universe and it is the giver of all physical laws of that world or universe. If now such configuration space is dynamically changed from a system outside the world or universe that sits on that configuration space, events in that world can be changed by such a change of the geometry of that configuration space. If we further take into consideration that we learned in Kabbalah that ‫ כתר‬of Adam Kadmon is the ‫רקיע‬, the demarcation between the created worlds and the Infinite with its Light, and ‫ כתר‬is ‫רצון‬, will of the Creator, we can imagine that this demarcation constitutes the configuration space of all Creation. We can also imagine that as the curve of the history of that Creation progresses on that configuration space, a change of its geometry could alter the laws of Nature in the appropriate dimensions and at the right space-time coordinates of such line of history. The miracle is made – by Divine intervention. Since we are part of Creation we live also on that configuration space, and to change its geometry is very unlikely if not impossible to be done by us or any other part of Creation, unless there exist again the same conditions as in physical space-time that it is dependent on the dynamics of the matter and energy it contains. But this does not really matter for answering our questions. Since Creation and Creator cannot ever be completely separated, not by a demarcation or anything else, we can rest assured talk about the unity of the Total Existence we and everything else are part of. Hence, also if we would change the geometry of configuration space at will and “perform miracles”, this would still constitute an act of the Total Existence or Creator. We can therefore conclude that any action performed by any part, subset or entity of Creation is an act of the Total Existence and because of that originally enacted by the ‫קדוש ברוך הוא‬, but blatant violations of the laws of Nature as defined by the configuration space of the Creation could possibly damage the entire Creation lastingly as it happened by the breaking of the vessels during the creation of the upper worlds, bringing forth the World of Points (‫)עולם הנקודים‬, and by the sin of Adam HaRishon as explained elsewhere. This is the reason, so called miracles are not to be performed irresponsibly, in particular not by the performance of practical Kabbalah. Such irresponsibility can shatter worlds as we have seen in the case of Adam HaRishon. Bearing in mind that miracles and other anomalies or temporary anomalies in the realm of the created worlds are within the possibility of the laws of Nature apparent in these worlds, we need to know their often far reaching consequences for the structure of these worlds. To understand these consequences we need to know the structures and mechanisms of the physical world and should make an explicitly careful attempt to understand the mechanisms of the Higher Worlds. As we have pointed out earlier, all the worlds of Creation are working together harmoniously and on very strict principles that can mathematically be formulated as consistent theories. Any mathematical inconsistency has to be treated by observation and study of the available relevant literature and hence to be eliminated by research, if at all possible. This research has to be carried out with the same rigor with that we carry out professional scientific work. King Solomon says in Proverbs 25:11: “A word fitly spoken is like apples of gold in vessels of silver.” The Rambam comments on this very lucidly: Solomon meant to say, “just as apples of gold in silver filigree with small apertures, so is a word fitly spoken.” See how beautifully the conditions of a good simile are described in this figure. It shows that in every word which has a double sense, a literal one and a figurative one, the plain meaning must be as valuable as silver and the hidden meaning still more precious, so that the figurative meaning bears the same relation to the literal one as gold to silver. It is further necessary that the plain sense of the phrase shall give to those who consider it some notion of that which the figure represents just as a golden apple overlaid with a network of silver, when seen at a distance, or looked at superficially, is mistaken for a silver apple, but when a keen-sighted person looks at the object well, he will find what is within and see that the apple is gold. The same is the case with the figures employed by the prophets. Taken literally, such expressions

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contain wisdom useful for many purposes, among others, for the amelioration of the condition of society… Their hidden meaning, however, is profound wisdom, conducive to the recognition of real truth. – Know that the figures employed by the prophets are of two kinds: first, where every word which occurs in the simile represents a certain idea; and secondly, where the simile as a whole represents a general idea. They are simply required to give to the simile its proper form and order, or better to conceal the idea. The simile is therefore continued as far as necessary, according to its literal sense. Consider this well.

To give the reader a feeling about the structure of the system of worlds proposed by Kabbalah we want to give now an overview of these worlds. Insert a full explanation of Adam Kadmon, Atzilut, Beriah and Assiyah. This structure of Creation gives us not only an understanding of the workings of the four worlds of emanation, creation, formation and making/action in the context of the creation process, but also gives us some understanding of the workings of the mind and the soul. This structure is a generalized pattern of attributes or functions of parts of Creation and its Mind. The descriptions in the Kabbalistic literature only give us examples of its workings and interactions, of the ways and paths the Divine Light illuminates, enclothes and creates, how partzufim interact and procreate and so forth. It does not describe every detail and its functionality, not physically and not spiritually or mentally. Research has to be done into two directions: •

•

Determination of the general principles of Adam Kadmon and the four worlds, comparing them with the principles of the Natural Sciences. It should be possible to determine experimental methods of at least a partial observation of these worlds in form of effects that are common with the physical or mental worlds of man. Analysis of the methods of practical Kabbalah and its underlying principles, attempting to recognize the mathematical structure of those principles. Interactions of kabbalistic structures should be mathematically modeled and analyzed. Simple experiments should be devised to verify or falsify influences of the higher mental worlds onto the physical world and vice versa.

Proposing such a treatment of the principles underlying Jewish philosophy or even the Jewish faith may seem a frightening if not irreverent undertaking. We think not, because the Jewish people have always been involved in the forefront of the development of the sciences and its derivative technologies. Jewish scientists and thinkers have shaped scientific thinking since ancient times as we can see in the ideas of the one and only Creator advocated by Avraham Avinu, and in today’s modern society Jews are still the leaders in all fields of science. One only has to count the Nobel laureates who are Jewish (about 32%) to verify that. On the other hand modern man became pragmatic, realized that ideals of antiquity do not hold stand to reality checks, in short, he became more of an empiricist thinking in finite terms. An infinite Total Existence that is the platform and source of existence of our finite 172 and indeterministic world became more and more remote in modern thinking. The achievements of man have become the object of honor and, yes, worship, but as we may say in the words of Rabbi Joseph Soloveitchik, if we give total trust to a finite being, no matter how noble, we engage in idol worship, any absolutization of a finite idea borders on idolatry. Idol worship applies not only to graven images, chiseled statues or sculpted idols, but foremost to ideas, social structures and systems of values. Modern man is an example of a deified object. Science is 172

Finite has to be understood as finite dimensional.

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worshipped as an idol which has actually overpowered man with its majesty. We stand in awe before the ingenuity of the human mind. Yet, science may conquer the immediate environment of man, but the universe as a whole comprising not only the five worlds of Adam Kadmon, Atzilut, Beriah, Yetzirah and Assiyah, but also the Infinite beyond them, is unconquerable in its totality. More so the Total Existence is unconquerable, since there is a measure of infinity to it, finite man can never gain173. Scientific method therefore may explain the function of the universe and maybe the higher worlds, but only from within, only from the viewpoint of a participant observer in its functioning, never from outside. That, however, does not exist; the Total Existence is One, as we have seen above. We will never explain to the full why the mathematical formulations and its quantification in Physics have the values we measure. The information can be processed, but the ultimate content of that information and the reason why it is that particular content and no other, we will very probably never be able to fully explain. Hence, we have to bear in mind that with the advancement of scientific method and knowledge our understanding of Creation and the five realms or worlds can become better, and G-d willing be used for human advancement in form of participating in the ever ongoing creation process, in attempting and understanding Tikunim and so forth, but the understanding of the Infinite will always be approximate and never complete, also in the times of Moshiach174. We need to see the quest of man for knowledge as not only an addition to theoretical knowledge but as an assumption of duty, a realization of responsibility to a Torah of truth 175 and moral action, otherwise the acquisition of knowledge can deteriorate and ultimately destroy man, in particular if he starts worshipping his abilities. The separation of so called secular knowledge from Torah study which today created a rift between secular and observant Jews, both in their education and in their outlook on Creation and the worlds we live in, needs to be removed. The Creator has given us all the information in Torah and Kabbalah, we only must unlock the seals of mysticism we have ourselves obscured that knowledge and understanding with. Only through scientific method and the application of the highest standards of objectivity as far as that is possible within the constraints and limitations we have learned about, can such a goal be achieved and the moral framework of the 613 mitzvoth and the halachot derived from them be willingly accepted by every Jew as well as the seven mitzvoth by every non-Jew. This said, let us now embark onto the last part of our journey, the outlook on things to be researched and hopefully to be understood: the quest to reduce the mystical by replacing it through knowledge. Let us start with the mind and its role in the system of physically observable realms. We have seen the significance of the role of the observer in quantum mechanical experiments and have realized the importance of demarcations between the observer and the observed. Only when communicable information is produced, an observation is completed. Physicists discuss to this very day the role of the mind of the observer in this process, whether it completes the communicability of the information gathered or whether it is sufficient to have an irreversibility of a registration of information in 173

We conjecture that there is a very high probability of other physical universes in other dimensions, if the Total Existence is really infinitely dimensional. They are beyond our observability and with that for us meaningless. 174 There is a very simple reason for that: we will never be able to process infinite amounts of information, because we cannot distinguish between infinitely many parts of information. We refer to our argument above that infinitely many symbols will contain many indistinguishable symbols. This implies that the differences of these sets of indistinguishable symbols would become meaningless. 175 Truth in the sense that we accept our inability to attain the totally absolute truth, but treat observed and understood truths as uncertain and malleable.

