Quinta Essentia - Part 1

QUINTA ESSENTIA A Practical Guide to Space-Time Engineering

PART 1 “Alpha to Omega” For Mike 2nd Edition Project Initiated: December 4, 2007 Project Completed: June 6, 2008 Revised: Thursday, 24 November 2011

GEOFFREY S. DIEMER

Edited by Riccardo C. Storti1

www.deltagroupengineering.com

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[email protected] © Copyright 2011: Delta Group Engineering (dgE): All rights reserved.

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Preface “One does not find gold prospecting in a field filled with miners. One must break new ground, not perpetually overturn familiar soil.” • Riccardo C. Storti We experience gravity every moment of our lives, yet most people rarely, if ever, pause to consider what the force of gravity actually is. To others, this question borders on obsession. Gravity is a mystery that has plagued scientists for hundreds of years. Although Newton and Einstein formulated ingenious tools for depicting precisely how objects will behave due to the effects of gravity on Earth and in the heavens, it may surprise many people to learn that their work does not actually reveal the root cause of gravity. In other words, we know that all material objects both generate and respond to gravitational fields, but science has absolutely no idea how objects cause gravity -- until now, that is. The answer that has recently been uncovered, as described in the Quinta Essentia series, extends the work of Newton and Einstein using a mathematical framework commonly employed in the field of thermodynamics. The physics is exactly the same; the only difference is in the way we choose to depict the gravitational model. In Sir Isaac Newton’s time, some three hundred years ago, people depicted gravity as being a “pulling” force which attracted objects to one another in the heavens, and invariably caused objects to fall to earth. It was also believed that gravity was transmitted across great distances of space and that when it reached a distant object a pulling force would be imparted upon it; thus this transmission of gravitational force was referred to as “action-at-a-distance”. Newton and his contemporaries surmised that a fluid-like substance of some kind must fill all of space, acting as the medium via which the force of gravity was transmitted. This mysterious substance was referred to as the “aether”. Even though Newton implicated the aether as the medium which transmitted the force of gravity, he could not logically reconcile how a “fluid-like” description of the aether could allow objects in the heavens to move as they do, simply because fluids act to impede the motion of objects. If the aether was in fact fluid in nature, its viscosity should cause the stars and planets to slow and fall out of their regular, seemingly perpetual orbits. The formulas Newton derived in his monumental work entitled The Principia have been used not only to predict the orbital motions of the planets; they are still used to this day to plan our www.deltagroupengineering.com

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spacecraft missions to the Moon, Mars and other planets. However, the triumph of Newtonian Mechanics overshadowed another more speculative theory of gravity posited by Newton, which has gone virtually ignored ever since. In his treatise entitled Opticks, Newton develops the mathematics describing optical principles of refraction, reflection and light spectra. This profound body of work is still fundamental to science today, and has brought about phenomenal technological advancements since the time of its development. In this work Newton briefly speculates on the notion that gravity is caused by optical characteristics of the aether. Newton surmised that just like a lens, gradual changes in the density of the aether (whatever it may be) in the presence of matter should cause light and the movements of objects passing through it to follow curved trajectories characteristic of gravitational attraction. A full two hundred years later, Einstein introduced his theory of gravitation called “General Relativity” (GR). Very much like Newton’s optical model for gravity, GR is essentially a geometric interpretation of gravity, derived from the way in which light propagates through space in curved trajectories in the presence of gravitational fields. The curved path of light in a gravitational field, in turn, defines whether the space an object moves through appears “flat” or “curved”. This curvature of space-time defines how objects behave gravitationally. Not only was Einstein’s GR found to be highly accurate and useful, it also removed the problem of action-at-a-distance. According to GR, objects aren’t being “pulled” by some mysterious force towards each other; rather, it is the curvature of the space-time fabric, if you will, which guides the gravitational motions of objects, hence no “force” is required. Since no force is necessary to keep a planet in orbit, the action-at-a-distance problem which plagued Newton vanished along with the aether. However, Einstein’s GR theory didn’t vanquish the aether completely; it merely replaced it with something even more abstract called “curved space-time”. And the problem of “action-at-a-distance” was only supplanted by a much thornier question of what, exactly, is being curved? In other words, how does a beam of light or an object “know” whether the empty vacuum of space it moves through happens to be “curved” or “flat”, and respond accordingly? Is matter actually curving space, and in so doing causing rays of light to bend as they propagate along a curved manifold? In this context, “spacetime curvature” is a completely ambiguous term because space is not considered to be a physical thing. In other words, how can “nothing” posses a curved “shape”? It is crucial that physicists take to heart the

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fact that curvature is merely a mathematical contrivance acting to describe (not explain) the physical phenomenon we call gravity. Thus we are still left to wonder what physical process might be responsible for conveying information about the gravitational field to the beam of light or the object passing through it. In 2002, physicist Hal Puthoff introduced an alternative optical interpretation of GR, referred to as “the Polarizable Vacuum Representation of GR”, which sought to answer such questions. Here, Puthoff substitutes the concept of “space-time curvature” with a “variable index of refraction” in space surrounding matter, which yields a congruent yet mathematically simplified interpretation of gravity to that of GR. According to GR the space-time geometry of a gravitational field surrounding a massive object is depicted as a depression in the fabric of space-time. As an object passes through curved depressions in space enveloping a planet or star, its path is caused to bend as it follows the natural slope of the curve, ultimately resulting in a gravitational effect. The key distinction between GR and the polarizable vacuum (PV) interpretation is that the PV model explicitly describes a physical manner in which space-time may, in effect, be “curved” and how an object might be able to sense the gravitational field it passes through. The PV model asserts that matter polarizes the vacuum surrounding it, generating gradients in the refractive index of space so that as a beam of light passes through, its trajectory will be refracted (i.e., bent) towards the object. However, if we follow Puthoff’s model and assume that a beam of light is bent due to refractive properties of the vacuum of space, rather than curvature, we are still left to wonder how matter causes the refractive index to change, and why polarized space (a “refractive index” within the fabric of space-time) should cause a gravitational force. These questions are answerable by first understanding how the vacuum of space becomes refractive, and how material objects act on, and react to a refractive space-time environment. Quantum Mechanics (QM) tells us that the “vacuum of empty space” is, in fact, quite the opposite. If you switch your television to an unutilized channel you’ll see thousands of dots of static buzzing about like bees in a hive. This imagery is physically reminiscent of what is occurring at the quantum level in the vacuum of space; a chaotic jumble of quantum energy fluctuations at all points in the Universe, whether in the inter-galactic voids of deep space or in the impossibly small spaces between sub-atomic particles! In this way, the Universe may be thought of as a container replete with www.deltagroupengineering.com

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energy which may never be emptied. When we consider the vacuum to be “something” rather than “nothing”, it suggests that the vacuum itself may provide the matrix supporting the indefinable “curvature” of space-time and the more physical “refractive index” of the PV model. But we are still left pondering the question of why objects produce and respond to gravitational forces. To solve this problem, we must look to other examples of such forces in Nature. The only other similar force in Nature is “inertia”. If you wish to change from one velocity to another, you need a push to overcome the acceleration reaction force of inertia. The force of inertia is only experienced upon acceleration, which simply refers to a change in motion. When we move at a constant rate of speed we don’t feel any force (other than gravity) even if we are moving incredibly fast. Yet once we change our rate or direction of motion, we suddenly feel a force pushing on us in the opposite direction of our acceleration. Nature tells us that uniform motion is relative but acceleration, in a manner of speaking, is absolute because you can feel it. But where does this strange force come from? Strange and mysterious as it may seem, this powerful force arises (like gravity) instantaneously out of the vacuum of space, as if by magic, to inhibit changes in motion. But how is it that objects feel the force of inertia and gravity even while separated from other objects by vast expanses of nothingness? This question hints at a deep connection between the forces we have labeled “gravity” and “inertia”, and their indissoluble connection to the quantum vacuum of space. In making this link, we take the first steps towards profound discoveries and unparalleled technological advancements; all based upon a fresh understanding of the quantum origins of inertia and gravity. This book presents an alternative model to that of GR, which presumes that matter must do “work” on the quantum vacuum manifold of space in order to generate so-called ‘”curvature” within it, and that the energy expended on the space-time manifold is electromagnetic (EM) in nature. The EM energy exerted on the manifold changes its configuration such that instead of being “curved”, space-time becomes “refractive” in the presence of matter. In this way, gravity may be definitively shown to be the byproduct of EM exchange2 between matter and the vacuum of space surrounding it. Objects and light passing through such regions of space behave in precisely the same manner as predicted by GR, except that they are guided according to “optical” principles of action (i.e., refraction) 2

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In accordance with the principles of QM. www.deltagroupengineering.com

rather than by metaphysical geometric imperatives. This new approach also eliminates the terms “gravity” and “inertia” from our vernacular, in that they are both shown to be byproducts of electromagnetism and not actual forces in their own right. Quinta Essentia: A Practical Guide to Space-Time Engineering (the series) describes the development of a mathematical method termed “Electro-Gravi-Magnetics” (EGM); so named because it facilitates the representation of gravitational fields solely in electromagnetic terms. One of the most valuable aspects of EGM is that it demonstrates how GR and QM are interrelated. In this regard, EGM is a unique method which reveals a single universal principle applicable from the subatomic scale to the cosmological. For example, the EGM method, originally designed to calculate the energy distribution of gravitational fields, has uncovered not only the framework underpinning the stability, order and coherent inner structure of the atom; it also reveals how this order and stability arises in Nature. EGM is an engineering tool, and as such it may seem somewhat unorthodox to many physicists. However, no “new physics” has been conjured in order to develop the EGM method. It is simply a novel application of time-tested engineering principles, physics and mathematics. The principal reason it may seem unorthodox has to do with the way in which problems are approached in physics and engineering. The physicist’s natural ally is reduction; where a “generalized phenomenon” is deconstructed into its basic constituents. An engineer’s ally, on the other hand, is an inductive approach; integrating basic principles and formulating a systemic solution congruent with experimental observation such that a phenomenon may be “reverse-engineered”. Based upon engineering methodology, EGM represents a new way of looking at an age-old problem. It employs conventional, well-founded engineering principles which have never been previously applied to the problem of gravity. Again, EGM treats gravity in terms of thermodynamic principles; i.e., as being the result of matter (mass-energy) establishing energetic equilibrium within the space-time manifold (as defined by QM) surrounding it. Modeling the dynamics of gravitation in this manner yields profoundly accurate and comprehensive results because EGM successfully reveals the common ground underlying GR and QM. Part One of the Quinta Essentia series provides the layman with a summarized presentation of the key results and findings in Quinta Essentia parts Two, Three and Four; furnishing the reader with the derivational details required to test one’s own theories, to make www.deltagroupengineering.com

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predictions, and to scrutinize EGM. It is the authors’ sincere hope and intention that the material presented in the Quinta Essentia series will convey the scope and utility of the EGM method and inspire new ideas and experiments dealing directly with space-time manifold modification, by either applying EGM methods or through the development of one’s own approach.

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Table of Contents Preface ................................................................................................ 3 Preface ................................................................................................ 3 1

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3

4

5

Nothing is Everything ............................................................ 13 1.1

The void.......................................................................... 13

1.2

The Platonic solids.......................................................... 15

1.3

The laws of motion ......................................................... 18

1.4

The luminiferous aether .................................................. 21

1.5

Michelson and Morely.................................................... 24

1.6

Space-Time..................................................................... 26

1.7

The Casimir Effect.......................................................... 30

All Things Being Equal .......................................................... 35 2.1

The cosmic counter-balance ........................................... 35

2.2

Expansion and compression ........................................... 38

2.3

The principle of equivalence .......................................... 43

2.4

Mass-Energy equivalence ............................................... 49

The Glass That is Always Full............................................... 53 3.1

Symmetry and unity........................................................ 53

3.2

Exploring the microcosmos ............................................ 54

3.3

The Quinta Essentia........................................................ 58

3.4

Quantum uncertainty ...................................................... 69

3.5

The substantive Universe................................................ 71

Making Something of Nothing .............................................. 79 4.1

Virtual reality.................................................................. 79

4.2

Mutually assured construction ........................................ 83

Mass Illusion ........................................................................... 87 www.deltagroupengineering.com

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5.1

A matter of terms ............................................................ 87

5.2

Intrinsic inertia................................................................ 88

5.3

Extrinsic inertia............................................................... 94

5.4

Bridging the gaps............................................................ 98

The Polarizable Vacuum ..................................................... 107 6.1

Blind-sighted ................................................................ 107

6.2

Optical gravity .............................................................. 109

6.3

Shaping the lens............................................................ 111

6.4

Conflux ......................................................................... 113

The Harmony of Nature ...................................................... 121 7.1

Ancient wisdom............................................................ 121

7.2

Music of the spheres ..................................................... 123

7.3

The quantum-harmonic axiom...................................... 126

7.4

Fourier’s legacy ............................................................ 128

Electro-Gravi-Magnetics (EGM) ........................................ 135 8.1

Introduction .................................................................. 135

8.2

Similitude ..................................................................... 136

8.3

Precepts and principles ................................................. 140

8.4

Space-time engineering ................................................ 142

8.5

Gravity.......................................................................... 145

8.6

Elementary particles ..................................................... 157

8.7

Cosmology.................................................................... 164

EGM Technical Summary................................................... 179 9.1

Overview ...................................................................... 179

9.2

The QV spectrum.......................................................... 185

9.3

The EGM spectrum ...................................................... 185

9.4

The ZPF spectrum ........................................................ 186 www.deltagroupengineering.com

9.5

The PV spectrum .......................................................... 186

9.6

The EGM, PV and ZPF spectra .................................... 189

9.7

The Casimir Effect........................................................ 189

9.8

Comparative spectra ..................................................... 190

9.9

Characterization of the gravitational spectrum ............. 193

9.10

“Planck-Particle” characteristics................................... 193

9.11 Cosmology.................................................................... 194 9.11.1 Fundamental........................................................ 194 9.11.2 Advanced ............................................................ 195 9.11.3 Gravitational........................................................ 195 9.11.4 Particle ................................................................ 196 9.12 10

Key point summary ...................................................... 196

EGM Results Summary ....................................................... 201 10.1

Harmonic representation of fundamental particles ....... 201

10.2

Periodic table of fundamental particles......................... 202

10.3

EGM vs. SMoC ............................................................ 203

10.4

Cosmological evolution process ................................... 203

Periodic Table of the Elements ..................................................... 211 Image: Spiral Galaxy..................................................................... 212 Bibliography 1................................................................................ 213