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a detecting system. The questions quantum erasure experiments have opened are far reaching, not only philosophically but also physically. The questions posed in the past about causality, the reversibility of a measurement process after the observable has already interacted with the detector, and the reversal of the order of time in those experiments as well as in optical phase conjugation, barrier tunneling and quantum entanglement experiments, and the questions about the loss of information in any completed observation process are experimentally answered to a large extent. Proposals such as objective state reduction by gravitational selfenergy of entangled systems brought us to grasp the idea of spontaneous breakdown of such entanglement. Such breakdown of otherwise constantly spreading entanglement by such objective state reductions appears to us as an at least partial verification of the action of the Creator sustaining and “re-creating” at every instant of time. Spontaneous actions we have defined as the most primitive and simple form of will of the Creator who sustains Creation permanently by e.g. such spontaneous entanglement breaking, but we are still far from understanding what will really is. The same is valid for consciousness and intention. We have tried to approach definitions with the reductionist approach of a scientist, and to our surprise, in Kabbalah such reductionist approach seems also to be a promising way to understand where are the limitations of human ability to observe the exact processes behind such will176. We can only “observe” the result. In cases where spontaneous effects take over from the classical, continuous, causal and deterministic picture the macroscopic world is showing us in our daily life, we start to have doubts about the correctness of our observation. Statistical physics was introduced to explain the many body problems. There is no way to assign an equation of motion to each and every single particle moving for example in the air surrounding us; we had to accept statistical methods to describe what is happening there177. In the microscopic realm we are confronted with the principles of quantum physics, in information theory we have to deal with the statistical and thermodynamic behavior of information, and in mathematics we realize that asymptotic behavior and approximations are necessary to understand the infinitely small and the infinitely large. Differential calculus and geometry are the best examples for that. We see that the physics of the microscopic realm is intimately connected with the physics of the astronomically large, our universe. Time and space or what we perceive as such are malleable, dependent on the movement of matter and its distribution, and with that causality or what we perceive as such becomes questionable in its very essence. Research has shown us a way how to better understand the mysteries of nature, but we had to change the way how we perceive the nature around us and how we perceive ourselves. In Kabbalah we are confronted with the mysteries of our surroundings as well. The age old question what makes man think, perceive and explore, how his spirit or soul interacts with his body and last not least what is the purpose of man in this world and in spiritual worlds is also here the center of interest. We learn about the structure and interactions of the worlds, we are taught about the breaking of vessels and a grave mistake made by Adam HaRishon. In ‫מטי‬ ‫ ולא מטי‬of Etz Chaim we learn about the indistinguishability of ten vessels in an “evolving” or “spreading” state; they only can be distinguished after they are in a “reduced” state. In the beginning of Etz Chaim we have seen the unmistakable similarity of the description of the emergence of the worlds from a singularity in infinity with the findings of modern Physics. We learned about the nature of such a singularity of being evolving into space and time by 176 177

For example, the exact actions and processes inside of Adam Kadmon are not knowable. Classical examples for this are Brownian motion and the zitterbewegung of atoms and molecules.

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stabilization originating from a line of light drawn from the outside of the spherical shape of empty space towards its middle point, but not touching that middle point, otherwise the creation would collapse. This, however, reminds again of quantum entanglement. Nowhere in the text is said how big such space is or was. We are dealing with infinities, we have to approximate and live with the uncertainties. This state of affairs in both Kabbalah and Science should be reassuring, but man’s perception is influenced by ideals of perfection and idealized forms. His quest for total determinism, wherever that comes from, lets him search for the absolutely causal, deterministic, ultimately precise and absolutistic dogma. We have seen the pitfalls of such thinking in Newtonian Physics, we have learned about Aristotle’s errors in his logic, and we have performed numerous experiments showing us the true nature of our surroundings and its dependence on us as the observers, but still we are uncomfortable with the indeterminism so fundamental to our world’s working, its stable and robust working. Absolute objectivity, as we have seen, is not attainable, because we would need at least two identical observations of the same event. This is not possible. Every independent individual observer has his own space-time coordinates, whether he is a human being or an atom that gets excited. Hence, the value of truth is also connected with uncertainty. The absolute infinitely thin line as a demarcation on a dimension defined by two opposites also cannot exist in practice or nature; neither can its location be determined with infinite precision. A ‫ רקיע‬is a demarcation, but we learn also about what such a demarcation can contain in the spiritual worlds178. If it can contain something, we have to suppose that in some dimension this demarcation is not a fine line but a space. How can we understand this? Let us look at the example of tahor and tamei in the case of the Red Heifer (‫)פרה אדומה‬. The Law says in Parshas Chukkas that after the burning of the heifer the priest performing the mitzvah must immerse in a mikveh and remain ritually impure until evening. Then a ritually pure person should gather the ashes and distribute them into three ritually pure places, the Beis HaMikdash, the Mount of Olives and outside the wall of the Beis HaMikdash. At the time of the encampment in the desert he had to place the ashes in a ritually pure place outside the camp. The gatherer had also to immerse in a mikveh and remain impure until evening. The ashes were added to the sprinkling water which is used for ritual purification. The production and gathering of the ashes render the person handling them impure, while they have to be placed in a pure place and later serve as a means of purification. The cow itself has to be extremely pure in regard to any blemish. This is not understandable at all by any means of common sense or logic; it is a ‫חוק‬, a supernatural law. It is also remarkable that the cow has to be slaughtered and burned outside the camp and outside the Beis HaMikdash which is in all other cases of sacrifices considered murder. The question is: Where is in this law the ‫ רקיע‬between pure and impure, and where do we place the two extremes relative to it? – Let us examine where the extremes are. First, the animal is clean. When it is slaughtered and burned it contaminates the priest and the gatherer. This could be explained by the conjecture that the person got contaminated by the impurity of death 179. So 178

Tractate Chagigah 12 We do not want to prove or argue in favor of this explanation; we are purely interested to determine the geometry of the demarcation between the states of pure and impure in this case. 179

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far, nothing can be seen as an anomaly or even a paradox. The fact that the animal is burnt (sacrificed) outside the temple area which normally would constitute murder, moves the distinction between murder and sacrifice to a clean place outside the sanctuary. A similar movement is constituted by the process of bringing the scape-goat to Azazel. The viewpoint changes to outside the sanctuary leaving the laws of sacrifice intact, beholding the boundary condition of Red Heifer or Scape-Goat. This constitutes a widening of the space of the sanctuary to another clean place to be included in it, and produces an uncertainty of position space herewith. By the rendering impure the person slaughtering and burning or pushing the animal concerned, the distinction between the sanctuary and an outside space is compensated for. The Rambam comments on this law as follows:

The idea taught by this law is this: Those who have defiled themselves would never be allowed to enter the Sanctuary, or to partake of holy things, were it not for the red heifer by which this sin is removed; in the same manner as the plate which the high priest wears on his forehead atones for uncleanness, and as a similar object is attained by the goats that are burnt. For this reason those were unclean who were engaged in the sacrifice of the heifer or the goats which were burnt, and even their garments were unclean. The same was the law in the case of the goat that was sent away for it was believed that it made unclean those who touched it, because it carried off so many sins.

As we can see from this comment, it seems that an uncertainty in position space is compensated by an uncertainty in “cleanness space” which should, by all considerations discussed above, be complementary to each other. Hence, the determination of the complementarity of such spaces is essential to resolve apparent paradoxes as that of the law of the Red Heifer. If we now invert these conditions for the ashes of the red heifer into a complementary space, they become clean inside the sanctuary, if dissolved in water. The water of a mikveh never can be contaminated, so it cleans the ashes and in addition the ashes enable purification from contamination from the dead. The symmetry of the uncertainty in cleanness space to position space becomes herewith obvious and shows that the distinction separated by the relevant uncertainty or uncertainty product is not necessarily sharp as a line or point, but has to be generalized into a space representing a hyper-point or hyper-line constituting a space which may be identified as the red heifer itself. Nevertheless, there is a restriction we can find in the Gemara (Tractate Chagigah ch. 3) concerning the laws of tahor and tameh: There are different levels of them depending for what purpose the tahara is needed. Hence, one can construct a space of several dimensions of tahor-tameh coordinates. Obviously there is a difference between something genuinely unclean which transfers the uncleanness to a person and remains itself unclean and something that is only a carrier of the uncleanness and loses same after contaminating someone. Uncertainties are only possible, if there is a possibility of a dichotomy or at least a double or multiple solution of the problem posed. Only if an object or person is considered unclean or clean in its essence, the distinction is an ideal sharp distinction. If the object or person is rather a carrier of such uncleanness, there is room for uncertainty, because the person might be clean as such, but only contaminated and with that a carrier. Obviously the question arises, when one is genuinely unclean and when only a carrier of such uncleanness. From both the Azazel and the Red Heifer examples one can conjecture, if the contamination is transferred by an action of a certain classification that is reversible in itself, we have the uncertain case, while in the case of definitive contamination like in the case of a pig, there are no uncertainty and no symmetry operations applicable.

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Hence, it follows that if there is an uncertain case, we have to increase the dimensionality of the space related to the dynamics applicable. We can construct a space or spaces that are complementary to each other similar to our physical model above which describes position and momentum. We can conceive that for the example Red Heifer position and tahor and tameh are complementary. Both can have multiple dimensions and different grading. The heifer becomes the uncertainty space produced by the product of position and tahara spaces. All these laws that categorize between opposites, i.e. all negative mitzvoth, are subject to the interpretation by the human mind in form of categorization. We have seen above that such categorization is dependent on the system of thinking of the individual or group of individuals. One of the main myths in practicing such categorization is that there exists an absolute ideal framework for such categorization, meaning the imagination that there is an absolute scale on which one can place distinctions with absolute certainty and precision. This is certainly thwarted by the individuality of any person or mind having its individual spacetime-mind coordinates relative to others. The emphasis lies here on relative to others, because as we have seen in the Machian and Einsteinian approaches to such coordinates, same are dependent on the distribution of the objects in a space-time and vice versa. We learn in general relativity that space-time curves or wraps around massive matter, but we also learn that if the space-time is curved or rippled, particles are produced. For us as observers of such a phenomenon180 there is no telling whether the mass causes the curvature or the curvature causes the mass. Let us explain this with an experiment. A charged particle is accelerated in a synchrotron to about 99% of the velocity of light in vacuo. Observation of the particle in a view-line perpendicular to its trajectory shows that it emits white light into the direction of the observer. As the particle accelerates and reaches its top speed the radiation direction shifts from perpendicular to a smaller angle towards the direction the particle is flying to. If the radiation is observed from that direction it will appear blue-shifted and not white anymore. The explanation for the change of the radiation angle is the folding of space-time around the particle due to its increase in mass, and the blue-shift is due to the Doppler Effect. Imagine now an observer flying on a trajectory parallel to that of the particle with 10% less velocity than the particle. He will perceive the particle radiating white radiation at a rectangle, no folding of space and no blue-shift. If he flies exactly parallel to it, he will not perceive any radiation at all; the particle for him is at rest. We can argue now, we know both the particle’s and the observer’s trajectories in the accelerator system and henceforth, we have a proof for the effect of folding of space around a particle of relativistic speed. We imagine now that the reference frame of the accelerator is taken away from the perception of the observers and there is no other “landmark” for them to orientate themselves on. They are also not aware of each other and cannot communicate during the experiment. After the experiment the observers meet and report their findings. We will get three different reports about the geometry of space-time around the particle, about the spectrum of light observed and so on. The three observers will, if they are not aware of the laws of physics relevant to reconcile their observations or if they are simply not aware of each other’s reference systems, completely disagree about what they have observed.

180

Experimental evidence for such a phenomenon is for example the effect of gravitational lensing in astronomical observations.

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Imagine now a panel of judges trying to reconcile the three observations. Suppose they are only aware of the acceleration process of the second observer. Hence, they will either dismiss the other two reports as untrue or conclude the other two observers’ minds are working differently from the one’s whose testimony they could “prove”, relative to their own knowledge of the experimental conditions. If the panel of judges knows the same as observer one or three, they will act in a similar manner, just that what they think is the truth is interchanged. We have in this case surely to deal with three different space-times as perceived by the three observers, and that is why they perceive completely different things. For that reason the outcome of the “reconciliation” has rather to do with the information that is available to the judges at the time of the hearing. This is, as we know very well, due to the principle of relativity. Space and time appear to different observers different, where in the non-relativistic frame of our daily life such differences indeed are negligible, in most cases. The judges are only able to come to an explanation of the differences of the reports of all three observers, if they have knowledge of the principle of relativity and are able to reconstruct the complete system or they have to have the knowledge an observer outside the accelerator system who can observe all three observers and the particle. Approximations of observations of different observers of the same phenomenon in the non-relativistic limit are, due to our rigid reference frame Earth, seemingly identical observations, but only seemingly. This seems to us the main reason for the human quest to find absolute and deterministic ideals in nature, spiritual realms and within his social surroundings. What is fact in such a situation? The fact is that despite we learn otherwise in Kabbalah and by empirical experience, the Newtonian principle of absolute space and time is ingrained in our minds181. The Newtonian principles are based on his refutation of a mistake made by Descartes in his Principles of Philosophy. Descartes argued that a body could play the role of reference to another body in motion relative to it. Since any other body could play the role of reference, any one body could be regarded as having many different motions. He allowed, however, a body to have one true “philosophical motion” which was its motion relative to the matter immediately adjacent to it. Descartes believed there was matter everywhere, so any body did always have matter adjacent to it. This idea rescued him from sure death by the hand of the Roman catholic court of inquisition, since he claimed that the Earth was carried around the Sun in a huge vortex. Since the Earth did not move relative to the adjacent matter of the vortex, he claimed it does not move. The fact is that Newton’s absolute space arose out of the proposition of Descartes’ law of inertia. Newton saw immediately the flaw in Descartes’ claim that a body could move on a straight line which presupposes absolute space and time of reference, what Descartes denied. Seeing the great potential of the law of inertia, Newton wanted to exploit it and came up with the idea of an absolute space and time 182 that was immovable and completely rigid. He admitted that space and time were invisible and one could directly see only relative motions and not the absolute motions in invisible space. He claimed that the absolute motions could be derived from the relative motions, but he never gave a full proof or even demonstration of this. Newton’s most famous critic during his lifetime was the German mathematician and philosopher Wilhelm Gottfried Leibniz who held against Newton the absolute notion of space and time that had to be without beginning, according to Newton, because the Creator would then never have been able to create the 181

By the same token, Aristotle’s, Plato’s, Descartes’, Laplace’s and Kant’s quests for the absolute ideal and absolute perfection are also ingrained in most minds, despite they might be Jewish. 182 May it be noted that we on purpose do not say space-time here. In Newton’s picture the time coordinate could not be interchanged with space coordinates.

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world, according to Leibniz. Fact is that Newton’s absolute space and time play a decidedly odd role. The first problem is their invisibility; the more serious problem is the little part they play in the story of Galilean relativity, and how irrationally they participate in the action of the universe. Mach, Einstein and Poincaré demonstrated this irrationality more than sufficiently: an absolute framework of the universe is not needed. We also learned that configuration space for that reason is also malleable. Our way of thinking evolved on the stable surface of the Earth which suggests a rigid frame of reference at least if phenomena are observed or experimentally demonstrated in a laboratory on Earth’s surface. We need to come to terms with the necessity of a more abstract way of thinking if we want to understand the workings of the universe around us. We need to find our bearings when the solid reassuring framework of the Earth is not there. This is the kind of mental preparation one needs to understand the ideas of Henri Poincaré who in this respect was even smarter than Einstein. Poincaré was the first ever to ask the question most precisely what information is needed to predict the future. If only relative quantities count, then Newton assumed too much structure, and Occam’s razor has to do its duty. Poincaré was the one who suggested finally after Hendrik Anton Lorentz’s assumption of a homogeneous rigid aether instead of a vacuum that some general principle should rule out all possibility of detecting motion relative to the aether. Reason for this was the incompatibility of the results of the Michelson-Morley experiment that was performed with great accuracy in 1887. The constancy of the speed of light in vacuo independent of the movement of the carrying reference frame Earth did not fit into a rigid framework, neither Newton’s nor Laplace’s or Lorentz’s desperate trial to fit electromagnetism into a rigid aether. Poincaré was the first to propose that a relativity principle might hold universally and not only in mechanics. While he was working with Lorentz on a solution, Einstein presented his stunning solution independently: the Theory of Relativity was born. Newtonian space and time were proven to be as malleable as they can be. Simultaneity and with that causality in a certain sense became questionable, experiments verified and are still verifying the principle of general relativity Einstein finally devised in 1929, the same year Heisenberg presented his uncertainty principle of Quantum Mechanics. This was an earthquake for the Aristotelian-CartesianKantian philosophy in favor of an old assumption we learned in Sefer Etz Chaim: there is no aether, there is a vacuum, and that vacuum has structure, mathematical structure that has influence primarily on electromagnetism and the other fields of interaction, this fact being verified experimentally by the Casimir effect. Another example for mathematical structure having a two-tier creating relationship183 with physical phenomena is: General Relativity allows geometrical shape of space-time to produce gravity and with that mass, but mass creates curvature of space-time, so it cannot be distinguished here what is cause and what effect. We also learned that gravitational self-energy of an entangled system is a very good candidate to explain spontaneous disentanglement as an objective state reduction process keeping Creation alive and physical objects in the universe distinguishable. We heard about the proposal that this gravitational effect dependent on space-time geometry and with that mathematical structure may be the key to unlock the mystery of consciousness and selfconsciousness, but all these effects only concern the physical part of information and how it is processed, they do not say anything about the content of such information. Even a spontaneous state reduction by gravitational self energy inside the brain does not explain any content of information, and definitely at this stage does not say anything about will or intent in regard to our definition of consciousness that it has to be intentional. Similarly, the 183