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Nothing is Everything “Among the great things which are found among us, the existence of Nothing is the greatest.” • Leonardo da Vincii

1.1

The void

The Sun, the Earth and all the planets of our solar system float in the vast expanse of space, effortlessly, almost magically suspended in a mystical, indefinable void. It may easily be assumed that few people today ever give a moment of thought to the question of what space actually is. To others, this question is an obsession. The nature of space has been a source of philosophical and scientific debate for thousands of years, beginning as a rational argument to substantiate the existence of “nothing”. Before humanity had any experiential knowledge of space, the debate raged over whether a three-dimensional volume could be completely devoid of all substance. If there was in fact a true void, could it even be thought to exist? Over the centuries, “the void” eventually gained acceptance as a truism, shifting the debate to questions concerning the physical nature of nothingness. Was the void truly nothing, or is it composed of an ethereal substance of some kind? The question posed by philosophers throughout the ages is: how can “nothing” exist as part of our reality, that is, since “nothing” represents a state of non-existence? This is a paradox and a contradiction in terms. Some ancient Greek philosophers expressly opposed the existence of the void for this reason. But the precise definition of the void at that time was considered to be a true and complete nothingness. One interpretation of the vacuum was related to the idea of “zero”, which is in many ways just as unfathomable as the concept of “infinity”. The Roman poet Lucretius is well known for the phrase: “ex nihilo nihil fit”, meaning, “nothing comes from nothing” – an idea originally expressed by the Greek philosopher Empedocles (495-435 BC). Empedocles’ view was that everything in our material Universe had to be born of something else, something tangible. Something cannot be created from nothing, nor could anything simply disappear into nothingness. To the Greek philosophers in this particular camp, everything that is, is and forever will be, so there was no rational way to include the idea of nothing or the state of non-existence into arguments regarding the nature of matter. www.deltagroupengineering.com

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This overlying concept marks the birth of “conservation of energy” in contemporary physics; meaning that energy can neither be created nor destroyed, but only transformed or exchanged. It’s like accounting, or balancing your bank account. Although we all may wish that money could magically appear in our bank account, or that we could just tack on an extra zero to the end of our balance, we can’t. The money has to come from somewhere. The same is true of energy – the currency of the Universe. Leucippus (5th century BC) and his student Democritus (460370 BC) are referred to as being “Atomists” because they introduced the notion that matter is composed of eternal, indivisible, fundamental units. A pure substance, the Atomists would say, could be divided and subdivided again and again until at some point it could be divided no further. The end-point of matter was called “atomos”; meaning “without parts”. But the philosophical and logical invention of the atom required something special – namely, a void. All of those unseen atoms which make up matter would need some free space to move around in – to rearrange themselves and form structures within. If there were no space, then there would be no movement and no transformation of matter witnessed in our commonplace experience. There would likewise be no cause-and-effect and the ever-dynamic motions of the Universe would cease. The Cosmos would be frozen solid without time. The Pythagoreans, as Aristotle wrote, believed that: “It is the void which keeps things distinct, being a separation and division of things”ii Aristotle (384-322 BC), however, didn’t completely agree with the Atomists. In fact, it was Aristotle himself who maintained that “Nature abhors a vacuum”. However, he didn’t necessarily disagree with them either, because his argument wasn’t actually rooted in a denial of the void. Hence, the argument became an issue of defining terms. When we speak of a vacuum, what do we mean? Aristotle would contend that if one tried to create new space where there wasn’t space before, something would always immediately rush in to fill that space. To use an example based in our own time, if one were to take a zip-sealed plastic sandwich bag, flatten it completely to remove all the air and then zip it shut, one will find that it isn’t possible to pull the sides apart in any way that could create a new space inside. Indeed, if one were to construct a similar experiment utilizing something more rigid like glass or metal, we know that it is possible to create a vacuum largely free of air and matter, but the creation of that vacuum doesn’t encapsulate a zone of “non-existence” which has been substituted in its place.

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This point is indicative of the direction the void would take in philosophical terms. The void was a necessity in the Atomists’ view; however, its existence remained impossible because a true void (as “nothingness”) could never be created by any natural process. Something, whatever it may be, must occupy newly created spaces. But what was it, exactly, that was “rushing in” to fill the space if it wasn’t some form of matter? The spaces that permeate objects and separate them from one another must be composed of something for this line of reasoning to be compatible with experience and observation. When a vacuum is created, that vacuum may be devoid of all matter, but according to Aristotle, it must still be something. It was the Hellenistic philosopher, Zeno of Citium (333-264 BC), whose teachings mark the beginnings of “Stoicism”3, so named because of the Painted Porch from which he taught. Like Aristotle, the Stoics also believed in a continuum of matter, or at least an absence of a true void in the presence of matter. They believed that there must be “some kind” of substance occupying the spaces surrounding objects and completely permeating them, as if to say that all matter was imbibed with a spirit imparting purpose of being. They called this substance “pneuma”, which was thought to be a mixture of fire and air – an energizing fluid. But unlike Aristotle, whose void-substance was somewhat static and eternal, the Stoics’ pneuma was dynamic and protected matter from dissolving into nothingness. It is this concept of nothing which has its roots in what Empedocles termed the “aether” – a mysterious and ubiquitous medium which surrounded and permeated matter. This so-called aether, supremely rarefied and quintessential, became the substance giving form to the void. The debate over nothingness (i.e., non-existence), became a futile endeavor beyond the realm of empirical study or solution. However, the nature and composition of the vacuum as a real substance termed “the aether” would be the focus of debate evermore.

1.2

The Platonic solids

Plato (427-347 BC) derived a mathematical interpretation of the aether in a similar manner to the Atomists by reducing matter into its quintessential, elemental constituents. Study of Pythagorean and Euclidian mathematics quite possibly provided the inspiration for his development of a rather poetic model of the Universe based on

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“Stoa” is Greek for “porch”. www.deltagroupengineering.com

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geometric symmetry. In his treatise called “Timaeus”, Plato describes a complete theory of matter based on what he called the “five perfect solids”. These solids represent the only perfectly symmetrical polyhedrons4 whose outer surfaces are entirely composed of a single type of regular polygon such as an equilateral triangle, a square or a pentagon. Other shapes, such as the hexagon for example, cannot form a polyhedron with a surface comprised only of hexagons. The first of these perfect polyhedrons is known as the “tetrahedron”; a three-dimensional shape consisting of four (4) equilateral triangles connected along their edges to form a threelegged pyramid structure. The next order of polyhedron is the “octahedron”; composed of two standard four-sided pyramids sandwiched together by sharing the square base of each pyramid, forming a diamond shape from eight (8) triangles. Even though the center of the diamond shape is a square on the inside, the surface is entirely composed of triangles. The third solid is the hexahedron (i.e. a simple cube). The fourth perfect solid, composed of twenty (20) equilateral triangles, is the “icosahedron”. The fifth and most unique solid, the “dodecahedron”, is composed of twelve (12) identical pentagons, forming a shape approximating a soccer ball.

Each of these five solids formed Plato’s version of a “periodic table of elements”. These elemental shapes were thought to form all material objects in the Universe5, forming the basis of alchemy practiced over the next few thousand years. Empedocles, before Plato, held the belief that only four elements existed, not including the aether, which formed the basic atomic constituents of all matter. Various concoctions of these four elements were thought to create all substances. The four elements themselves were Earth, Air, Fire and Water. The existence of five Platonic solids implied that an additional “fifth element” of matter must exist, called “Quinta Essentia”, which represented the aether. Plato’s Quinta Essentia was the substance that the heavens were made of. It was considered to be 4 5

Three-dimensional shapes. Each solid represented one of “the five” elements.

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eternal, immutable and the source of all things. In fact, ancient philosophers considered the fifth element, symbolized by the dodecahedron, to be so important that its existence was kept secret from the general population6. The belief that the aether was a substance made from the fifth perfect solid marked a different manner of viewing the aether, transforming the formerly featureless void into the quintessential origin of all things. The Quinta Essentia didn’t infuse matter with spirit in the way that the pneuma was believed to, rather, it was considered to be the fabric of the void and the basis of matter. Plato surmised that these five elements, unlike Empedocles’ four elements, could split and merge into entirely new and larger atoms and thus form different substances, whereas the four fundamental elements of Empedocles were combined in various recipes to form substances with unique characteristics. In Plato’s model, the five elements correspond to each of the five perfect solids, Element Earth Air Fire Water Aether

Geometry Hexahedron Octahedron Tetrahedron Icosahedron Dodecahedron

Plato describes how the first four elements could recombine to form new elements; however, the dodecahedron was unique. The aether could not be broken up into more fundamental subunits or recombined with other elements like the others could. This is due to the fact that the surfaces of the other four solids may be further subdivided into two types of right triangles. One of these is formed by slicing a square diagonally through its center. The other is produced by dividing an equilateral triangle by drawing a line from one tip through to the center of the base, thus dividing it in half. What makes the dodecahedron unique in this case is that it is not possible to build a pentagon from just these two types of right triangles, as it is for the other shapes. The other elements were malleable, whereas the aether was eternal. The Quinta Essentia thus became the fabric of the Cosmos upon which all matter was thought to be embroidered. Oddly enough, triangular symmetry is mirrored in the subatomic particles and quarks comprising the atoms as we have come to understand them today. Our contemporary atomic model is 6

Carl Sagan, “Cosmos” television series. www.deltagroupengineering.com

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composed of three subatomic units; protons, neutrons and electrons. Moreover, the proton is composed of two “Up” quarks and one “Down” quark; whereas the neutron is composed of one “Up” quark and two “Down” quarks. These quark triplicates (and the triplicate subatomic components of the atom) can be likened to Plato’s sub-elemental triangles! Even though we now know that Plato’s conjectures were nothing more than philosophical representations of reality, it is quite surprising that the basic tenets of his theory display such prescience. One is forced to consider the possibility of a deeper order in Nature which Plato was able to illuminate through his careful study of mathematical symmetry.

1.3

The laws of motion

Fast forward to Sir Isaac Newton a full two-thousand years later and the aether remains. From Roman times, to the dark ages, through the middle ages and the Renaissance, the Platonic solids formed the basis of physics and alchemy. The Quinta Essentia remained a key ingredient in the many concoctions of alchemical practice. Furthermore, it was the practice of alchemy, in the western world at least, that would contribute greatly to the development of the Scientific Method and the field of chemistry; in effect, generating the disciplines of science we know today. For the sake of brevity however, it will suffice to mention that the wealth of information available from over two thousand years of world history relating to alchemy shall be delegated to the reader for further investigation. However, what cannot go unmentioned, in at least some detail, is Newton’s philosophical and scientific stance regarding the aether. In his writings, Newton’s stance concerning the aether was rather two-sided. On one hand, in his treatise called Opticks written in 1704, he employs the aether as the basis for most of his observations related to the nature of light and optical phenomena. In his Principia, in which he develops the laws of motion and gravitation, the aether is also present as the medium by which force is transmitted to objects

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separated by some distance in space. On the other hand, in his writings7 Newton was very careful to remind his readers that he would “feign no hypotheses” for what the aether could physically be, even though the aether remained the basis for his reasoning throughout. Newton felt that the aether should remain in the realm of the occult and metaphysics, even though he consistently relied upon the aether as a physical justification for his mathematical theories. In Newton’s laws of motion, gravity was thought to be a “force” which attracted bodies to each other in the heavens, just as it seemed to do here on Earth. Objects invariably fall to the Earth and it was thought that an actual, physical force pulled everything to the surface. It was the force of gravity that pulled the legendary apple from the tree that fell on Newton’s head, inspiring him to eventually decipher the laws of gravitation. Even to this day, this colloquial notion of what gravity is persists in our language. We still call gravity a “force”, and we still, erroneously, talk about it as though it has the ability to reach out and pull in objects from afar. Gravity in Newton’s time was thought to be transmitted instantaneously through space via the aether, imparting a “pulling” force on other objects. Even though Newton implicated the aether as the medium transmitting the force of gravity, he could not logically reconcile how a “fluid-like” description of the aether could allow objects in the heavens to move as they do, simply because fluids act to impede the movements of objects. The planets moved eternally and without resistance through the aether, so how could objects move in a fluid without any resistance to slow their motion? If the aether was some kind of substance, it should induce resistance to the orbital motion of planets and cause them to spiral into the Sun. Newton writes in his work, Opticks: p.528 Qu.28. “A dense fluid can be of no use for explaining the phenomena of Nature, the motions of the planets and comets being better explained without it. It serves only to disturb and retard the motions of those great bodies, and make the frame of Nature languish; . . . so there is no evidence for its existence; and, therefore, it ought to be rejected. . . . the main business of natural philosophy is to argue from phenomena without feigning hypotheses, and to deduce causes from effects, till 7

“Principia” (1687) and “Opticks” (1704). www.deltagroupengineering.com

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we come to the very first cause, which certainly is not mechanical and not only to unfold the mechanism of the world, but chiefly to resolve these and such like questions. What is there in places almost empty of matter, and whence is it that the Sun and planets gravitate towards one another, without dense matter between them? Whence is it that Nature doth nothing in vain; and whence arises all that order and beauty which we see in the world?” Thus, Newton recognized that “something” occupying the spaces between objects accounted for transmission of gravitational force (it just couldn’t be fluid-like). Otherwise, how could one object like the Earth affect the motion of the Moon so far away with just empty space between them? In Newton’s time, this strange, disconnected cause-and-effect relationship was referred to as “action-at-a-distance”, sparking another great debate in physics that raged until Albert Einstein’s development of General Relativity (GR) approximately two hundred years later. Newton’s work, however, was immune from this argument even though it remained a point of great contention that pestered and haunted him ceaselessly. Newton was immune from the action-at-a-distance debate because he eloquently demonstrated how simply understanding the regular, predictable behavior of Nature can often suffice, i.e., it is sometimes adequate to formulate a mathematical description of Nature’s laws “without feigning hypotheses” for why they occur. He formulated a mathematical structure describing the motions of the planets without espousing a mechanical, physical manifestation of its behavior. If it works, so be it; thus, it became possible to discuss the aether in purely philosophical terms without invoking it as a necessity for the laws of gravitation and mechanics. Newton’s equations have allowed us to design rockets and enabled planetary exploration in our solar system. It is also Newton’s principles of optics which enabled the invention of the photographic equipment used to document these great adventures. All of this technology has been made possible without ever having to understand the mechanics of the aether. Thus the need for the aether evaporated, even though its existence could still be debated; its precise nature remaining as mysterious and indefinable as ever.

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1.4

The luminiferous aether

One of the most triumphant and influential discoveries in human and scientific history was James Clerck Maxwell’s development of the four equations for electromagnetism in 1864. Based upon earlier work by Michael Faraday, the introduction of the laws of electromagnetism would provide the spark that would transform the world forever. In much the same way that Newton derived the laws of motion and gravitation from first principles, by feigning no hypotheses, and through uncorrupted observation of Nature, Maxwell was also able to successfully merge the forces of electricity (E) and magnetism (B) into a system of interactions he called “electromagnetism”. His set of equations describes the behavior of electric and magnetic fields and how they interact with matter. He was also the first to show that light itself was simply an oscillating wave composed of intertwined electric and magnetic fields.

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The development of electromagnetic theory hailed the development of Relativity and Quantum Mechanics (QM). Maxwell’s equations were a monumental achievement, not only because of their elegance, or because of their immense usefulness for technological purposes, but because they proved that a deep connection between electricity and magnetism existed. Electricity and magnetism were once thought of as entirely disparate phenomena. This was one of the first so-called “unification” theories, illustrating that forces once thought to be unique were, in actuality, one-and-the-same. During the latter part of the 19th century, British physicists (particularly those following Maxwell’s lead in the search to explain the inner workings of electromagnetism) tended to continually turn back to the notion of the luminiferous aether in order to help prove or disprove emergent theories. This embodiment of the aether was sonamed because it was believed to be the medium that carried light, i.e., electromagnetic waves, and was thus called “luminiferous”. During the Victorian period, technological advancements that spawned the industrial revolution contributed to the rapid development of a mechanistic world-view. British society was bearing witness to the triumph of the machine, and the machine rapidly and drastically transformed the social and cultural landscape. The new technological developments of the age would shape the spectacles through which British scientists would view the Universe as well. These new lenses skewed the vision of theorists at the time, causing them to view the fabric of space in terms of cogs and wheels — an invisible yet intricately and seamlessly connected clockwork of interactions via which objects and light travelled through space. This emerging industrial revolution gave physicists cause to try and explain electromagnetism in terms of this new mechanical language of the day. Light itself was discovered by Maxwell to simply be an electromagnetic wave propagating through space. But what did this actually mean? What were these waves of light propagating in? What were they made of? We can easily imagine waves of light propagating through space like waves on the surface of the ocean, which emanate from a source and roll in towards the shore. But the very idea of a wave implies movement through a fluid, or some kind of medium. So the question was: what kind of substance carried these waves of light? The aether was an attempt to provide a physical explanation for a rather abstract mathematical representation of Maxwell’s equations for electromagnetism. The form of this physical substance was modeled after the most prevalent mechanistic imagery of the time. Even today in our own era, some theorists argue for an

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“information” philosophy as the basis for conceptualizing elementary particle phenomenon, so that matter itself could be thought of in terms of binary bits of information. The fundamental constituent of our Universe, according to information theory, is not really bits of “stuff” but rather bytes of informationiii. In our contemporary society, this being the “information and computing age”, we are naturally tempted to create philosophical models reflecting our own zeitgeist in precisely the same way that the Maxwellian physicists did in their quest for a mechanical interpretation of physical reality. If nothing else, the aether provided scientists at the time with a convenient pedagogical tool for describing the way in which electric and magnetic forces interacted. However, there was a driving desire to actually prove the physical existence of the aether, and in doing so provide a physical description of the seemingly magical effects of electromagnetism. The Maxwellian cohort was envisioning a poetic and monumental concept that could unify physical phenomenon as purely mechanical movements of the aether, and thus provide a new paradigm that was fully in-line with the late 19th century’s mechanical view of the Universe. If the problem of the aether could eventually be solved it would certainly be a scientific triumph to rival all others, and provide instant fame and glory for those who developed it. Any mechanical proof of the aether’s structure would also be the perfect way to eliminate the nagging problem of action-at-a-distance, which was a source of debate since Newton’s time. The Maxwellians wanted a complete theory that would finally quiet metaphysical questions regarding exactly how not only electromagnetic signals were propagated, but also how planets separated by vast distances in space could interact with one another gravitationally. Following the lead of Descartes, theorists even developed models to try and show how matter itself might be understood as a manifestation of the aether in the form of “vortex rings”. In this model, atoms could be thought of as tiny stable vortices within the aether “fluid”. But why hold on to these purely hypothetical models of space if one could successfully predict and harness the phenomenon of electromagnetism through pure mathematical reasoning alone? The fact of the matter was that for some time, the aether models simply supported the theories being put forth. They held up mathematically as a framework for theories that were often too abstract to make any real sense to the average person, or to the average physicist for that matter. The classical physicist could present a working hypothesis to explain electromagnetic waves and demonstrate how they might be mechanically propagated through the aether. www.deltagroupengineering.com

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Physicists at the time wrestled with this conundrum between the concepts of “theory” and “method”. If the method works beautifully, is there any real need to provide a concrete theory to explain why the method works? Is it not enough to simply provide an elegant set of formulae which can be used to describe how Nature works even if we still don’t understand why it works that way? The fervor with which the Maxwellians sought to solve the structure of the aether was largely motivated by a desire to unify physics in its entirety. This desire remains just as strong today as it did in Maxwell’s time. Born of a desire to provide an allencompassing theory of electromagnetism, the aether was invoked because it was convenient, manageable and contemporary. It seemed that a working theory was not only attainable, but almost within reach. Unlocking the inner-workings of the aether became the Holy Grail for the British Maxwellians, not only to make their work on electromagnetism credible, but to also render it immune to doubt and criticism. Even more persuasive was the tantalizing hint that by defining the aether, they would also finally unveil the mysterious inner structure of the Cosmos. This idea of the aether actually had great philosophical value overall, but only in its use as a tool. Eventually, with a greater reliance on purely mathematical approaches to the problems of electromagnetism, and due to the results of the Michelson-Morely experiment, the aether was eventually abandoned. As the 19th century began to ebb away into the 20th, Einstein later explained that: “mechanics as the basis of physics was being abandoned, almost unnoticeably, because its adaptability to the facts presented itself finally as hopeless”iv.

1.5

Michelson and Morely

The final nail in the coffin for the luminiferous aether came in the form of a famed experiment performed by Albert Michelson and Edward Morley in 1887v. The experiment itself was formulated on the premise that if the Earth was actually moving through a fluidlike medium, we should be able to detect our movement through it. Imagine you are traveling on a train. Let’s say you decide to walk to the diner located two cars ahead of you to have lunch. As you walk along the aisle in the direction the train is traveling, and you walk at a rate of 4 kilometers per hour (k.p.h), your speed relative to the ground outside will be 4 (k.p.h), plus the train’s velocity which is 100 (k.p.h), yielding a total combined velocity of 104 (k.p.h). When

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you walk back to your seat after lunch, your velocity relative to the ground would be the train’s speed minus your walking speed. If the aether existed in the form envisioned by the Maxwellians, then the speed of light through the aether should be shown to have a velocity relative to some “ground speed” of the aether. Michelson and Morley tested for the presence of the aether by sending out two perpendicular beams of light from a single point source, which were reflected by mirrors back to a single detector. The design of their experiment relied on the wave-like nature of light.

In 1803, Thomas Young demonstrated that when light was directed at an opaque screen with two slits cut in it, the two beams of light that came through each slit would interfere with one another to form a pattern on the wall behind the screen. Known as the “two-slit” experiment, Young discovered that light was “wave-like”; waves of light could interfere with each other just like waves on the surface of a pond, creating peaks and troughs of interference. But these results also spawned great debate and fascination about the mysterious nature of light which continues to this day. Paradoxes raised by variations of www.deltagroupengineering.com

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the two-slit experiment continue to baffle scientists and have brought to light some of the most perplexing and bizarre behavior ever to be found in Nature.

Because of Young’s pioneering two-slit experiment, Michelson and Morley knew that if they directed two perpendicular beams outwards and then reflected them back to a detector, the two beams would generate an interference pattern indicating whether the beams of light travelled at different rates due to variance in “ground speed” relative to the aether. Taking into account the rotation and relative motions of the Earth around the Sun, they demonstrated that no matter what relative direction the beams of light were traveling in, no interference pattern was generated indicating a preferred direction, or flow of the aether. This experiment silenced the debate over the notion that there could be a mechanical, fluid-like aether filling space, or one that acted as the medium through which light propagated. But Michelson and Morley more accurately demonstrated that there is no preferred reference frame from which to measure the propagation of light signals. It is this idea that became the spring-board for Einstein’s Relativity theory, where light speed is constant and everything else, including time, is observed relative to the speed of light.

1.6

Space-Time

Michelson and Morley may have disproved the existence of the mechanical, luminiferous aether, in such form as it was thought to exist in Maxwell’s era, but this didn’t stop another more contemporary version of the aether from emerging with a vengeance.

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Einstein is at least partially responsible for both destroying the rusty, mechanical aether of old and replacing it with a brand new aether all his own. Although this time, unlike the Maxwellians, Einstein feigned no hypotheses for what physical manifestation the aether might take. Einstein’s development of Relativity and the notion of a new aether termed “curved space-time” removed the idea that gravity was a force mediated by the ill-defined aether of Newton’s time, and thrust a revamped version of the aether into the limelight. Einstein’s equations show how an object’s motion in a gravitational field will be determined by its “geodesic” path, or shortest path in units of time between two points in a curved spacetime manifold. This means that as an asteroid, for example, enters the gravitational field of the Earth, it will be bent into a path which makes it appear as though some kind of attraction towards the Earth is taking place. The asteroid may even enter into an elliptical orbit due to this changing trajectory. But this is not to say, as Newton implied, that some mysterious force is at work, acting from a distance on the asteroid and pulling it closer to the Earth. Einstein introduced the concept of curved spacetime to remove the notion that a “force” pulls the asteroid into a new trajectory. The most common example of how a planet or a star produces this curved space-time effect is often depicted by the analogy of setting a cannon ball on a taut rubber sheet. The cannon ball will sink down into a depression produced in the flexible sheet. If a marble is rolled in from the edge (here representing the asteroid) the marble’s path will be changed due to the curved topology of the rubber surface it rolls upon. It will accelerate as it rolls downward in a direction towards the cannon ball and then curve around it. If we weren’t able to see the rubber sheet, we might conclude that the marble was somehow being attracted to the cannon ball. This analogy of curved space-time works brilliantly to describe precisely how objects behave in gravitational fields! There is no real force required to change the trajectory of the asteroid, it www.deltagroupengineering.com

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merely follows a path of least (or zero) resistance through a curved space-time manifold induced by the presence of the Earth. The geodesic motions of objects in curved space-time may be likened to the flight path an aircraft takes when it travels between cities. If one were to take a direct flight from San Francisco to Paris for example, it might come as a surprise to some passengers that the flight doesn’t travel directly from west to east, over Denver, then New York, across the Atlantic and on to Paris. It flies north in the direction of Seattle, over Canada and Hudson Bay, then past the tip of Greenland and finally southward towards Paris. At first glance, this route seems very odd and inefficient, but if you were to use a piece of string to try and find the shortest length that will connect San Francisco and Paris on the globe, you will notice that the polar route is indeed the shortest and thus, most efficient path. This path is considered to be the most direct “straight line” route on any curved three-dimensional surface. In the case of Relativity, the curvature of space-time is four-dimensional: including the three dimensions of volume and the fourth dimension of time. Thus if we consider the asteroid again, it isn’t being pulled by any magical force towards the Earth, it is simply following a straight-line path of zero resistance, characterized by its shortest time-interval distance between two points in the curved manifold. This notion of curved space-time provides the basis for Einstein’s GR. The equations describing gravitational fields work by modeling this four-dimensional curvature mathematically. This geometric contrivance has led to the theoretical predictions for “black holes” and other strange phenomenon in the Universe. But the problem is this: just what, exactly, is being curved? And if the vacuum of space is indeed a formless void, then how can “nothing” have a shape? GR not only invokes, it requires the existence of some kind of medium or manifold to form the basis of this curvature, and this medium must be capable of conveying information indicating whether the space-time an object travels through is curved or not. On May 5th, 1920 at the University of Leiden in the Netherlands, Einstein gave an address on the issue of the aether and said: “According to the general theory of relativity space without aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any spacetime intervals in the physical sense.”

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The physicality of the space-time fabric was as undeniable as it was indefinable. GR still works beautifully to this day and has extended the classical framework of Newton’s laws of gravitation and motion into the modern age. However, it is extremely important to remember that GR is simply another method we have at our disposal for making calculations predicting the behavior of objects in the Universe, particularly in extreme gravitational fields or when traveling at velocities near the speed of light. Curvature should not be misinterpreted as an actual, physical interpretation of space itself. It is commonplace today to substitute the GR model for the real thing, instead of the other way around. In this regard, Relativity should be regarded as being a word which may be utilized to express an idea or describe an object; in language, we would rarely confuse the word for the real thing. Scientists of this era wish to formulate a true and complete explanation of gravity, in much the same way that the Maxwellians needed to interpret the physical meaning of electromagnetism through an understanding of the luminiferous aether. Newton, like Maxwell, feigned no hypotheses in his explanation for why his equations were true, he only demonstrated that they were. Einstein did the same with Relativity. However, we must not take this notion of curvature too literally, and we must keep our minds open to other, potentially more complete interpretations of Nature. But alas, even with Relativity, we are still left wrestling with the “imponderable” demon that is the aether.