We learned above about the curvature of space-time and mass-gravity relationship.

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derivation of the coupling constants in the interlude above, in particular that of 1/137, says nothing about will or intention. Those descriptors of natural law only set a framework or structure for the creation of a universe or universes. Only experimental observation brings in the question of free will and intention as shown by Simon Kochen (ArXiv 0807.3286v1 [quant-ph] 21 Jul 2008). This experimental observation must be extended to elementar particles interacting with their environment including the universe itself. An interesting feature of his free will theorem is, free will is half-deterministic; hasgacha pratit can only exist when free will exists and vice versa. Furthermore, certain interdependencies of interactions make a complete randomness of even the most primitive free will impossible. There is a problem with intentional consciousness and will or free will that is so fundamental, it seems insurmountable by scientific method. Will or free will in its most primitive form is only observable or measurable as a spontaneous effect. Intended will to make choices, at least in a living creature, can only be measured by the action following that will and is henceforth to be classified as a spontaneous action. The reason for this is that the true intention of a living creature cannot be monitored, at least not at the time of writing this treatise. Even if such will and/or its intentions are communicated before the choice is made, we have to take into consideration that all categories are fuzzy and uncertain in space and time and as an amplifying factor we have to take into account instabilities of the language in which such communication is attempted. Furthermore, the exact timing of such a willed action is impossible to determine, even if clocks are used, the minimum uncertainty will be determined by the precision of the time measuring device, and that has a finite error. Again, only the outcome of the will in form of an action and its results is observable and measurable, and any interpretation of actions by reconstructing intentions is guesswork, even if numerous boundary conditions are taken into consideration. To speak of “proof” regarding intentions is in the strictly mathematical sense meaningless, to accept as “proof” a plausibility argument “beyond reasonable doubt” is a necessary relaxation of rigor in this respect. If we take these limitations into consideration, we can only conclude that what is valid for natural law is also valid for man-made law and spiritual or divine law 184 interpreted and carried out by man. The relativity principle does not exclude inversion of causality or uncertainties in available knowledge to make a judgment about a certain phenomenon, its observation or interpretation, be it in the scientific or more so in the legal or moral realm. Common interpretation of law often assumes some unattainable absolute knowledge that we cannot have, because we do not have the resources of the Total Existence or the Creator. We have to remind ourselves all the time that we are and remain human and that our quest for absolute and dogmatic infinitely precise interpretations of phenomena in any thinkable realm is not attainable because of the very nature of our worlds we live in and the ‫ רקיעים‬inside these worlds. Those ‫ רקיעים‬are most of the time made by ourselves, and that means individually or by negotiated consensus of individuals who sometimes may call themselves authorities. We have learned that only the production of communicable information makes an observation complete and irreversible. We also learned that setting a demarcation or ‫רקיע‬ between the place where such communicability is ensured and the rest of the system that includes the observed phenomenon is essential to break the entanglement of the observer with the observed, and that it is important that such a demarcation exists and not so important 184

We include the 613 mitzvoth into the “laws of nature of the higher worlds”.

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where exactly it is located or what its own shape may be. The interaction of the mind of the observer with the observed phenomenon only comes into being when communicable information is produced in the detecting system. As we have extensively discussed in our treatment of the quantum mechanical experiments, the information becomes communicable with the discarding of complementary information; otherwise the process is reversible even if the detecting system has already interacted with the phenomenon and the complementary information can be reconstructed. It is completely sufficient in all cases that communicable information has been produced irreversibly. This can be done by a simple recording device that can be read at any time at the convenience of the observer. In contrast, objective state reduction does not need an observation process, but shows another way of producing communicable information irreversibly. It causes an irreversible decay of one entangled object into at least two disentangled objects. We described above the gravitational mechanism of such disentanglement and conjecture now that the geometry of space-time can cause disentanglement and can be seen in the same way as an observation or measurement. On the other hand the term “communicable” depends on the mind of the observer and determines what can be seen as communicable and what not. Another rather strange phenomenon is that two entangled systems can be arbitrarily far distant from each other to interact as if they would be one system. An example for this is Anton Zeilinger’s experiment of two entangled electrons of opposite spin. It suggests, however, the question whether the flipping of the spin of the electron which is not interacting with a magnetic field is really communicable information. If it is, we suggest checking whether the particles’ entanglement may be temporarily interrupted. The entangled wavefunctions as well as the space-time curvatures of the objectively disentangling particles are mathematical structure of that same space-time construct made by the particles in question and their surroundings. This suggests that there should be a link between mathematical structure of space-time and the criterion that makes information communicable. One trivial link is that if information is to be communicable, it must be imprinted on a physical and massive185 carrier. Is there, for these reasons a possibility that we have overseen the interactions between a mind of Creation in form of mathematical structure and physical effects? Is this mind or “soul” physically real, maybe only in higher dimensions, and is it measurable? – To attack this question we need first to make sure what constitutes a physical carrier and ask the question whether the vacuum that constitutes “empty” space-time in our physical universe can be such information carrier. It seems we can answer such question at least partly in the affirmative if we examine effects like the Casimir effect and the Aharonov-Bohm effect. Both effects act via electromagnetism. The Casimir effect is manifested by a physical force exerted between separate objects due to all-pervasive energy fields in the intervening space between the objects. The effect can be understood by the idea that the presence of conducting metals and dielectrics alter the expectation value of the vacuum energy of the electromagnetic field in second quantization. Since the value of this energy depends on the shapes and positions of the conductors or dielectrics, the Casimir effect manifests itself as a force between such objects. This force can be, depending on the shape of the material objects involved, attractive and repulsive. The Casimir effect is only fully explicable by quantum field theory where fields like the electromagnetic field need to be quantized at each and every point in space. Canonically, the field at each point in space is a simple harmonic oscillator, and second quantization places a quantum harmonic oscillator at each point in space. 185

We here remind the reader that also a photon has a relativistic mass. It only has no rest mass.

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Excitations of the field in second quantization correspond to the particles we can observe. Even the vacuum has a vastly complex structure and all calculations of quantum field theory must be made in relation to this model of the vacuum. According to this model the vacuum has all the properties that a particle may have (spin, polarization, energy etc.). On average, all of these properties cancel out; the vacuum is after all empty, except for the vacuum energy or better, its expectation value. This expectation value cannot be zero; the lowest or zero-point energy is E0 = ½ ħω. Summation over all possible points of space yields an infinite value which means trouble in cosmology. There is currently no compelling explanation for how this infinity should be treated as essentially zero. A non-zero value is the cosmological constant and should be a very small number. We propose to look at the negative nature of gravitational energy and propose to sum up over the positive and negative field energies to arrive at that small number. This also shows us how urgently a unified field theory is needed that includes the gravitational field. At the time of the writing of this treatise such a theory had not been devised yet. The Aharonov-Bohm effect displays the action of a magnetic field that is shielded off on electromagnetic waves. To illustrate the workings of the effect we recall Young’s experiment and place an infinitely long solenoid between the two slits. In switching on the magnetic field we can observe a phase shift in the interferogram of Young’s experiment. Since the magnetic field is definitely only to be found inside the solenoid, it cannot interact with the light. The vector potential A(r) which is related to the magnetic field by ×A(r) = B(r) and to an arbitrary scalar function like the wavefunction by A(r) = (1/c) ∫ d3r’ ([J (r’)/|r – r’|] +  ψ(r)) acts on said phase shift of the interfering light. The vector potential is seen in classical physics as an abstract field with no direct physical effect as it is to be understood as an integral of the magnetic field. Since the magnetic field is shielded off from the light, there is no classical effect on it, but only a quantum effect. Mathematically this can be formulated using complex calculus where the phase of the light is the complex part of the vacuum dispersion relation. Both effects show that in quantized fields the vacuum carries energy and with that information, if only phase information which can occur instantly. The consequences are the possibility of the transmission of instant quantum information186. If such instant action at a distance which Einstein coined as “spooky action” can be explained only by quantum phenomena using complex functions, this could be the opening of the possibility to do measurements beyond our (classically perceived) physical space. We remind the reader here again of the fact that quantum information or phase information can only be transmitted in conjunction with classical information and needs at least two carrying particles that need be entangled. The retrieval of such information as communicable information needs state reduction and the loss of complementary information. Again the communicability is governed by the imprint of that information on a physical carrier that can be read or its properties measured. Up to now it seems there is no other evidence of any interaction of a mind with an observed object than the fact that the information produced by the observation or measurement needs to be in a communicable form. This presses to ask the question, what is communicable information and to what minimal entity has it to be communicated to? – We are trying to find 186