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1.7

The Casimir Effect

If we look to water as a source of inspiration, in all of its whorls and spirals, waves and currents, one can see a microcosm of the Universe. In each spiral whirlpool one sees the same form as a typhoon as viewed from space, and looking out into the Cosmos, one sees spiral formations in the many billions of galaxies inhabiting our visible Universe. Waves and ripples moving across the surface of water may be likened to sound waves in the air, or waves of light traversing the vast distances of space. The sea is indeed a mirror of the Universe. Simply by observing the elemental forms the ocean creates, and by

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studying its movements and behaviors, one may observe the fundamental shapes of Nature — the language of Nature itself. The writing is on the wall, so to speak. All we need to do is learn how to read. One way to read the language of Nature is through the simple act of observation. Our understanding of Nature is instinctive and innate, but sometimes we lose our ability to observe objectively. Our innate reflex to analyze counters our equally intrinsic ability to understand. We may become so clouded by our preconceived beliefs about the world that we begin to see only what we expect to see, as if our minds are lenses that have been warped by the weight of rules and expectations. We rush to make sense of an observation within the context of our own consensual reality, culture and value system. Because of this, it is important that we remember to hone our objective observational skills. Great personal and scientific discoveries are made when we clear away the flotsam and jetsam of preconceived beliefs and simply observe a process in Nature. We may also draw analogies from what we observe in the natural world to foster a better understanding of complex theoretical predictions that seem to defy common logic. With the advent of QM and QED our understanding of the inner sanctum of matter has increased exponentially, and as our understanding of such highly complex and un-seen phenomena expands it becomes increasingly difficult to find commonplace examples enabling us to make sense of these strange new concepts. Instead of inventing culturally subjective mechanisms to explain the physical world, like the British Maxwellians did in an attempt to explain electromagnetism, we should cite examples from our direct and unfettered experience of Nature. Max Born, one of the fathers of QM said: “My advice to those who wish to learn the art of scientific prophesy is not to rely on abstract reason, but to decipher the secret language of Nature from Nature’s documents: the facts of experience”. As we come to learn more about QM, we also begin to understand more about space. We assume that the vacuum of deep space is a true and complete void, and that material objects occupy a three-dimensional volume within it. Space, in this view, is really nothing more than a dimensional matrix containing matter, and when the matter is removed, we are left with a volume of empty space equal to the volume of matter that was removed. Quantum Field Theory (QFT) models the vacuum of space as being something quite different than what most of us imagine it to be. Quantum theory tells us that if we were to take a volume of space here www.deltagroupengineering.com

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at the surface of the Earth for example, pump out every last molecule of air, and shield all thermal radiation so that the vacuum was at absolute zero temperature, we would still be left with a vacuum of space filled with energy fluctuations. Energy, therefore, can never be completely “pumped out” of a given volume like air can. Energy will always be propagating throughout the volume of the vacuum because the vacuum is, in a sense, composed of energy. This is due to the fact that energy, as it propagates as an undulating sine wave, can never fully come to rest. Even at its lowest energy state the energy must cycle about its ground state; in other words, energy never flat-lines, it must always cycle. When all the quantum states of lowest energy are summed across a given volume of space, it adds up to form what may be considered to be a sea of quantum energy, with waves propagating and fluctuating about with random direction and intensity. This model suggests that the vacuum is actually composed of electromagnetic waves (i.e. photons of light), that together form an ocean of energy termed the Quantum Vacuum (QV). A ball floating on the surface of a roiling sea will be jostled about by the waves; it wouldn’t just sit there motionless. Likewise, when we think of the vacuum as being an undulating sea of quantum energy fluctuations, it is no longer possible to disregard the effect that the vacuum has on matter, and likewise, the effect matter has on the vacuum. Building upon this conceptual framework the Dutch physicist, Hendrik Casimir, predicted that the vacuum should have a rather strange effect on matter.vi The phenomenon he predicted has since been dubbed the “Casimir Effect”. The QV is composed of a near-infinite spectrum of electromagnetic waves of different frequencies8 (cycles per second), amplitudes (wave “heights”) and direction. The QV is somewhat like quantum “white noise”, analogous to the random static seen on a dead television channel9. In free space, far from the presence of any matter, the quantum static of the QV is uniformly random. The Casimir Effect emerges when matter is placed within this finely rippled terrain of the QV. The effect is observed when two flat metal plates are placed parallel to one another in a vacuum. Here, a “boundary condition” is established in this otherwise uniform space, changing the nature of the wave conditions existing in the QV. Each plate establishes a boundary, physically separating the region between 8 9

Termed “modes”. Entirely random and incoherent.

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the plates from everything else outside them. This simple point may seem ludicrously obvious, but the importance of boundary conditions cannot be overstated. They are the essential hallmark of all dynamic systems. Surrounding the plates, and in the space between them, energy fluctuations exist within the QV as waves, each moving in a random direction and impacting the surfaces of each plate from all sides. However, the waves between the plates will begin to “calm” (figuratively speaking) as the plates are drawn closer together. The calming effect the plates have on the QV between them is due to the fundamental quantum nature of photons. Each photon comprising the QV is a wave and QM states that, it is impossible for a “half-photon”, or any fraction of a photon, to exist. Each photon can only exist as a whole wave represented by a complete 360° cycle10. Thus, no QV modes11 with wavelengths wider than the gap can exist between the plates! There cannot be one-third of a wave between the plates, for example. If the distance between the plates is one micrometer, for instance, then only modes with a complete wavelength less than one micrometer may physically exist within that space. As the plates are drawn very close together, more and more energy modes become excluded from existence between the plates, and conversely, more energy modes exist outside the plates than in between them. Thus, a net difference in energy density between the outside and inside the boundary is established by the plates. Because there is, in effect, more energy on the outside than the inside, “pressure” builds on the outside of the plates, pushing the plates together with a force inversely proportional to the separation distance between them. That is to say, as the gap between the plates gets smaller and smaller, the force pushing on them becomes greater. However, this “Casimir Force” is only observed when the distance between the plates is exceedingly small. Likewise, the magnitude of the force pushing them together is equally minute.

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A “quantum” bit of energy. Electromagnetic waves. www.deltagroupengineering.com

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It wasn’t until 1997 that the attractive force that Casimir predicted was actually confirmed by two independent experiments. The first measurement was made by Steve Lamoreaux, then at the University of Washington in Seattlevii. The measurement was taken utilizing a slightly curved gold-plated lens mounted on the arm of a torsion balance. The lens was gradually moved towards a flat plate, and as the lens face attached to a balance arm was brought within fractions of a millimeter of the plate, the torque produced by the attractive Casimir Force between the lens and plate was measured by the change in electrical force required to compensate for the torque being produced. Umar Mohideen and Anushree Royviii independently confirmed the Casimir Force measurement just a year after Lamoreaux published his results. In an experiment similar to that of Lamoreaux, Mohideen and Roy used an atomic force microscope to measure the Casimir Force. The Casimir Effect marked a key turning point in the philosophical debate on the true nature of the vacuum. Casimir’s discovery provided strong evidence, in the form of a physical, measurable force, that the so-called “empty” vacuum of space is in fact, something more resembling a plenum of energy. Just as a boat is moved by the waves of the ocean, matter suspended in the QV sea affects, and is affected by, the vacuum surrounding it. From this sea of energy, an ocean of possibilities emerges. For when we consider the vacuum to be “something” rather than “nothing”, it suggests that the vacuum itself holds the key to understanding the concrete physics behind the abstract interpretation of GR.

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2

All Things Being Equal “Give me a firm place to stand and I will move the earth.” • Archimedes (287-212 BC)

2.1

The cosmic counter-balance

For thousands of years the aether has been invoked as a means of explaining various physical phenomena. But all attempts to explain the aether have been relegated to the realm of speculation and philosophical exercise. There is nothing shameful about conjuring up the aether to make sense of the world, however. Our understanding of Nature seems to require “some kind” of medium acting as a background for the exertion of force and movement. Birds in the sky fly by manipulating the air, fish swim by manipulating the water surrounding them and human beings walk by pushing off the solid ground beneath our feet. All these natural actions are brought about through the action and reaction of forces, and we observe this balancing of forces in every moment of our existence, whether we are consciously aware of it or not. Sir Isaac Newton learned from Galileo that the nature of gravity was to cause objects to always fall at the same rate of acceleration regardless of their mass. He applied this observation to objects that not only fell, but to objects that were thrown as well. Newton found that it was indeed possible to mathematically predict how far an object could go and where it would land if thrown or ejected with a given amount of force. For example, if one fires a cannon, the distance the cannon ball travels before it falls to the ground is dependent upon the angle at which it is shot, the mass of the ball itself, the force with which it is shot and the constant acceleration of gravity acting on it (not taking into account friction from air, etc.). The same is true for a bullet for that matter, or any object one might wish to launch, throw or shoot. The revelation enabling Newton to demonstrate that it was gravity keeping the planets in orbit, and not some mysterious or www.deltagroupengineering.com

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divine structure of the heavens, was born of his ability to predict the precise behavior of falling objects. Newton wondered what would happen if a cannon atop an enormous mountain reaching high into the sky fired a cannon ball with any amount of force he wished. He demonstrated mathematically that firing the cannon ball straight ahead with sufficient force, the ball wouldn’t land until it reached half way around the globe, or with even more force, fully around the globe. If the cannon ball could be shot with sufficient force, Newton imagined, the ball might never land! Instead it would enter into orbit around the Earth, perpetually falling around the globe.

In a flash of brilliant insight, he likened this to the motions of the planets as they orbit the Sun, and to the motions of the Moon about the Earth! We take this knowledge for granted, but in Newton’s time this was an absolutely monumental discovery. The planets and the objects in the heavens were all behaving according to a single, fundamental law of gravity pertaining to cannon balls and planets just the same. Gravity was found to be just as ubiquitous and ever-present across the vast distances of space as it is here on Earth. In Newton’s time, gravity was regarded to be a literal force. We continue to colloquially use the expression, “the force of gravity” but we now know that this is not an accurate description. The argument raised by Newton’s gravitational model of planetary motion supposed a constant force existed, always pulling on the planets in order to keep them in motion. The force of gravity had to act on a planet even at great distance from the Sun, which was also the source of that force, and had to do so with nothing but empty space in between. This was a real conundrum for many physicists at the time

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because it was unclear how the force of gravity was transmitted across such vast distances of emptiness. However, the concept of “force” remained the central focus in Newton’s laws of motion and would remain an inescapable conclusion of Newton’s thinking despite its thorny point of contention. In order for an object to change from one velocity to another, it needs a push to overcome the acceleration reaction force termed “inertia”. Objects in uniform motion, or at rest, will remain in uniform motion unless otherwise acted upon by an outside force; this is Newton’s first law. Of course, if one considers common earth-bound examples such as the acceleration of a boat or car, there are other factors at play like friction between the object and the surface it travels upon, adding to the complexity of this relationship. However, in simplest terms, Newton’s first law states that it is fundamentally necessary to supply energy to an object to alter its uniform motion. Let’s suppose you are riding inside a rocket, traveling at constant velocity through interstellar space, and you suddenly spot an asteroid in your path. You would immediately power the thrusters in an attempt to avoid the collision. If your seatbelt did not happen to be properly fastened at the time you fire the thrusters, you would be abruptly slammed up against the opposing side of the ship. By firing the thrusters you are using chemical energy to impart a force on the exterior surface of your rocket, pushing the rocket into a new trajectory and allowing you to successfully dodge the oncoming asteroid. But when traveling inside the ship, without a seatbelt, you are really only moving with the same relative uniform motion as the ship. So for a moment, when the ship suddenly veers to one side, your inertial mass wants to maintain its straight-line path of motion. The Gforce you feel as you are slammed to one side of the cockpit is a result of your being squeezed between the side of the cockpit pushing you in a new direction, and the inertial reaction force countering your change in motion, impinging on you from the opposite direction. The energy from the thrusters is really only necessary to counter the inertial reaction force experienced when changing direction; however, this isn’t only true in free space. We feel inertial forces all the time. In a car, you feel inertial force when you accelerate, make a sharp turn or slam on the brakes. It’s the same inertial force which makes you sink into your seat in an airplane when you are about to take off. Imagine for a moment that you are riding in a car and feeling the force of inertia pushing you into your seat when you accelerate. Now, imagine that everything disappears aside from you in your seat – no car, no road, no landscape outside the window, nothing – just you being pushed into your seat as www.deltagroupengineering.com

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you speed up. Moreover, let’s say you take your foot off the accelerator and you resume a constant rate of speed. Suddenly, the force you had felt pushing you into the seat subsides and you feel no force, other than gravity holding you in your seat. Since nothing else exists that you know of in the Universe – no road, no other cars or trees going by as you look to your left or right; how do you know if you are moving? The only way you can really tell if you’re moving is if you accelerate or change your motion and thus, feel the force of inertia. Let us also assume that even though you can’t actually see the steering wheel, you can still feel it in your hands. If you were to suddenly rotate the steering wheel to make a sharp turn, an invisible force would abruptly push you in the opposite direction of your turn. The turn itself merely marks a change in the otherwise constant motion you were in before you turned the wheel. Whether you are traveling in empty space or on Earth, inertial force is felt when accelerating or change in motion occurs. The force felt is immediate and local to you, wherever you might happen to be in the Universe. Trying to escape the force of inertia would be like trying to out-run your own shadow. It can’t be done. It is the inescapable nature of matter itself. But where does this strange force come from? Strange and mysterious as it may seem, this powerful force arises instantaneously out of the vacuum of space, as if by magic, to physically inhibit changes in motion.

2.2

Expansion and compression

How is the Universe arranged so that we feel no force when we are stationary or in a uniform state of motion, but we suddenly experience a force when changing from one state to another, no matter where we may happen to be? Why does matter resist acceleration if there is nothing in the way to impede it? And how is it that objects feel the force of gravity in space, separated from other objects by vast expanses of nothingness? These questions hint at a connection between the forces we have labeled “gravity” and “inertia”. This connection is, in many respects, responsible for the development of modern physics. The Czech-Austrian physicist, Ernst Mach, proposed a possible mechanism for inertial force and its connection to gravitation in the late 1800’s, while Einstein was only in his teens beginning to explore the frame of thought that would lead to the development of Relativity a decade or so later. In fact, it was Einstein himself, who in

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describing Mach’s ideas on the subject of inertia, coined the term “Mach’s Principle”. Mach’s Principle is based on the notion that all matter in the Universe is connected by an invisible bond. Mach surmised that objects felt forces countering their acceleration because all objects were linked together by a web of gravitational interactions. If one imagines an infinite Universe with matter in the form of stars and planets peppered throughout space, one may assume a fairly uniform average distribution of matter throughout the Cosmos. All of these planets and stars, Mach reasoned, would radiate gravitational fields into the space surrounding them. Mach figured that if all the gravitational fields from all the matter in the Universe were averaged across space, then at every place in the Universe one should feel the effects of this unified field. No matter where one might find oneself in the Universe, one would always feel a gravitational resistance opposing any change in motion. It is as though matter is locked in a gravitational web and when an object attempts to change its position within it, the web compresses in the direction of acceleration and is stretched out behind it. Mach is historically noted primarily for his development of the “Mach Numbers” (i.e. the “Mach Scale”12), and he predicted what we understand today as being the “sonic boom”. Mach also studied the work of Christian Andreas Doppler in great detail. Doppler, another Austrian physicist, is noted for the “Doppler Effect”. As an ambulance races along, its siren emits waves of compression in the air. These waves rush at high speed to our ears, and we detect and interpret these compression waves as sound. The rate at which the sound waves travel through the air is generally constant, so the additive motion of the ambulance causes the waves to be compressed in its direction of motion. As the ambulance approaches, the siren sounds higher in pitch13 than it does as it passes by. As the ambulance rushes past, the sound of the siren will quickly bend down to a lower pitch. Because the sound waves are compressed in the direction of motion, the waves are squeezed together, raising their frequency14. The more sound waves heard per second, the higher the pitch will be. As the ambulance drives past, the sound waves left behind are stretched out and reduced in frequency, thus we hear the pitch bend down to a lower register. 12

The ratio of an object’s speed to the speed of sound in the fluid the object is traveling in. 13 An indication of sound wave frequency. 14 The number of sound waves heard per second. www.deltagroupengineering.com

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Mach’s Principle for the origin of inertia may be likened to a gravitational Doppler Effect. According to the principle, objects are pulled uniformly in all directions by the average gravitational field in space, acting like the air through which sound travels. When an object accelerates, it feels an immediate opposing force – as if the field was being compressed in the direction of acceleration. Energy input is required to counter inertial resistance, or in the case of Mach’s Principle, to compress or decompress the static gravitational energy in the direction of acceleration or deceleration. The Doppler Effect doesn’t only apply to sound waves; it also applies to light waves. This is most commonly known in astronomy and cosmology as “red-shift”. “Blue-shifts” and other frequency shifts exist as well – it all depends on a light-emitting object’s motion relative to an observer.

Our modern-day cosmological creation story begins with the “Big Bang”, as it has come to be known. This paradigm states that the Universe was born of a single, unfathomably powerful explosion which gave rise to not only all the matter and energy in the Universe, but the Universe itself! According to the Big Bang theory, everything was packed into a single, infinitesimal speck before the Universe was born. This “singularity” was the seed of our Universe from which all things grew. Even time emerged as a result of the Big Bang; but how is it that we have come to this profound, albeit, bizarre-sounding conclusion? All one has to do is listen for the answer in the changing pitch of the ambulance siren as it passes by, for our Big Bang creation story owes its origin to the Doppler Effect. High in the mountains east of Los Angeles, the famed astronomer Edwin Hubble spent many a night throughout the 1920’s observing nebulous smudges in the night sky from the Mount Wilson Observatory. These fuzzy points of light, on much closer observation,

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were found to be whole other galaxies much like our own. This discovery expanded the scale of the known Universe by several orders of magnitude. Before Hubble’s time, the Universe was thought to be only slightly larger than our15 galaxy. At that time, the Milky Way was the Universe and when Hubble demonstrated that these fuzzy nebulae, once thought to be part of our own galaxy, were in fact distant galaxies themselves, the range of the Cosmos expanded beyond all comprehension. Along with his colleague, Milton Humason, Hubble set out to measure the distances of these galaxies by studying the Cepheid variable stars within them. Cepheid stars fluctuate in brightness and possess a narrow range of intrinsic luminosity. Because these stars possess such similar luminosity, their relative brightness may be applied as a standard by which to measure the distance of the galaxies containing them – the dimmer the Cepheid, the more distant the galaxy. However, this isn’t what Hubble is historically noted for discovering. Hubble is famous for having combined his Cepheid data with measurements taken by Keeler, Campbell and Slipher, which measure the red-shifts associated with the same galaxies Hubble was observing. What he discovered, as a result of this marriage of observations, would come to be known as “Hubble’s Law”; which brought about the Big Bang history of the Universe we are so familiar with today. Here’s how he did it: Light waves, like sound waves, can Doppler shift. As a light-emitting object moves through space, the light waves emanating in the direction of movement are compressed in frequency. Hence, light waves compressed to a higher frequency are thus shifted towards the blue end of the visible spectrum. Similarly, light emitted in the trailing direction of the object’s motion is decompressed and shifted towards the red end of the visible spectrum. Hubble noticed that the light coming from the most distant galaxies, based on his Cepheid data, were more red-shifted than ones close by and the magnitude of red-shift was directly related to the galaxy’s distance from us; implying that all the galaxies in the heavens were moving away from us. However, the implication was not that the galaxies are moving away from us per se, but that space itself, in which we reside, is expanding in all directions. Strangely, this requires that every point in the Universe represents the point of origin of the Big Bang! Thus, all matter in the 15

Milky Way. www.deltagroupengineering.com

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Universe was not ejected from a central point into a pre-existing expanse of space such that it moves away from an origin; instead, the fabric of space is expanding, carrying along the matter forming stars, planets and us. Distant galaxies appear to be the most red-shifted because the space between them and us has expanded more than galaxies closer to us. Mach’s view of inertia implies that an object’s motion relative to the fabric of space (i.e. a pan-universal gravitational matrix), is the root cause of inertial forces. However, this view continues to sound, walk and talk a lot like the aether model of old, as if to say that an object’s movement through space induces a wake to form through it, and would thus require energy input to counter the opposing force as it moves along. This presents a problem because we know that objects traveling with uniform motion do not experience inertial forces. If Mach’s Principle were true, then objects should experience an inertial force at all times, whether they are moving uniformly or accelerating. The force of inertia, however, is only experienced upon acceleration, which simply refers to a constant rate of change in motion. But how is this so? What strange property of the vacuum could cause this peculiar physical phenomenon? When we move at constant speed we don’t feel anything, even if we are moving incredibly fast. Yet once we change our rate or direction of motion, we suddenly feel a force.

When a ship cruises through water, the engine must be constantly running, providing the force that pushes the water out of the way and keeps the ship moving; but adding energy to keep an object in uniform motion simply isn’t necessary in space. Once you give an object a push in space, it will maintain that rate of speed (in open, flat space) indefinitely without needing a constant force behind it to keep it moving. However, if you want to speed up, slow down, or change direction, energy will be required to counter the physical, powerful force of inertia we feel, arising as if out of nowhere. “Uniform motion” is defined based upon one’s motion relative to external points of reference, such as the position of nearby stars. However, acceleration is fundamentally distinct; it wouldn’t matter if

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you were the sole object in the Universe, if you accelerate, you will know it immediately because you will feel the force of inertia. The physical nature of inertia has remained a mystery for eons. Historically, inertia is considered to be an intrinsic “property of matter”, full-stop, no explanation required. However inertia, with its uncanny nature, holds the key to understanding the physicality of space itself! Elucidating the inner workings of inertia will lead directly to the most complete generalized understanding of the Universe ever to be gained by humanity. Although Mach’s Principle of inertia was never formally developed into a quantitative, physical theory, there is a strongly compelling aspect to it which cannot be disregarded. Despite its inadequacies, Mach’s conceptualization was at least partially correct in its premise that inertia was a manifestation of the same force we experience as gravity.

2.3

The principle of equivalence

The primary basis for this idea of self-consistency between inertial and gravitational force has a long-standing history and has a very solid foundation. So solid in fact, that this connection provided the basis for Einstein’s theory of General Relativity (GR). The concept is termed the “Equivalence Principle” and states that the inertial force of acceleration in free space is the same as the gravitational force experienced on the surface of the Earth. The origins of this idea go all the way back to Galileo, who showed that if you drop a very heavy object like a large stone, and a light object like a pebble at the same instant, they will hit the ground simultaneously. This observation seems counter-intuitive because one might naturally expect that the heavier object would fall faster and hit the ground earlier than the pebble. On the Earth of course, the air provides resistance to falling objects and we observe that a piece of paper or a feather falls slower than a boulder. However, this isn’t due to gravity or the relative mass of the objects; it only has to do with the air having to be pushed out of the way as objects fall through it. On the Moon however, no atmosphere exists to impede the acceleration of falling objects. During the Apollo 15 Moon landing, the astronaut David Scott tested Galileo’s conclusion by dropping a falcon feather and a geology hammer at the same time, and was able to reassure any skeptical viewers that light and heavy objects fall at the same rate due to gravity; the hammer and the feather landed at precisely the same time. www.deltagroupengineering.com

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Gravity’s affect on mass is what we call weight, but weight is not synonymous with mass. David Scott, although he was the same size and composed of the same quantity of matter on the Moon as he was on Earth, he weighed less on the Moon. This is due to the fact that on the Moon, gravity is weaker than it is on Earth – “weaker” meaning that the acceleration of gravity on the Moon is less than on Earth. Weight is a measure of the force required to counter the apparent acceleration of gravity. This is Newton’s “Second Law”, expressed by the equation16 “F = ma”, which can either be caused by inertial acceleration in free space, or the acceleration of gravity. For example, as the Apollo 15 rocket was launched, all the astronauts experienced intense G-forces and were much heavier than when the rocket sat on the launch pad. The rocket’s acceleration during launch is added to the acceleration of gravity. Therefore, the total combined acceleration impinging on the astronaut’s means that the force required to counter the total acceleration is greater. This larger counter-force is felt as weight; so, the greater the rate of acceleration, the heavier a given mass appears. When we talk about gravity, we’re talking about acceleration. When you drop a ball, it doesn’t fall at 9.8 meters per second, it falls at 9.8 meters per second, per second. Let’s say you are standing next to a long, straight stretch of road lined with reflector posts spaced 10 meters apart. A car driving along at uniform velocity might be covering a distance of 10 meters between each reflector post, per second, based on your stopwatch. The car’s speed would then be measured to be 10 meters per second or 36 kilometers per hour (k.p.h). Then you watch another car start from a stationary position and accelerate at a constant rate. You might measure that; in the first second the car travels only one meter, 10 meters in the next second, 20 meters in the “3rd” second, 40 meters in the “4th” second and so on. The car would therefore be accelerating at a rate of 10 meters per second, per second or 10 meters per second squared [i.e. 10(m/s2)]. Acceleration can be measured in reverse as well. This occurs when one applies the brakes in a car to slow down. A constant rate of change applies to both cases, and is called “acceleration” whether the car is speeding up or slowing down. The same magnitude of inertial force will be experienced when the driver accelerates to speed up, or puts on the brakes to slow down. The only difference is the direction with which the force pushes on the driver. However, no forces will be 16

i.e. force (F) is equal to an object’s mass (m) multiplied by its acceleration (a).

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felt in the direction of, or against, motion when the car is traveling at a uniform speed. Gravity is synonymous with inertia because it is a sensation of being accelerated even though you may be sitting stationary in a chair; and because gravity is acceleration, the feeling of force one experiences while being held stationary at the surface of the Earth is the same force one would feel due to inertia if one were to accelerate at the same rate in free space! Einstein imagined a similar “thought experiment” to illustrate the Equivalence Principle, and in so doing, developed the framework for what would come to be known as GR. Imagine you are in a large box, like an elevator, without windows, and you can’t look outside to determine anything about your movement within the environment. All you know about your movement is based on what you can feel from inside the box. While standing inside a stationary box at the surface of the Earth, you feel the acceleration of gravity pushing you to the floor at 9.8 meters per second, per second [i.e. 9.8(m/s2)]. Now imagine that you are floating around weightless inside the box, which itself is floating in empty space. Then suddenly the box begins to accelerate in one direction so that the opposing side of the box moves up to touch your feet. Let’s say the box begins accelerating through space at a rate of 9.8 meters per second, per second. Without knowing anything about your environment, you are quickly able to stand up on the floor. What you would feel in that instance would be indistinguishable from what you would feel standing stationary on the surface of the Earth! The inertial force of acceleration is the same, whether you are accelerating through free space, or sitting stationary in a gravitational field. When Einstein applied the Equivalence Principle to his geometric interpretation of curved space-time, he was able to demonstrate in a very elegant manner why gravity is, in effect, the same force as inertia. Let’s go back to the explanation of curved space-time and geodesic motion mentioned earlier. As an asteroid enters the Earth’s gravitational well, its path will be bent around the Earth according to the most direct geodesic path possible within the curved space-time manifold. The asteroid, however, doesn’t actually experience a force as its trajectory is altered. To the asteroid, it is simply following the path of zero resistance in a curved topology. Let’s also imagine that the asteroid enters into orbit around the Earth. Even though it travels in an ellipse circling the Earth, it still feels no force keeping it in that path. If the asteroid approached the Earth on an impact trajectory, heading directly towards the Earth, even though it is being accelerated by gravity it would still not feel any force! www.deltagroupengineering.com

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The asteroid is simply falling along with the acceleration of gravity, like a feather floating on water, pulled along by the swift current in a river. If you held the feather stationary so that the current rushed along underneath it, the feather would then feel the resistance of the current, and a force would be required17 to resist the feather’s natural tendency to move with the current. Similarly, the asteroid would require some counter-force to push it away from an impact trajectory. An impact trajectory is a geodesic path, just like an orbital path, and a force would be necessary in order to push the asteroid into another orbit or out of orbit all together. Einstein demonstrated that any diversion from an object’s geodesic path of motion in a curved space-time manifold results in an inertial reaction force. If you are traveling through free space18 and you decide to change your direction, you will feel an inertial reaction force. Simply put, if you don’t “go with the flow” of the space-time topology surrounding you, you’re going to feel an inertial reaction force; and any time you want to change your path, you will need to expend some energy to do so. Think of space-time as a landscape of hills and valleys. An object’s geodesic path through that landscape is like the path of a river following the lowest possible elevation within that landscape. The river, or a feather floating on the river, will naturally want to flow from high to low with the current. If you decide that you want to push the water up and over a hill, it’s going to require some effort to do so. When gravity is considered to be a well in space-time and not a force in its own right, an object “floating” in a gravitational current of least resistance will only require energy input in order to move itself out of its natural path of least resistance. Einstein tells us that gravity is nothing more than space-time curvature. Inertia is felt when changing the path of motion against the natural path of least resistance within the landscape of space-time. It is even possible to describe the strange predictions made by GR using this kind of imagery. No doubt, one of the strangest predictions made by GR is the existence of the “black hole”. Black holes are the result of the gravitational collapse of the most enormously massive stars. As a massive star pulls in more and more matter from its surroundings, it can eventually reach a point when it can no longer hold itself up against the gravitational field it generates. At this point, the star will collapse under its own gravity to form a warp within the fabric of space-time so deep that nothing entering this 17 18

In this case, the force of your fingers holding the feather in place. i.e. in a straight line in flat space-time.

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gravitational well can escape – not even light. As matter or light falls towards the black hole, it will be forced to follow such a steeply curved, inwardly-bent topology in space that it could never acquire sufficient energy to escape the well. Perhaps an easier or more intuitive way to describe what is going on here is by way of fluid-dynamics19. Sound waves travel much more quickly in water than they do in air because the molecular density of water is higher than air. This simply means that molecules of water are much more closely packed together per unit volume than air molecules. The speed of sound in water is approximately 1,500 meters per secondix – roughly three times faster than in air.