This might, in a further development, lead to an explanation of instant action at a distance.

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a criterion for a “minimum mind” that can make the observation irreversible, for example by making an irreversible decision. For this purpose we propose a solution of this up to now unresolved problem in form of an experiment. We propose a modification of the quantum erasure experiment in double delayed mode in the following manner: The experiment shall have a detector system that can make a decision on its own free will. This should be achieved by the use of a material that can make simple decisions whether it wants to register the measurement or not. If it does decide not to register, the other device should show the complementary information and if it decides to register, the other device should lose the complementary information. The detector should be equipped with a material that can make decisions as described by Abraham Shanzer and his colleagues187. To make sure, no human mind or computer is involved in the process of making the measurement irreversible, we propose the following measures: The process should take place fully automated and no human observer shall be used. Two quantum erasure experiments shall be combined in a way that the decision making detector creates an asymmetry in the output statistics in a way that if the detector is removed or shut down, this symmetry will be restored. It remains open where the threshold is to define a device as having a “most primitive mind”, and whether such threshold (mind / no mind) which constitutes a demarcation or ‫ רקיע‬is definable, and under loss of which type of information that should be complementary to the gained one. If Penrose’s proposal of gravitational objective state reduction is correct, and it seems as if it has a good chance to be correct, the most primitive mind is to be found in any unstable particle or composition of particles188. Hence, chemistry and biology should be full of such minds. Up to now, decisions of composition of particles or molecules are in general limited to decay or not decay and react or not react, decision to go or not. A three or more way decision influenced by processes like learning or other indirect environmental influences may lead us to understand at least assemblies of such “minds”, while the single molecule will remain rather renegade and make a whimsy decision, if the statistical behavior of particles and nuclei holds also for such “intelligent” molecular entities. However, the statistical behavior of assemblies of such entities such as intelligent molecules may be a nice model mimicking the function of a precursor of a brain. With this we arrive at the question how to define the term brain or ‫מוח‬. In Kabbalah we are confronted with the brain of worlds. All the worlds are seen as an image of man, the head is seen as the combination of ‫( חכמה‬wisdom) and ‫( בינה‬understanding), crowned by ‫כתר‬, where ‫ כתר‬is not part of the head or ‫ ראש‬of the world or Partzuf. We have learned above that wisdom is consciousness in unstructured, totally abstract form, while understanding brings distinctions and classifications into the consciousness. This requires that conscious decision making or mind depends on an evolving indiscriminate state of information processing which becomes irreversible by categorization and analysis, placing demarcations and making decisions which information to process further or which to store and make to knowledge or ‫דעת‬. The parallel to our quantum theoretical process of observation is as obvious as stunning. Will which is represented by ‫כתר‬, however, can consult the mind or not. Not consulting meaning making a go or no-go decision at whim is the classical case of a spontaneous action and the minimal use of the mind, where the statistical time for such action 187 188

Cite Shanzer’s paper and the others. Any (rest-) massive particle that occurs in Nature decays: the proton has a half-life of about 1032 years.

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‫ספר‬

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is given in case of for example the onset of Creation or the decay of a nucleus by the parameters of the relevant space (-time). Not without reason it is written in the Preface of the Zohar about the letter ‫א‬: “Aleph, Aleph, although I will begin the Creation of the world with the ‫ב‬, you will remain the first of the letters. My unity shall not be expressed except through you, on you shall be based all calculations and operations of the World, and Unity shall not be expressed save by the letter ‫א‬.” The ‫ א‬symbolizes also the upper and the lower ‫י‬, to both sides of the ‫ ו‬which symbolizes the ‫ רקיע‬and with that emphasizes the ‫ א‬as a symbol for the complete mind, the ‫רקיע‬ incorporating the facility of the demarcation between evolving and reduced thought of the mind, the brain being the carrier. Such carrier, as we have seen above in several cases and examples does not necessarily need to be a biological brain. Even the vacuum of our universe has enough structure189 to facilitate as such carrier. From this we feel to have the right to conjecture that a mind can be carried by the physical vacuum if we strictly follow our definitions justified above. At least this is a strong possibility, as obviously the mind of the Total Existence uses gravitation, i.e. deformation of space-time, to ensure the continuous breaking of entanglement so that the universe is in reduced rather than evolving states. An interesting example how such evolving and reduced states behave is described in Etz Chaim, ‫דרוש מטי ולא מטי‬. Consciousness as defined as “intentional consciousness” is, as we have now definitely understood, not a very convenient descriptor of what happens in the entity we call “mind”. We still battle with terms like “corporeality” and “spirituality” that are often taken as opposites, and we still have tremendous difficulties in understanding the demarcation between body and mind. We are trying to idealize both where we should have learned by now that both approaches, the purely measurable physical part in form of the brain or similar entities on the one hand, and the purely incorporeal spiritual or mind part in form of some inexplicable immeasurable soul or not necessarily reduced information content on the other, both as they are do not lead us to any useful answers about how the mind works empirically and how it interacts with Nature and influences same. A little better understanding we have about how the mind is being influenced by Nature in form of that mind’s environment, but that does not give any greater insight into the opposite way of interaction. We think there are new perspectives needed in addressing the profound issues raised by the measurement paradox of quantum mechanics as we have discussed at length. Questions of locality and non-locality inherent in EPR effects and the issue of quantum entanglement have been brought further to a scientific solution, but still the “way out” of pinpointing the real cause of the “production of communicable information” with all the ‫ רקיעים‬necessary to stabilize selected states as well as the nature of such demarcations is still far from being fully understood. If the measurement paradox is really deeply interconnected with general relativity and gravitation, new experiments should lead to at least some deeper understanding. In the following we want to argue for a promising area of research that should be done into that direction: the investigation of space-time geometry and the distribution of matter as a possible trigger or demarcation to replace mind dependent measurement or observation by the “observation” through matter adjacent to the phenomenon in question. It should be investigated whether such “observing” matter needs to be able to be conscious in the sense of being able to make a decision and whether the most primitive decision making is sufficient to 189

… Meaning mathematical structure as per our definitions above.

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reduce a state. Perhaps there will be types of experiments exploring the nature of quantum gravity such as those designed to test the possibility of higher dimensions. The more deeply we probe the fundamentals of physical behavior, the more we find ourselves in mathematical rather than physical structures. Concerning the mind-matter interactions such things as mathematical structure seem to us most promising to investigate. A very promising beginning for such structure investigation is the physical vacuum and systems mimicking its structure and behavior such as superfluids like liquid Helium190. This is also very important to understand the concept of a reshimo and its interaction with light forming sfirot and vessels. An analogy for that are topological defects in superfluids. These topological defects may also be a key to understand the interplay between physical and spiritual realms using mathematical structure – matter interactions as an example for such interplay. Collective state reductions inducing phase transitions due to purely geometrical change over large distances and the like are good candidates for such investigations as their structure is very rich191. In particular, low dimensional systems seem to excellently mimic such effects as “hidden” dimensions. The conceptual similarity between condensed matter and the quantum vacuum gives some hint on the origin of symmetries and also allows the simulation of many phenomena in highenergy physics and cosmology related to the quantum vacuum using quantum liquids, BoseEinstein condensates and superconductors. All particles of the Standard Model have energies which are extremely small compared to the Planck energy scale. That is why one may propose that all of them originate from the fermionic or bosonic zero modes (collective modes) of the quantum vacuum. If this is the case, we need to describe and to classify the possible zero modes of quantum vacua which represent either the true or a false vacuum. These zero modes are represented by the bosonic collective modes of the quantum vacuum, the dilute gas of the particle-like excitations or quasiparticles which play the part of elementary particles, and topological defects which have their own bosonic and fermionic zero modes. Quantum liquids provide examples of how the metric field gμν of the Einstein equations naturally emerges as the low energy collective mode of the quantum vacuum. Using Andrej Sakharov’s theory of 1967 one can derive the action of this mode, and even the curvature term of space-time can be reproduced in some condensed matter systems. From this point of view gravity is not the fundamental force, but is determined by the properties of the quantum vacuum. Gravity is one of the collective modes of the quantum vacuum. A possible direct experimental demonstration of this fact is the Casimir effect. If we now recall gravity’s role in objective state reduction, where we postulated similarity of that type of interaction with an act of observation, we see that both types of state reducing agents, gravity and the production of communicable information, are derivatives of the respective more fundamental entities really initiating the state reduction. In case of gravitational state reduction the properties of the vacuum itself generate the gravitation which means that for example if geometrical constraints are imposed on the vacuum, the low energy collective modes or gravitation will change at the location where such constraints are 190