Let’s assume for the sake of argument that we may substitute the idea of space-time curvature for an accelerated flow of water from left to right towards the central “drain pipe” of a fluid-model black hole. Let’s also substitute the light waves traveling through space for sound waves in the fluid. Now let’s imagine that we are traveling in a submarine suspended in the water and that we are sending out sonic pings which allow us to echolocate objects in our vicinity. Each of these sonic pings (sound waves) will radiate outwards in concentric rings away from our ship. But what will happen to the sound waves

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William Unruh of the University of British Columbia in Vancouver is credited with the original concept described by this thought experiment. www.deltagroupengineering.com

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we emit as we pass by a black hole and travel through its gravitational “current”? As we move closer and closer to the drain (the black hole), we reach a point where the flow rate of the water around us starts to surpass the speed of sound in water. If an observer in a boat on the surface of the water happens to be listening to our ping signals, far from any gravitational current generated by the black hole, the observer will hear the pings get progressively lower and lower in pitch (i.e. lower in frequency), until they eventually come to a stop. Even though our submarine is still sending out pings, the flow rate of the fluid we are immersed in has surpassed the speed of sound and the signal can no longer escape to the surface. The boundary point at which this occurs is called the “event horizon” of the black hole, and refers to the point of no return where the black hole becomes black – the point which light can no longer be detected by outside observers. In the case of a real black hole, the event horizon marks the boundary at which the acceleration of gravity surpasses the speed of light. In this case, using fluid-dynamics to describe the more bizarre predictions of GR yields the same results as the curved spacetime analogy. Einstein’s GR describes the link between gravity and inertia, and how objects behave in inertial reference frames according to gravity. However, Einstein’s GR is nothing more than a geometric interpretation of gravity, just like our sound wave analogy. It is important to remember that GR is just that – an analogy. In the GR analogy, space-time is represented by fourdimensional geometry, yielding a topological map of space in the presence of matter. Even though Einstein admitted the necessity for some manifestation of the aether as the basis for his space-time manifold, many physicists today insist that space is indeed a complete vacuum. If this is in fact the case, then the obvious question remains: what mysterious property of the vacuum is capable of being “curved”, and how does an object “know” whether the space it travels through is curved or flat? Alas, we are left with the mystery of the force we call inertia – a physical force we feel, arising as if by magic out of the vacuum of space. And we are still left with the force we call gravity, which somehow causes objects to directly affect one another from afar with nothing between them aside from “nothing” itself. In this regard, it is important to remember that GR is merely a highly effective descriptive tool, but not a literal, physical explanation of Nature.

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2.4

Mass-Energy equivalence

Shedding light on the fact that GR is merely a descriptive tool is not meant as a criticism or denial of either Special or General Relativity. Indeed, Einstein’s theories have proven themselves to be some of the most magnificent predictive tools ever constructed, and are directly responsible for revealing some of the most mysterious and compelling aspects of the Universe ever to be imagined. The most farreaching of these, and arguably the most famous in the history of physics, is the notion of mass-energy equivalence described by the equation “E = mc2”. The expression “E = mc2” is misunderstood by many people to mean mass-energy “conversion” – that is to say, when one form of stuff we call matter is converted into another form of stuff we call energy. We have become well acquainted with this erroneous idea because of the atomic bomb. We have witnessed first-hand that a staggering amount of energy may be unleashed from a mere handful of matter in an intensely violent explosion. However, the expression “E = mc2” literally, or more properly, refers to mass-energy equivalence. In much the same way that the Equivalence Principle implies that inertial and gravitational forces are one-and-the-same, so are mass and energy. It is important to begin on this semantic point, with this conceptualization firmly in mind: that matter may be described, expressed and calculated in terms of its energy alone. One of the most difficult concepts to grasp in relativistic physics, however, is the notion of mass-energy equivalence as a literal expression. “E = mc2” is without a doubt the most famous equation in history, but very few people actually know what it truly means. And even now, after having seen with our own eyes the horrifying truth of mass-energy equivalence through the development of nuclear weapons, it seems that very few people fully, intellectually accept the notion of mass-energy equivalence as a literal statement. Even though we have lived with and utilized the “E = mc2” equation, we seem unable to accept that mass is energy and energy is mass. We demand that the explanation for this statement be consistent with our everyday experience and intuition. We inhabit a material world and live-out a material existence. We observe with our senses that we and all objects around us have substance. Objects have weight and form, are solids, liquids, gasses, and material things are ascribed a three-dimensional volume in space. It is no surprise, therefore, that a literal understanding of mass-energy equivalence is not an easy thing for us to grasp or accept. Our minds are constructed around and have adapted to the immutability of our material Universe. www.deltagroupengineering.com

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Einstein realized the connection between mass and energy while considering inertia; in that energy is required to accelerate an object or to alter its geodesic path through curved space-time. For example, if we want to accelerate a spaceship through empty space, we find that the faster we accelerate it, the more inertia the ship will feel. This means that the energy required to change the motion of mass is directly proportional to the mass itself. So, by that logic, mass and energy are equivalent! In a sense, the only literal modeling of nature arising via the interpretation of space-time geometry is that mass is a measure of energy. Relativity states that if you were able to accelerate an object to light-speed (which according to Relativity can never be reached) an infinite amount of energy, in the form of thrust, must be applied to the object. Mass, or weight as we commonly think of it, is defined by an object’s resistance to acceleration – its inertia. This is why mass is relative, and one of the reasons why GR is termed “relativity”.

The mass of an object also appears to change based on your motion relative to it. If all of our measurements are relative to our own apparent speed or position then what, exactly, can we measure with any certainty? In this relativistic reality, the only parameter physicists and engineers can actually measure is force. So when we speak of mass, we are actually referring to an object’s inertia because mass scales according to the force required to accelerate it. For example, if you were to travel in interstellar space at uniform velocity there is no way to discern, other than by observing external objects, whether you were stationary or moving. In fact, you wouldn’t even be able to determine whether you were stationary and objects were moving past you, or if you were moving past stationary objects. The only way you could know for certain whether you are moving or not is if you accelerate; acceleration is absolute (in the sense that you can feel its effect on your body) and is typified by a constant rate of change in motion.

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Mass is like a bank account for the currency of energy. When we push an object like a car or a rocket, we are adding energy to the system. However, because energy and mass are equivalent, the energy we add causes an increase in the mass of the object. This may initially seem very odd, but it is a completely natural consequence of the way our Universe works. The Universe is a closed system. Energy and matter are neither created nor destroyed in physical processes, but merely transformed. In this respect, “mass” is an energy input-output system. The energy being added to the system to accelerate it gets “banked” as mass. Energy is associated with all processes in the Universe and is inextricably linked to the fabric of space itself. We are all made aware of this connection and indivisibility of mass and energy every time we accelerate. We feel it hundreds of times per day. We experience the sensation so often that that we have almost become unaware of its omnipresence. However, in becoming so desensitized to it, we subject ourselves to the risk that we might not learn from its subtle innuendo and never uncover the most fundamental and important truths about our Universe. Understanding the nature of inertia allows us to understand the true nature of space and matter. If we come to understand the cause of inertia, we might understand how to manipulate it as well, and in turn, manipulate the fabric of space. What would happen if we could somehow block or negate inertial forces? We could perhaps accelerate freely without being subject to relativistic constraints, and avoid being crushed by intense G-forces when accelerating at incredible rates. The Equivalence Principle necessitates that if we can affect, modify or negate inertial force, then we would also be able to manipulate gravity! Imagine for a moment we could somehow harness the powerful force of inertia, and give ourselves that “firm place to stand” in Archimedes’ challenge. Could we, in fact, “move the Earth”?

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3

The Glass That is Always Full

3.1

Symmetry and unity

As if by some serendipitous logic, the deeper we penetrate into the mystery of matter, the more we learn about space. This connection seems almost mystical. Many popular science books written in the latter decades of the 20th century have sought to link the discoveries made by Quantum Mechanics (QM) to Eastern philosophies20. Whether a basis in fact exists for these conclusions or not, it comes as no surprise that it has proven useful to draw upon forms of human understanding which are based upon philosophical ideas. QM has uncovered truths about the inner sanctum of matter that are so strange, they sound more like magic than reality. No matter how we may choose to interpret the data, QM reveals deep connections between matter and space. Plato developed his group of five perfect solids as a way to explain a much deeper and intrinsic symmetry in Nature. We now realize that his model has no real basis in fact, but we still respond to it nevertheless through an innate human faculty appreciative of the aesthetics of symmetry. Even today, an uncanny semblance of truth remains in Plato’s model of matter. This raises the question of whether we respond to symmetry because it is the nature of our Universe, and thus in our nature as well, or perhaps that our appreciation of symmetry is a synthetic product of the human mind which we consistently attempt to impose upon Nature. Whether we are making objective observations or are just seeing what we want to see, much has been discovered and predicted through analysis of symmetry and unity in Nature. Plato’s perfect solids, based upon geometric symmetry alone, hint at the true nature of the subatomic world which we have come to better understand in the last century. Likewise, the “holy grail” many physicists seek today is a single formula describing the elemental symmetry of the Universe – a single “Grand Unification Theory” (GUT) or “Theory of Everything” (ToE) explaining all physical phenomena we observe, and one that will allow us to predict what we have not yet observed. Natural symmetry has spawned the legend of the GUT; it is not known whether it will ever be possible to formulate such a theory, but there is quite a lot of justification for thinking that it will be. 20

e.g. Fritjof Capra’s, The Tao of physics. (Boston: Shambala, 1975). www.deltagroupengineering.com

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We understand that mass and energy are equivalent, just as gravitational mass and inertial mass are equivalent. Faraday coined the term “electromagnetism” as a result of having unified electricity and magnetism, formerly thought to be distinct forces of Nature. It is this discovery, however, that marked the birth of our modern civilization. The modern world is literally built upon the foundation of electromagnetism and it is manifest in virtually every aspect of our modern lives. It was Faraday’s successor, James Clerck Maxwell, who discovered that light is an exquisitely intertwined pair of electric and magnetic waves. Richard Feynman and Murray Gell-Mann further demonstrated that an interaction involving “the weak field”, which helps hold atoms together, was simply another aspect of electromagnetism; now referred to as the “electro-weak interaction”. Feynman and Gell-Mann’s discovery was born of the belief that because the mathematics of their theory was so elegant and beautiful, and based upon symmetry, that it should be correct – even though they lacked key experimental evidence at the time the theory was being developed to prove it. Feynman’s theory, as it turns out, has since proven to be one of the most precise and accurate theories ever developed! And all this is due to what was originally a “faith-based” approach to physics, reliant solely on principles of symmetry. Science will often yield, without much resistance, as theoretical physicists make new claims which are initially, or at least partially, based on mere aesthetic appeal. The favorable compatibility of prediction and observation, based upon symmetry, has proven itself to be an arrangement worthy of trust and is continually reinforced as we grow closer to achieving unity.

3.2

Exploring the microcosmos

If mass is so inextricably linked to the fabric of space, then similarly, shouldn’t space lend itself somehow to the nature of mass as well? Our bias as material beings in a material Universe has given us the somewhat erroneous impression that our investigation into the nature of matter is a one-way street ending in the foggy cul-de-sac of QM. But what have our deep investigations into matter revealed about space? Let’s start with the atom and work our way down. Let’s pretend that we are in a spacecraft that can change in size from the scale we live in, down to infinitely small dimensions. As we shrink ourselves down to millionths, then billionths of a meter in size, and zoom in on a tiny fragment of matter, we begin to see the vague outlines of individual atoms. The atoms themselves would likely appear to have a fuzzy or hazy surface because the “surface” of

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an atom is nothing more than a cloud of electrons buzzing around a nucleus centered deep within the interior of each atom. We may imagine that the electrons themselves are tiny pinpoints of negative charge encircling the massive nucleus. If we measured the electron fog we just travelled through at the surface of the atom to be one kilometer (km) thick, we would have to travel another 50,000(km) until we reach the nucleus! One of the most startling aspects of the atom, and matter itself, is that it is largely composed of empty space! The nucleus is comprised of positively charged protons, clumped together with generally equal numbers of neutrons, which carry no charge. The proton and neutron are roughly equal in mass and are each far more massive than the electron. But unlike the electron, which is a fundamental subatomic particle, protons and neutrons may be further deconstructed into more fundamental particles called “quarks”. Protons are composed of two “Up” quarks and one “Down” quark, and neutrons are composed of one “Up” quark and two “Down” quarks. A remarkable symmetry emerges allowing physicists to predict the existence of many other particles. Firstly, simple symmetry exists in the arrangement of charge within the atom21. A balanced symmetry also exists in the configuration of quarks within the protons and neutrons22. Many subatomic particles like quarks, for example, cannot exist in the standard energy conditions of our everyday environment. In order to detect or measure subatomic particles like quarks, protons must be smashed together at extremely high energies. This is rather like crashing two cars together at great speed. Crash them together at a slow speed and they may just bounce off one another with minor damage, but crash them at enormous speeds and they will explode into bits. Higher-order particles like quarks are generated as a result of such collisions, existing for fractions of a second, and only in the high-energy conditions created by colliding particles at velocities approaching the speed of light. As the energy is turned up on these collisions, the array of particles produced becomes more varied and bewildering.

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A negatively charged electron cloud encases the positively charged protons of the nucleus. 22 Quarks are arranged in balanced triplicates. www.deltagroupengineering.com

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We have learned that force-carrying particles exist as well. These particles, called “gauge bosons”, in effect, help to hold the atom together. The boson carrying the electromagnetic force keeping the electron in place around the nucleus is termed the “photon”. This is the very same photon we commonly describe as “light”. The force carrier boson mediating the “strong nuclear force”, which holds the positive charges of protons densely packed together with neutrons in the nucleus, are called “gluons”. Although it has never been experimentally measured, the Standard Model of particle physics predicts the existence of the “graviton” as well, which is much like a photon except that instead of mediating EM force, the graviton is thought to mediate gravitational attraction. Particles are categorized based upon certain characteristics like mass, charge and spin, as well as other traits like direction (termed “flavor”) and handedness (termed “chirality”), etc. These characteristics are based upon various forms of symmetry. For instance, in our everyday experience we know that if an “up” exists, then a “down” should exist; if a “left” exists, a “right” should exist and so forth. According to theory, symmetry suggests that particles possess equally yet oppositely charged counterparts termed

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“antiparticles”. For example, the electron’s antiparticle is the “positron”. The Standard Model also maintains that theoretical objects composed entirely of antiparticles may exist, behaving as normal matter. However, if pieces of matter and anti-matter collide, the two will annihilate each other in a burst of energy. In fact, all the particles in the subatomic particle “zoo”, as it is called, are expected to have corresponding antiparticles based upon this principle of symmetry. But most importantly, symmetry allows particle physicists to predict, or presume the existence of particles before they are directly observed. As elementary particle physicists probe ever deeper into the atom, and smash particles together at higher and higher energies into smaller and smaller bits, the details become increasingly coarse and ill-defined. The characteristics of matter which we can easily describe in our macro-reality begin to lose all meaning in the abstract landscapes of the microcosmos. We seem to be approaching the terminal limit of how far we can travel inwardly into matter, and strangely, what we find at the end of the line tells us more about the structure of space than it does about matter. This new world of quantum-space is a very strange and alien place indeed. As we venture into the scale of the subatomic particle, we may no longer count on the predictable, mechanical clockwork rules governing our reality. This is a realm of probability and indeterminate outcome, where even consciousness sometimes appears to affect quantum events. It is a reality standing in stark contrast to the cold, indifferent, cause-and-effect nature of the Universe we know. The notion that the fundamental nature of the Cosmos is probabilistic and random was initially quite unsettling to physicists like Einstein, who “[could not] believe that God would choose to play dice with the Universe”23. An ordered, elegant Universe seems to be the one our sense of aesthetics, symmetry and beauty favors above the chaotic, topsy-turvy game of chance proposed by QM. Like it or not the rules of QM, however strange, reflect the truth of things. But this quantum world of the microcosmos is nothing to be afraid of. In fact, the more we dispassionately embrace what we are shown in the quantum realm, the more we stand to discover about the Universe we inhabit. By delving ever deeper into the depths of matter, further subdividing and slicing it into thinner sections, a point is reached 23

Often paraphrased as “God doesn’t play dice with the Universe”, In a letter to Max Born dated the 12th of December, 1926; quoted in Einstein: The Life and Times, Wings Books, (1995) Ronald W. Clark. www.deltagroupengineering.com

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where matter and space finally converge. It has only been through such investigations into matter that the fine threads and fibers weaving the proverbial “fabric” of space-time have begun to be revealed. The true, quantum nature of space is uniquely strange and wonderful – so strange, in fact, that it is doubtful whether we could have deduced its curious characteristics based on symmetry alone.

3.3

The Quinta Essentia

Coming to know the inner workings of the atom spurred scientists to make a critical and drastic shift in perspective. This shift in perspective brought us out of the purely classical, mechanistic view of the Cosmos and into the quantum realm. This, in turn, allowed us to view the Universe from an elevated perspective, from where we could observe space and matter coexisting in a reciprocal relationship – contrary to the prior notion that matter floated inertly within an unknowable “void”. The most accepted model of the atom prior to the development of QM was an object resembling our solar system, in which electrons were depicted as tiny planets orbiting the massive Sun-like nucleus at the center. Every atom had a massive nucleus at the center, composed of protons and neutrons, orbited by much less massive electrons. But if we were able to travel in our subatomic spacecraft, and fly amongst individual atoms, we would not see individual, spherical electrons in orbit around the nucleus. Instead, we might find something akin to fog, vaguely defining the outer surface of the atom – if we were able to see anything at all, that is. An imaginary dividing line exists separating our macro reality from the subatomic realm. We might not be able to see electrons buzzing around an atom because at this scale, matter no longer exists in the solid, objective form we are familiar with in our commonplace experience. When we describe how matter behaves, it is convenient to use analogies pertaining to solid objects like billiard balls bouncing off one another and such. And when we use the term “particle” to describe elemental structures of the atom, our minds immediately draw upon imagery of equally solid and objective bits of

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stuff. At the subatomic level, however, matter doesn’t actually exist in this form. It is really only convenient and practical to talk about subatomic particles in terms of their energy alone. We know that light possesses wave-like characteristics which may be likened to a wave propagating through a fluid. Waves of light interact and interfere with one another, forming interference patterns like ripples on the surface of a pond. Yet light also carries momentum, behaving as though it were composed of individual objects, like tiny grains of sand. These so-called particles of light are termed “photons”. It is this particle-wave duality conundrum which spawned the development of QM, and fostered an entirely new understanding of matter. If one shines light on metal, and the light is of just the right frequency, an electric current may be produced in the metal. A simple, yet somewhat dangerous proof of this is to put a crumbled piece of aluminum foil in a microwave oven. The microwave radiation induces an electric current in the metal, which will arc and spark between the creases and folds in the foil. In 1887, Heinrich Hertz first observed this effect as he shined a beam of UV light on a metallic coil separated from a conducting electrode by a small spark gap, in a configuration very much like a common “spark plug”. The UV light caused sparks to jump between the electrode and the coil. Hertz also found that if he placed a pane of glass between the spark gap and the UV source, the glass blocked much of the UV light and the sparks decreased in intensity. When he replaced the glass with quartz, which doesn’t block UV radiation, the sparks resumed with their standard intensity. However, Hertz never developed a working theory which could adequately explain this observation. It wasn’t until Einstein published a paper in 1905 titled “On a Heuristic Viewpoint Concerning the Production and Transformation of Light”x that a description was finally offered explaining this strange effect. In this paper, Einstein referred to the phenomenon as the “Photoelectric Effect”. When light energy impacts electrons in the atoms of metal, some of those electrons are knocked off the atom and begin to flow through the metal producing an electric current. But this only happens if the light has enough energy (i.e. momentum) to knock them out of place.

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Einstein’s Photoelectric Effect is based on the supposition that light is particulate in nature, as if the light was composed of tiny grains. These grains of light could be ejected from their source with great force, as if from a sand-blaster, to etch away the electrons from the surface of metals. It was this brilliant insight which earned Einstein the Nobel Prize in 1921. Brilliant as his explanation was, it still invoked a very classical way of thinking that flew in the face of convention. Light was previously experimentally demonstrated to be wave-like. Maxwell’s equations of electromagnetism were rooted in the notion that light propagated as waves. In the context of electromagnetism, light itself was understood to be nothing more than a braided pair of electric and magnetic waves propagating through space. The famous two-slit experiment demonstrated unequivocally that light could interact to produce interference patterns, just like waves on the surface of water. The other concern was that if photons had no mass, how could they have momentum? Momentum is a measure of an object’s mass multiplied by its velocity. Light is known to have a velocity, of course, but if a photon’s mass is zero then where does the momentum come from that allows a photon to blast the more massive electrons away from their respective atoms? The reason that mass-less photons may be considered to possess “momentum” is due to the fact that they have inherent energy; “E = mc2” states that energy is equivalent to mass.

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Einstein’s explanation for the Photoelectric Effect was profound because it adequately predicted experimental observations utilizing a particulate basis for light. However, the key discovery in this instance was that it is not the intensity of light which produced a stronger electric current in metals; it was the frequency of the light that mattered. Spanning the EM spectrum are radio waves at the low frequency end, then as the EM spectrum increases to higher frequencies we find microwaves and infrared radiation, then visible light, then ultraviolet (UV) light. Even higher in frequency still are Xrays and Gamma rays. As the frequency increases along the spectrum, so does the energy associated with each of these kinds of EM radiation. The higher in energy (i.e. frequency) the photons are, the more particle-like they begin to behave.

X-ray light is composed of photons of very high frequency – much higher than visible light, for example. We know this empirically because X-ray light can pass right through materials visible light cannot, like soft tissues of the human body. The wavelengths of X-ray light are much smaller than visible light, or microwaves, or even radio waves for that matter, which may be meters in length. The photoelectric effect demonstrates that if higher frequency radiation, such as X-ray light is directed at a metal, the current produced will be proportionally greater than if UV light or any other lower-frequency radiation is used. This means that unlike water or sound waves for which energy is measured based on the amplitude (the height of the wave), the strength of an EM wave of light is based on its frequency. X-rays can pass through materials which visible light cannot, not only because the wave is physically smaller, but also because X-rays are

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also much higher in energy than visible light, and thus carry greater momentum. It’s like the difference between firing a football and a bullet at the same speed. The football would likely bounce off an object or explode on contact, but a bullet has a much better chance of penetrating most materials if shot with sufficient force. X-ray photons may also cause physical damage to the cells they pass through, specifically to the DNA, in very much the same way that a bullet causes damage when it strikes an object. X-rays actually tear right through DNA and potentially have the ability to cause harmful mutations in genes, which may result in cancer. This is why your doctor or dentist wants to know the last time you had an X-ray taken. It’s important not to let your average X-ray radiation dose exceed a given damage tolerance threshold of the cell, in order to minimize the risk of diseases caused by genetic mutations. Max Planck derived a mathematical relationship for light momentum and energy in the form of his equation “E = hv”, which states that the energy (E) of light is equal to its frequency (v), sometimes denoted (f), multiplied by Planck ’s constant (h). Planck’s constant is a measure of light energy as a function of frequency, but more importantly, it describes how the energy is “packaged”. For example, a volume of water may be divided and divided again until one is left with a single water molecule composed of one oxygen and two hydrogen atoms. However, it is not possible to further sub-divide that molecule and still have water. You can have one molecule, or two, or how ever many you like, but it isn’t possible to have “two and three-fourths” molecules of water. Planck’s constant effectively describes the notion that light energy, as related to frequency, comes in whole increments (i.e. quanta) per whole cycle of the wave. Wavelength is measured from crest to crest, or trough to trough, so the cyclic quality of a wave must be factored into the equation, and this is served by including Planck’s constant. The most important point to remember is that the frequency of light is synonymous with its

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energy, just as mass is synonymous with energy in Einstein’s massenergy relationship. Armed with this understanding it is now possible to appreciate how Nature has constructed the atom. Materials, composed of atoms, absorb and emit light-energy. Heat up a piece of iron and it glows orange and red. A key factor leading to the development of QM was the observation that light was absorbed and emitted by various substances in discrete and specific wavelengths, and that these wavelengths were, in turn, always characteristic of the kind of matter they were absorbed by or emitted from. The spectral characteristic of light emitted by matter can thus be used as a signature, allowing us to identify the composition of distant objects in space, and the composition of matter in the laboratory just the same24. But how and why is this true? This observation was in direct conflict with the pre-quantum “solar-system” model of the atom. When we look at our solar system, the planets are in orbit at specific distances around the Sun, but this doesn’t mean that each planet has to maintain any specific orbital distance. An object can orbit the Sun at any distance chance might allow. It’s not as if the Earth, because of its mass or some other physical factor, has to inhabit a certain orbital distance from the Sun, it just happens to be so. Also, if an object in the solar system decays from one orbit to another nearer to the Sun, it may change position in a gradual manner as it spirals inward from point A to point B. This, however, isn’t the case for electrons surrounding the atomic nucleus. Electrons only “orbit” at discrete, quantized levels – they cannot exist at any “in-between” distance from the nucleus. If the orbit of an electron decays and changes from one orbit to another, no intermediate position exists that an electron may occupy during that transition. It has one position at one moment, and then instantaneously shifts to a different position. It is as if at one moment you might be sitting at home reading the newspaper, and then suddenly find yourself at the café down the street! All this sounds truly bizarre, that is, unless the notion of particle-wave duality is considered.

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This method is termed “spectroscopy”. www.deltagroupengineering.com

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When Louis de Broglie was a student at the University of Paris in the early 1920’s, Relativity and the Photoelectric Effect were new concepts beginning to take root in science. Based upon Relativity he learned that “E = mc2”, which states that mass-less photons possess momentum because they possess intrinsic energy. He also learned that “E = hv” from the Photoelectric Effect, and that a photon’s frequency was a measure of its energy. De Broglie astutely realized that E was equal to these two, apparently different things – namely frequency and mass. So if photons of light possess frequency, could things with mass, like electrons, also have characteristics of waves? Or greater still, could perhaps all forms of matter, from particles to pebbles to planets, all have wave-like characteristics as well? The answer, de Broglie discovered, was yes! Three years after de Broglie derived his hypothesis25 it was experimentally verified by Clinton Davisson and Lester Germer at Bell Labs. Experimental confirmation of de Broglie’s hypothesis earned him the Nobel Prize in 1929. Here’s how they did it. X-rays cause current to flow in metals, and the X-ray light may also be reflected and refracted as it bounces off the atomic lattice forming the regular structure of metals and other crystals. The diffraction patterns reflected may be utilized to deduce the molecular lattice structure26 of the atoms comprising metals and crystals. Davisson and Germer decided to turn this idea on its head by directing a “beam” of electrons at a piece of nickel. They found that the electron beam was refracted in the same way one expects to find with X-rays. The electrons forming the beam were behaving much like photons of light traveling as waves and were being reflected and refracted off the metal’s surface, forming diffraction patterns on a detector. From these interference patterns, the wavelength of the electrons was precisely calculated in the same manner as one calculates the wavelength of X-ray light! Based on what was learned in this experiment, electrons surrounding the atomic nucleus could no longer be considered as little particles in orbit around the nucleus.

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That matter possesses wave-like attributes. The three-dimensional arrangement of atoms.

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Electrons not only appeared to move in waves, they could be considered to be waves. One might ask how a pebble, or a planet for that matter, may be represented as a wave. We observe objects to be solid and they don’t appear to quiver with wave-like ripples, or move along in a serpentine manner. This is because as an object increases in mass, its wavelength becomes exceedingly and undetectably small. It is only when matter reaches the subatomic scale that its matter-wavelength becomes physically important or detectable. The de Broglie wavelength denotes the basis by which the macro and quantum realms are divided; matter becomes subject to its wave nature below a certain scale and the fine topological details of quantum-space become apparent. To us, space appears completely smooth and featureless, but to an electron, or any other subatomic particle, space is a roiling, rough landscape. By analogy, it’s similar to viewing something smooth under a microscope. To the naked eye a substance may appear to be quite smooth, but place it under a microscope and it might look pitted and rough. As the magnification gets finer and finer, matter also loses its tangible, objective characteristics and enters a state of duality – being simultaneously particle and wave-like. As we transform our perspective and view the electron as a wave rather than a single particle orbiting the nucleus of the atom, suddenly things start making sense. If the atom was really like a miniature solar-system, we would expect the electrons to crash into the nucleus almost instantaneously due to the mutual attraction between the negative electron charge and the positive proton charge of the nucleus. But the electrons never crash into the nucleus. Why is this so? The Danish physicist Niels Bohr was the first to apply the wave nature of the electron to the orbital model of the atom. Bohr reasoned that the wave nature of matter explains how and why atomic electrons maintain stable orbits. If we consider Planck’s constant, we recall that energy comes in bits (i.e. quanta) based upon the cyclic nature of the wave. Bohr found that electrons occupied discrete atomic orbitals directly corresponding to complete cycles of the electron wavelength. Moreover, the electron wavelength of each orbital was associated www.deltagroupengineering.com

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with a specific amount of energy. Imagine the classical model of the atom once again, with its electrons orbiting in circular paths around the nucleus. If one cuts a circular path at a specific location, unwinding it into a straight line of precise length, the orbital path becomes analogous to a guitar string held fixed at both ends. When a string of length “λ” is plucked, it vibrates at specific frequencies which represent harmonic divisions of its length (as depicted below).