We refer here to the extensive investigations by G. Volovik. We refer here to an invited conference paper of one of the authors (P. BA) on the Kosterlitz-Thouless transition in two dimensional Helium films. 191

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imposed. This means that topological defects in the quantum vacuum could give rise to anomalies in the space-time geometry itself. It appears to us that there is a similarity of these topological defect structures and the structures of the reshimo in Kabbalah. We therefore propose that the experimental investigation of condensed matter systems could give a lot of insight into the production of mass as well as quantum state reductions initiated by gravitational anomalies192 as well as they may enable us to mimic the conditions of structure interactions described in Kabbalah. A further very interesting point arising within the treatment of the Standard Model and the trans-Planckian physics by mimicking it with a quantum liquid is that some analyses like the velocity of light in an anisotropic vacuum or a stability analysis of its ground state energy cannot be obtained by an observer living inside the vacuum or the quantum liquid. He will always see the velocity of light as constant and independent of its propagation direction, while an outside observer can see differences. From this we can conclude that it is absolutely in the framework of possibility that we do not see such anomalies or anisotropies either, and some of the physics we try to understand is closed to us, unless we find a way how to access a system that contains our observable universe and observe “from there”. Mimicking experiments with analogous systems can thereby help us to find criteria we have to look for to achieve such a goal. It turns out that the only fundamental constant not emerging from condensed matter systems mimicking the Planck state followed by inflation and the Big Bang with its decoupling of the electromagnetic interaction is Planck’s constant h. With this all uncertainty relations are fundamental to the Physics we can observe and even mimic by analogous systems. Where it comes from and what determined its value is still a mystery. Planck in 1906 published a paper where he used the electric charge which is definitely quantized as a basic unit to describe physics in “natural” units. He defined the charge of the electron as e = –1 and obtained according to his scheme a value for his own constant ħ = 137.036. It was John Wheeler who emphasized the importance of these ideas of absolute units in many of his writings using ħ rather than Planck’s choice of the electric charge. The importance of the only fundamental constant of the Planck state of the pre-inflationary universe speaks for itself. Planck’s constant and its relationship to charge and mass of elementar particles as well as the fine structure constant α = e2/ħc that defines the strength of electromagnetic interactions and has a numerical value of 1/137.036 suggested already in 1946 that there must be a fundamental connection between quantization and the fundamental interactional forces in Physics. α itself is still unexplained in the literature up to today, and Sir Arthur Eddington for example tried to produce a fundamental theory of Physics with the value of 137 as a fundamental constant. This quest for a purely mathematical reason for such specific values is today more and more abandoned and replaced by so called “running coupling constants” making such constants of Nature to low energy limits of these running values, but without energy dependence such constants would not at all appear fundamental. The question in Science still remains open, why 137 is fundamental in such a way that it does not emerge out of theory or measurement of any system that mimics our physical universe. It is one of the parameters that determine the shape of the configuration space of our physical world. We still have no answer in Physics where exactly its numerical value comes from, but we can offer an interesting observation in Kabbalah. If we take into consideration an error to 137 rendering it as 137.036 or similar deviating measured values and accept that such values 192

Such anomalies have to be understood as anomalies in the space-time curvature as discussed in our radioactive nucleus problem.

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cannot be determined exactly to the last digit after the point, we should look at the following facts:

• • • • •

The sum of the gematriot of the two names ‫ ע"ב‬and ‫ ס"ג‬is 135+2 = 137. The gematria of ‫ תהו ובהו‬is 430 which, divided by π, yields roughly 137. The gematria of ‫ תהו‬is 411 as is the gematria of ‫ יש מאין‬or something from nothing, and divided by three this yields exactly 137. A word with the gematria two times 137 is ‫רעד‬, to shiver, to tremble. A word with the gematria 137 is ‫– קבלה‬

Is this all coincidence? Is the Holy Language giving us hints to the origin of the world using the most fundamental constant in Physics that is not even possible to deduce from a system mimicking our universe or has this language been developed to show this knowledge given to us in ancient times even if we should have forgotten what those words really mean? As we have shown in or interlude about mathematical structure where we looked where in a generalized Heisenberg uncertainty relation with continuous multi-dimensionality we can find 137, and allowed us to come up with an equation that produces a function where all interaction constants lie on, the observer interaction cannot be excluded. This results in a system with 10 four dimensional nested Riemann spheres with continuously increasing dimensionality which is an amazing parallel to the kabbalistic structure of our world. Also amazing is that the shape of the line of light or ‫ צינור‬as described in Etz Chaim and Emek HaMelech coincides exactly with the shape of our momentum space we multiply with spherical position space. Do we now have to re-discover painstakingly by scientific research what the Creator had given us anyway? It seems to be necessary that mankind discovers these things by its own efforts. As we have discussed above, it is very difficult to describe phenomena to people whose experience lacks any connection to such phenomena. The necessity to use similes from their realm of expertise to describe a phenomenon totally not graspable for them brings so much uncertainty with itself that the phenomenon itself becomes camouflaged completely and gives henceforth way to falsification of the facts by misinterpretation193. It seems to be necessary for any civilization to gain experience and expertise by their own efforts and then re-discover what they were taught at a time they were not ready for such revelation. Only after such effort such revelation becomes useful for any civilization. This is very much in the sense of what we have to understand as repairs or rectifications (‫ )תיקונים‬of the world, be it through the performance of mitzvoth or through the learning about how this world works. Let us refer again to Sefer Yetzirah 2:6 as cited above where substance was formed out of chaos or ‫ תהו‬that before was engraved and carved from water (1:11). Chaos here is referring to the most primitive and first stage of matter, as commented by Rabbi Aryeh Kaplan. This necessarily needs to refer to the Planck state in Physics, if it is the first manifestation of matter. Now we can argue that space and time as geometry depends on the distribution of matter and vice versa, and use this argument to conjecture that the emergence of space-time and matter were one process. ‫ תהו‬itself comes according to the Kabbalists from the verb ‫ תהה‬meaning to be confused or astounded, another hint to uncertainty. The Zohar 3:27a and 193

We remind the reader of the Rambam’s remarks in this respect.

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the Bahir 135 teach that ‫ תהו‬is associated with the Klipot, the forces that prevent one from visualizing the spiritual worlds. Despite this seems to be a nice conjecture, we have here to do with a process that takes place in the higher world of Yetzirah. The completion of such creation then is finalized in the world of making, the world of Assiyah. The present conjecture, however, proposes that this very process took place all at once. All at once, because before any dynamics existed, no time could be defined. An interesting fact is also the word we found with double the gematria 137. Trembling means uncertainty and this very uncertainty is described by the physical constant that does not “emerge” out of any theories, it can only be experimentally determined and not further “explained” – coincidence? We leave this to the reader to decide as well as the interpretation of the gematria for the word Kabbalah. If one accepts the Divine origin of the Hebrew language, we can understand this as a hint to use the knowledge of that part of Torah to further explore our universe and its origin with scientific method. Important is that we will only accept scientifically proven results to verify or falsify such hybrid research, but we have good confidence that Kabbalah will not mislead us. We definitely are of the opinion, it is very well worthwhile to examine the writings of Kabbalah for further clues that could help to find a theory that bridges the still open very tiny gap between the singularity of the very beginning and the definition and inflation of physical space-time. There are several avenues open to eventually reach this goal, but one very important constraint will be in the way to verify such a theory, if we ever arrive at it: we sit in the lowest dimensional realm. The possibility to test such theory from higher dimensions than we physically exist in will always be limited to effects that are actually measurable and observable in these finite dimensions of our space-time. Any higher dimensions will be only accessible either via the human mind or we learn to extend our physical senses in dimensionality by accessing these dimensions one day physically by the use of new technology. Both are possibilities that cannot and should not be ruled out but pose today some serious problems that would lead any discussion or proposition totally into the field of speculation, because the level of study of the human mind or if we want to say so, minds as we have discussed them above, is still very much on a beginner’s level. The only proposition we can make is to try to analyze the information about the mind of humans and the mind of the worlds as presented in the works of Kabbalah. An interesting subject is the subdivision of the human soul in Kabbalah, namely Nefesh, Ruach, Neshamah, Chaya and Yechidah. These subsets of the soul have different functions as they are related to different sfirot. Otzrot Chaim describes in detail how these subsets are acting and interacting for different partzufim, how they descend from and ascend to the mouth of Adam Kadmon. Generally Nefesh is understood to give the life force to everything; it is the spiritual information of physical existence and remains with the body after death. It is said to be divided in humans into Nefesh behemit which is the animalistic part of the soul ruling instinctual behavior, and into Nefesh elokit which is the g-dly part of the soul ruling human behavior. Ruach enables intellect, while Chaya is to be understood like an umbilical cord to the Infinite, where Yechidah is part of the Infinite Total Existence. On this level individuality is lost. Ruach signifies that which remains of man after his death and is not subject to destruction, but it is supposed to return to its source, the Creator. The Rambam explains that

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divine inspiration, intention and will are in the realm of Ruach, while will in the realm of Nefesh is the Creator’s will. Chaya signifies according to the Rambam a living sentient organism, growing and having sensation, but it is also seen as the faculty of acquiring wisdom or ‫חכמה‬. Yechidah refers to a state of the soul which is part of all souls connected to the Infinite. In this state there are no distinctions, it is the evolving state of souls where individuality is only latent and not state reduced. This leads us to the question of the necessity of an observer in form of a sentient being to enable the universe to exist in reduced states as we know it. Inevitably we have to ask here about the validity of the anthropic principle. In the inflationary picture of Creation the anthropic principle is often invoked. Its argument postulates that the universe we perceive must be of such nature producing and accommodating beings who can perceive it. Science does not give much of a clear understanding about how to prove the validity of the anthropic principle, because we have not much of an idea what conditions are actually necessary for the production of sentient life. Furthermore, as a scientist one gets the impression that the anthropic principle can be too easily used as a “bail-out”, when theoretical considerations have seemed to reach their limit. Arguments that we could not exist, for example, without a certain energy level in carbon nuclei allowing the production of heavier nuclei and with that our periodic system of chemical elements in stars, finally being spewed out in supernovae, are too often used to advocate a belief in an intelligent Creator who made sure about specific values of natural constants by pre-ordination. There is a difficulty with such a point of view not only in Physics but also in Kabbalah. In both views, as we have seen above, the beginning was simple and smooth; there was only a very simple structure from that everything emerged. We have seen also the difficulty to track back the history of our universe to the Planck state, a state where dynamics as we know it and with that space-time as we know it, does not make any sense. The physics of such a grand unified state cannot be measured; only the results of the first symmetry breaking can be measured or observed which is exactly what makes the Total Existence in the grand unified state ineffable. Again, the Torah is right, but we have the right to search for exactly that first symmetry breaking, and we have the duty to make sure it is the first one. A pre-mediated “fixing” of the natural constants makes no sense, because of exactly that argument about simplicity and smoothness. The uniformity of the Big Bang and the flatness of our universe make it very difficult to accept a principle that requires the presence of sentient life as a reason for numerical values of physical constants. We feel this argument is elliptic: without sentient life no universe, without the universe with its peculiar properties no sentient life. We should rather concentrate on a much more interesting question: How do we define conscious observation as a first cause for a first state reduction? – Gravity and objective state reduction seems a much more appropriate candidate for an explanation how geometrical structure in infinity actually transformed into energy, time and dynamics of a material world and mental worlds. This type of consciousness is precisely what plays the ultimate role of the observer. Conscious mentality needs to be supported by the universe in Physics or the system of worlds in Kabbalah right from the onset of any dynamics leading to a first symmetry breaking. Our proposal of the definition of a most primitive form of will may be sufficient enough to meet that requirement, while the anthropic principle is unusable in a flat and uniform universe with a smooth beginning, because in such a universe any configuration of matter will occur somewhere in it by pure chance, making even statistically unfavorable conditions for sentient life allowing that life. But to start our universe from a singularity we need a first state reduction without such complicated life as we normally define it, if we take the secrets of the Torah for serious and are optimistic that the fundamental constants of Physics are mathematically determinable numbers. So far, we are

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relatively near the phenomenological completion of the history of our universe, about 10 -35 seconds, on the other hand we are far from a mathematical theory of everything in Science. We think the consideration of the first evolutionary state leading to the first and second Tzimtzum in Kabbalah may be the key to such a theory, but only qualitatively. Time will tell whether we will be able to quantify it and describe it in the language of Mathematics. We asked for a reason of Creation. A simple, but uncertain and maybe unpleasant answer is that it is inevitable, at least according to the laws of Nature. We have seen that absolutely nothing as such and by itself is non-existent. We need to start from one, if we want any creation to happen, and the uncertainty of that One represented by the geometrical construct discussed at length in this treatise seems to be inherent to any positive existence. Our proposal of this very dichotomy of everything and nothing in an evolving state of a grand unification of a Total Existence needs only a little noise, a little irregularity or uncertainty to make the first state reduction and with that explain the onset of Creation as such in a qualitative way. A quantitative description, however, is far from attainable at the moment, not to speak about experimental verification, so to speak about a reason of Creation at this stage of knowledge is too early – or is our quest for knowing a reason for Creation meaningless, because there is no reason? This question can only be answered by the Creator, ‫הקדוש ברוך הוא‬, because He willed the Creation and Himself to evolve and reduce to what we can observe or know by tradition, and of that will only the results can be observed and known. Can we ask ‫ הקדוש ברוך הוא‬what was His reason to create? Can we communicate with Him? – Scientifically the answer to this question will be very poor. We know far too little about the physics of consciousness and the mind, the mind not only of human beings. We do not know in the scientific sense, how the soul and its parts interact within the context of the Total Existence, we only have clues from tradition, from Kabbalah. Tradition tells us about the structure of souls, about reincarnations or ‫גלגולים‬, and about the formation of zivugim for the purpose of creation and formation in the higher worlds. For example the marriages of Ya’akov with Leah and Rachel have significance in the higher worlds, as we learn in Etz Chaim and other kabbalistic literature. A detailed treatment of questions arising, how the mechanisms of such phenomena work must be subject of another treatise, but one thing is sure: a detailed treatment of the soul would be a very interesting subject of research regarding fundamental mathematics as an expression of the ability of the human mind, brain research and physics and chemistry of the brain as well as biology and psychology. All this is beyond the scope of this volume, but we want to encourage in particular Jewish scientists and talmidei chachamim with an interest in the sciences to engage in active research into these directions. A communication with the Creator at this stage is limited to prayer and Kabbalah Ma’asit, which is not yet the subject of discussion in scientific terms, but we believe there definitely is reason to pray and communicate with the Creator this way following our traditions until we will have the means of observation and can develop scientific methods to systematically understand such communication. We believe, it is worthwhile to think into this direction, because we learned that the descriptions of Creation in the kabbalistic literature are “spookily” precise pictures of what we learn scientifically about our universe. Hence, we do not dismiss the term “angel” as a “messenger of the Creator” either, but support the view of the Rambam. He writes in Moreh Nevuchim 2:6: As for the existence of angels, there is no necessity to cite any proof from Scripture, where the fact is frequently mentioned… We have already stated above that angels are incorporeal. This agrees with the opinion of Aristotle: there

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is only this difference in the names employed – he uses the term “intelligences”, and we say instead “angels”. His theory is that the Intelligences are intermediate beings between the Prime Cause and existing things, and that they effect the motion of the spheres, on which motion the existence of things depends. This is also the view we meet with all parts of Scripture: every act of G-d is described as being performed by angels. But “angel” means “messenger”: hence, every one that is entrusted with a certain mission is an angel. Even the movements of the brute creation are sometimes due to the action of an angel, when such movements serve the purpose of the Creator who endowed it with the power of performing that movement; e.g. “and an angel of the Lord came up from Gilgal … (Judges 2:1)… It is also used of ideals perceived by the prophets in prophetic visions, and of man’s animal powers, as will be explained in another place. When we assert that Scripture teaches that G-d rules this world through angels, we mean such angels as are identical with the Intelligences. In some passages the plural is used for G-d, e.g. “Let us make man in our image” (Genesis 1:26) … Our Sages explain this in the following manner: G-d, as it were, does nothing without contemplating the host above. I wonder about the expression “contemplating”, which is the very expression used by Plato. G-d, as it were, “contemplates the world of ideals, and thus produces the existing beings”… These passages do not convey the idea that G-d spoke, thought, reflected, or that He consulted and employed the opinion of other beings as ignorant persons have believed. How could the Creator be assisted by those whom He created! They only show that all parts of the universe, even the limbs of animals in their actual form are produced through angels: for natural forces and angels are identical.

He explains further: “One angel does not perform two things, and two angels do not perform one thing” (Bereshit Rabah 1). “This is exactly the property of all forces.” He clearly is of the opinion that angels are natural forces, representatives of the laws of Nature, including psychological forces. Those psychological forces depend, however, on the laws of information theory and with that mathematics. Information depends on a carrier to enable its processing and communication and with that on the laws of Physics. State reductions are possible by gravitational effects. These facts may finally open up a gateway to understand communications and interactions with higher worlds. Quantum entanglement and the possibility of processing quantum information may even open up a physical gateway to the Ein Sof that is measurable. Of course, we are here not talking about ministering angels, but angels that are produced by thought and perish after that thought is processed. If the Rambam is correct, we should one day have the possibility to communicate with higher worlds and the Ein Sof on a physical basis. Until this is possible and “science fiction” becomes hard science, we need to do it the old way: pray according to the traditional siddurim and what we learn in Kabbalah. We think we have made it clear up to now that all the information given to us from the time of Adam HaRishon through the generations of Noach, Avraham Avinu, Moshe Rabenu, the two Temples and our Prophets, Mekubalim and Sages is authentic and in accordance with the laws of Nature; we only have to open our eyes to see, and use our ever growing knowledge in the sciences and in scientific method to understand. The most dicey question needs still to be answered. Are the laws of Nature divine will or created inevitably or by chance? – We suggested in our treatise earlier on that there was no choice for Creator and Creation than to spring into an evolving existence. The reductions into stable creations and distinguished worlds, however, are subject to debate: are they caused by divine will or are they spontaneous symmetry breakings? As we have discussed above, an evolving state cannot be measured classically, but only via quantum information in a very limited way. Hence, “deliberations” preceding will are not accessible with the state of the art in a way that would reveal pre-will processes in a satisfactory manner, meaning that such will is proven to have a deterministic cause. This might not at all be the case. As long as we cannot determine the “fixing” of constants like the fine structure constant, we cannot answer this question in a scientifically acceptable way. On the other hand we cannot “bail out” by the mere assumption of a pre-determination of such fundamental constants and with that the laws of Nature by an ineffable Creator and leave it like that.

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For that and many other reasons, we want to present some unresolved issues in the sciences tackled in this treatise, and suggest studying Torah and Kabbalah to find ‫ חב"ד‬to solve, with G-d’s help, some of these open problems. A very interesting problem arising out of this treatise is how the term hashgachah pratit has to be understood in the context of uncertainties, quantum behavior and relativistic causality of our universe, information we receive, process and communicate; how can statistical and stochastic processes be reconciled with the seemingly deterministic and absolutistic phenomenon of hashgachah pratit? – We want to propose the structure of voluminosity of a large sphere in relation to dimensionality.

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Concluding Remarks In our treatise we have discussed some very fundamental ideas and facts about the principles that govern Creation and our physical universe. We have made attempts to understand some of these principles from the viewpoint of Science and from the viewpoint of Kabbalah, reaching the conclusion that Kabbalah seems to show a very good resemblance of some principles we learned in Physics and Mathematics. We have found no significant contradictions that would be self-exclusive, but we might have shattered an age old dream forever – the dream of the Ideal as such. Even in Mathematics we must concede to uncertainties, to loss of information and to ambiguosity; when we deal with infinity we can only approximate. Noise and uncertainty are always part of physical observation. Causality and ideal absolutism are never found in their “pure” representation, but exactly this seems to make our world stable in the sense that it is not hopelessly entangled but clearly observable. Maybe we ought to listen to these noises, to these uncertainties, to the “small voice” who spoke to us in the Beis HaMikdash. Maybe we have to accept effects like objective state reduction as evidence for ongoing and permanent Creation and Sustenance of our world carried out by the Creator at every instant of what we perceive of time. Maybe in letting go of the unreachable, super-ideal, absolutist world view, in letting go of the rigid classifications we are trying to maintain at all costs for the sake of an ideal that is unattainable, and in looking closer at the empirically realistic, experimentally verifiable with all its uncertainties, relativities, and despite lost information we will attain the goal to understand our world how it is, not like we want it to be. Knowing how it is and how it works, not why, not what it is in the sense of an absolute classification or categorization, shall bring us to the goal the Almig-ty has asked us to reach: the ‫תיקון העולמות‬, the repair of the worlds that shattered and gave us reason to exist. Only when we know how our worlds we populate work, when we understand all the mechanisms including their uncertainties and inherent noises, all indeterminisms and statistical behaviors, we will know how to work on such repair. Only if we know that there is only One absolute truth, the existence of an all-encompassing Creator who is at the same time, from our point of view, completely detached from His Creation, we know that all the other truths and names are only aspects of His, and henceforth subject to uncertainty, relativity and paradoxes. The world exists, not as Plato’s, Aristotle’s or Kant’s ideal world, but as a world that is made stable and robust by its uncertainties and its statistical behavior, a world that is running and returning, evolving and reducing, with always moving ‫רקיעים‬, according to our individual points of view. Let us explore it, without prejudice. The deeper we explore, the deeper we have to ask new questions, ad infinitum. In communication with the Creator we should, if we have learned the principles of the Torah and its secrets, make use of special means provided by practical Kabbalah only sparsely and only in cases we know that we do not bring harm to any part of the worlds, G-d forbid. We should only use what we have learned and understood properly. We should use a critical and self-critical mind to decide what is understood by proof and what only by repetition of traditionally handed down facts and methods. Unless we explore the literature and learn from our sages applying scientific method at all times, we cannot ask the right questions. If we do, we can ask deeper and deeper, ad infinitum.

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‫ספר‬

‫בס"ד‬

A last remark we want to make about the use of divine names, names of angels and the use of so called kabbalistic amulets and astrological interpretations as treated in the literature. First of all, the use of any such items should not be leading to worshipping them, because this constitutes idol worship. Prayer or blessing is a communication of an individual with the Creator, not one or more of His aspects. We have learned what different “names” mean, what the Creator did and does with them in the process of an ever renewing Creation. We are so used by our daily life to address others with their name, a name is significant, and it is polite to use a name of a person one talks to, writes to or otherwise communicates with him or her. The Creator is not a person, He does not need a name, and that is why He does not have one. Since He is all that exists, He is One. That we learn twice a day when we say

‫שמע ישראל יהוה אלהינו יהוה אחד‬ once in the morning when we rise and once at night when we go to sleep. Let us keep it that way, He is our Lord, our angel, our Creator, our anyone and everyone, everywhere, in anything we see, all, including ourselves, we see aspects of His. Nothing and no one is separate from Him. When we address Him, we should know that we are a tiny part of His, and then we do not need a name or special names, we can regard those as variables in an equation denoting the Total Existence, ‫הקדוש ברוך הוא‬. An angel, tzaddik or other person should only be asked to pray together with oneself or to pray on someone’s behalf who is not able to do so. This should not be understood or seem like in any manner like someone would pray to such an entity. One should also be careful always to have in mind that one prays to effectively only one, ‫הקדוש ברוך הוא‬. The wearing of amulets as a charm is forbidden. Some authorities allow amulets as a protection, but we hold it with those Tzaddikim who just sign their name on such a piece to assure that their prayers are with that person. Anything else is in our opinion idol worship and denigrates the almig-ty power of ‫הקדוש ברוך הוא‬. Mazalot or the astrological meaning of constellations of stars and planets can be subject of very interesting study, but should be not taken as predicting an immutable fate, nor should the name of a person be used to praise or condemn his or her character because of the related mazal. It should be born in mind that any person can through study of Torah, its laws and secrets in all their aspects in a manner using logic and strictly scientific reasoning, and in the study of mathematics, the sciences, arts and humanities on the basis of Torah refine his or her character beyond such rather prejudicial mazalot. He need not fear the dark forces, an evil eye or any other object from the “other side”, because he or she is connected and knows to be part of ‫ הקדוש ברוך הוא‬by ‫קידוש שמים‬. May all readers of this treatise be encouraged to learn the Torah and its secrets so that we may merit

‫הגאולה שלמה‬ speedily in our lifetime in this beautiful and wondrous physical and spiritual world.

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