Between the fixed end-points of the string, fractions of waves cannot exist. It’s like our collection of water molecules. Three-and-ahalf molecules of water cannot exist; they may only exist in wholes. In this case, only whole harmonic multiples (e.g. 1, 2, 3, 4, 5 etc.) of the fundamental frequency27, defined by the orbital circumference can exist. In this way, the electron is treated as a “standing wave”

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The “½λ” condition depicted in the diagram; also termed the “1st” harmonic.

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wrapped around the nucleus; the only maintainable orbits are the harmonic frequencies physically fitting the circumference. This quantum, harmonic model explains the stability of electrons in the atom, and why “in-between” states of electrons don’t exist. With this new perspective, the “orbital” model of electrons was replaced by “energy levels” – a harmonic model as a result of QM. Bohr also realized that the energy levels associated with the electrons in atoms describe the absorption and emission spectrum of the hydrogen atom. The hydrogen atom was used to model this effect because of its simple configuration – having one electron circling a single proton. As the electron jumps from a lower harmonic state to a higher one, the frequency and energy of the electron increases. However, in order to alter the energy level of the electron, energy needs to be added or subtracted. The law of conservation of energy ensures that energy cannot “magically” appear out of, or disappear into nothing; it must come from somewhere. When an electron jumps from a higher to lower energy level, it is also jumping from a higher to lower frequency. When this occurs, energy is released as light. The phenomenon of photon emission from atoms was actually quite well understood even before Bohr fully developed his theory describing why it occurs. Atomic photon emission wavelengths obey a precise harmonic pattern, which was determined by the Swedish physicist, Johannes Rydberg. In the Rydberg formula, the wavelengths of the photons radiated from atoms as electrons jump between energy levels can be accurately predicted by simply substituting whole-number harmonic intervals into an equation, along with the Rydberg constant for a given atomic element. Rydberg’s formula, used to predict the frequencies of light emitted from atoms, was subsequently explained by Bohr’s model of the atom. Bohr demonstrated that the harmonic pattern derived by Rydberg and others28 works because the frequency of the photons released from the atom directly corresponds to the frequency difference between electron energy levels! It is as if the atom is a musical instrument which may be strummed with light to produce a musical scale of colors. On a musical instrument, each sound-wave is produced at a particular frequency, differing from others based upon the harmonic interval between the notes. Instead of sound waves, an atom emits 28

Ritz, Lyman, Balmer, Paschen, Brackett, Pfund and Humphreys all contributed to and further developed the original formula to apply to other atoms. www.deltagroupengineering.com

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specific frequencies of light based upon harmonic intervals. The frequency of light is, of course, what defines the attribute of color. The atoms of any element absorb photons at exact frequencies because a “perfect fit” is required to boost the electron to a new energy level. Similarly, when the electron drops to a lower energy level, a photon is released with a frequency precisely equal to the difference between the frequency shifts in the electron’s energy level. These differences in energy levels are governed by the permissible harmonic states of the electron in the atomic system. When a blacksmith heats a piece of iron in the furnace, heat energy is absorbed, boosting the energy levels of electrons in the metal. Similarly, when the metal is removed from the fire it glows orange-red in color. As the metal cools, electrons in the iron atom fall to lower energy levels, releasing a cognate spectrum of photons in the transition, observed as orange and red light; color is the hallmark of this energy exchange. In fact, all the colors in the material world are born of this indissoluble interaction between energy and matter29. This model of the atom is truly beautiful in its elegance; all matter is locked in a ceaseless dance with light. Thus, Einstein’s mass-energy equivalence relationship becomes easier to comprehend because matter is not separated from its energy environment – it is uniquely dependent upon it. Attributes such as wavelength and frequency are the characteristics by which we describe subatomic matter and energy. Although macro-scale matter may be described in mechanical language, the subatomic world can only be adequately described in the language of energy. The concept of wave-particle duality exists in the quantum realm, providing the basis for mass-energy equivalence. This matterenergy relationship is revealed at the subatomic level because subatomic matter may only be adequately described in terms of energy relationships. Energy is the currency of the Cosmos, and energy is constantly being shared and exchanged in a perpetual dynamic interaction with matter. So if we consider the fabric of space as being filled with energy, it becomes clear how space may be perceived as being the basis for all matter, and the foundation upon which the ever-changing dynamic reality we experience in the material world plays out. This is why Plato had it right, even if the particular model he used was incomplete. According to Plato, the fifth element (the “Quinta Essentia”) was reasoned to be the ethereal substance of the void, but it was also the substance upon which matter was 29

Based upon the theory of Quantum-Electro-Dynamics (QED).

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constructed. If we think of the Quinta Essentia as being energy itself, then this purest substance of the Universe is indeed the basis for all matter.

3.4

Quantum uncertainty

Erwin Schrödinger was instrumental in sailing this new harmonic model of the atom into uncharted territory, and in so doing, established the field of Quantum Mechanics. In 1925, Schrödinger defined the many configurations wave-like electrons may take in different atoms. Atoms come in much more complex and flavorful varieties than just the hydrogen atom, and these atoms have not just one, but many electrons, existing at various energy levels. Schrödinger was able to unravel the complexities of the atomic animal by demonstrating that electrons didn’t always have to occupy the same “orbital distance” from the nucleus, i.e., based upon the outdated solar-system model. He determined, rather, that the electron could exist in a variety of shapes and configurations based upon its “quantum state”. A quantum state defines the characteristics of an electron’s energy level, which includes its placement hierarchy (energy), magnetic torque and orbital configuration. The quantum state may also be defined by what Schrödinger termed its “wavefunction”. Schrödinger’s wavefunction interpretation implies that the electron itself is a continuous wave-form and that, for all practical purposes, it is in all places at once (within its quantum state) around the nucleus! Schrödinger’s wave is not so much a physical wave, like those found on the ocean, but is instead a representation of a statistical probability for where an electron is likely to be detected around the nucleus at any given moment. In the laboratory, certain properties of the electron and other elementary particles may be readily detected and measured. The particulate nature of subatomic matter remains, and is just as valid as our notions of wave-functions and so forth. However, if particles may www.deltagroupengineering.com

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be accurately represented by their wave nature, then why is it that we are still able to measure them as distinct particles? The particle attribute that we detect, as it turns out, may be explained through Schrödinger’s wave-function and the “Heisenberg Uncertainty Principle”. When a particle is physically measured, its wave-function is said to have collapsed; the act of measurement reduces the state of the “potential” into a single point of “being”30. It’s a bit like popping a balloon. You may prick a balloon with a pin anywhere on the surface you wish, but the effect will be the same – no more balloon. But unlike a balloon which has a surface, the “surface” of a quantum state is a transitory illusion. Consider a propeller driven aircraft or a helicopter. As the propeller blades spin faster and faster, the detail blurs and we end up seeing a ghostly, translucent shape representing the full range of motion the propeller blade traverses as it spins. Now, if you tried to throw a dart in hopes of hitting the propeller blade as it spins around, just by throwing the dart within the range of the propeller’s movement, there are going to be instances when the dart passes right through and times when the dart hits the blade dead-on. It’s really just a statistical game of chance. A similar effect is at play when attempting to detect electrons in an atom. Areas exist where we might expect an electron to be, but sometimes it isn’t detected. For example, although it might be possible to accurately measure the propeller’s rate of rotation, it would also be very difficult to guess the exact position of a single propeller blade at any specific moment. Werner Heisenberg discovered that mutually exclusive bits of information may only be determined independently in a quantum system, as with the spinning propeller. When dealing with quantum systems, one may only accurately determine either position or momentum, but information about both of these characteristics cannot be determined simultaneously. Because of this, an inherent uncertainty exists in 30

This concept originates from the “Copenhagen Interpretation” of Quantum Mechanics: http://plato.stanford.edu/entries/qm-copenhagen/

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quantum measurements. This is referred to as “Heisenberg’s Uncertainty Principle”; it is not possible to know how a particle is moving and precisely where it is simultaneously, because the act of measurement changes the system. So when a wave-function is measured, its characteristics are particle-like; a specific point contains well-defined information about some aspect of the system. Once the system is measured, the information gained is only representative of a single state of being. Consider a balloon again, only this time we are trying to prick an oddly shaped, asymmetric balloon in the dark, having not seen it before. If we randomly stab at the air until we happen to hit any surface of the balloon it will pop, and we may state with certainty that one part of the surface was located where we jabbed it with the pin. However, we will not have complete information about the shape of the entire balloon before it was popped just by touching one point on its surface. Information about other surfaces once existing on the balloon vanishes at the moment we pop it. Popping the balloon in this case is analogous to “collapsing the wave-function”. The singular identity of quantum information results in the measurement of particle-like qualities. It’s a yes-or-no answer. The balloon either popped or it didn’t. Prior to the measurement being performed (before the balloon is popped) the system is defined as a set of probabilities. Upon measurement, one coordinate from many is “selected” and thus the information retrieved is one-dimensional, distinct and singular, i.e., “particle-like”.

3.5

The substantive Universe

At the commencement of this chapter, it was stated that much may be learned about the nature of space by delving deeply into the depths of matter. In so doing, we may travel full-circle to find that matter and energy are inextricably locked in a dynamic interplay which, in turn, defines the physical reality of our Universe. The wonders of the quantum world are breathtaking and bewildering. However, the most astonishing achievement of QM is not what it teaches us about matter; it’s what it teaches us about the vacuum of space. It tells a tale so strange that we would likely never have imagined it otherwise. It speaks of a mystery so deep and shadowy that science is only now beginning to grasp the full significance of what a quantum interpretation of space implies. The chronicle of a quantum interpretation of space begins with Max Planck in the year 1900, who discovered a deep connection between matter and light. In order to better elaborate on the www.deltagroupengineering.com

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importance of his contribution, a more detailed explanation of the thermodynamic property of matter we call “temperature” is necessary. All material objects are subject to the attribute of temperature, which is a measure of the average kinetic energy (motion) of all the molecules contained in a substance. All the molecules comprising any material object are jostling about and banging into one another. The intensity with which the molecules impact one another is a measure of the object’s temperature. The more energetic the collisions, the higher the temperature will be. Similarly, the less energetic the motion, the lower the temperature will be. At any given temperature however, not all molecules comprising a given material possess identical kinetic energy. It is the average kinetic energy of all the molecules in the system which defines the temperature of the substance. If one were able to plot the energies of all molecules in the system individually, they would form a kinetic energy distribution fitting a statistical bell-shaped curve. The ends of the curve would be representative of the small number of the least and most energetic molecules, but the greatest proportion of molecules will have energies clustered around the average value at the center of the bell curve. Max Planck discovered that radiated energy may be modeled in a similar manner to temperature. The thermal energy radiated into space by any material object, like the Sun for example, is distributed throughout the space surrounding it. The Sun emits infrared radiation (part of the EM spectrum) comprised of frequencies below the color red that the human eye cannot see, but that we can feel as heat. The Sun, of course, also emits frequencies we can see like red, yellow and orange, and much higher frequencies like ultra-violet and X-rays that we cannot see. However, the peak energy emitted by the Sun spans the visible and infrared bands of the EM spectrum31. Planck discovered that the distribution of energy in the EM spectrum surrounding any material object is solely dependent upon the object’s temperature. This collection of energy is termed “blackbody radiation”. If we took an empty metal box out into space and somehow trapped the Sun’s radiation inside, we would be, in effect, taking a survey of the photons emitted by the Sun. In this regard, the blackbody radiation spectrum is analogous to a telephone survey. In a standard survey, the interviewer attempts to achieve a statistical representation of the whole population by measuring the opinions of a 31

The sun, with a temperature of “5,780(Kelvin)”, yields a peak radiation spectrum of roughly “500(nm)” [the visible light range].

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smaller, randomly selected group of individuals. People have vastly varying opinions, but most people surveyed will tend towards a general consensus; few individuals adopt an extreme stance. When the surveyor plots the answers on a graph, the shape of the curve is typically bell-shaped, with most of the people sharing the same answer to a question, and fewer people strongly agreeing or disagreeing. The larger and more random the survey population, the better it represents the entire population. Planck determined that the radiant energy distribution from an object is dependent upon the object’s temperature. In other words, the collection of photons constituting the blackbody energy distribution surrounding any object changes in a very particular way. The composition of the object is irrelevant; temperature is the sole factor defining the prevalence of frequencies that are present. Planck demonstrated how this occurs using an ingenious modeling system. He treated an energy-sampling box as being filled with millions of individual bits of energy termed “harmonic oscillators”. This is analogous to considering the box to be filled with billions of water molecules. In this case, let’s pretend that energy may be decomposed into imaginary fundamental energy “molecules”; analogous to a set of tiny strings of equal length32. The kinetic energy of water molecules causes them to bounce around and impact one another, and this is a measure of the water’s temperature. However, the energy of each oscillator is measured by the frequency with which the “string” vibrates. Each imaginary energy string is the same length, so the frequencies with which the strings vibrate may only be quantized harmonics of the fundamental frequency. In a volume of water, most of the molecules possess values of kinetic energy near the population average. However, some will have much higher and others will have lower kinetic energy. Similarly, in the case of blackbody radiation, most of the oscillators filling the volume of the sample box will be vibrating with a frequency representative of the average energy of the whole, but some strings vibrate at very high or low frequencies. If high and low frequency strings “collide”, the energy is shared between them. However, the energy exchange isn’t a transfer of kinetic energy; it transfers energy in the form of frequency. For example, a collision between two oscillators might cause a high-frequency string to drop to a lower harmonic, and cause the low-frequency string to jump to a higher harmonic via the energy transaction. 32

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We may imagine that when a fast moving water molecule collides with a slower one, energy is transferred in the same manner as when a cue ball impacts a stationary billiard ball. The fast-moving molecule recoils with a reduced velocity because it loses kinetic energy as it transfers momentum to the other molecule. In the case of blackbody radiation, a similar situation arises. The energy of oscillators inside the box is based upon the frequency of oscillation (E = hν) and not the kinetic energy as occurs for water molecules. Blackbody radiation, like temperature, can dissipate or increase in intensity. For example, if boiling water is poured into a cool container, the water’s temperature slowly decreases as the kinetic energy of the water molecules is transferred to the cooler molecules of the container. The water continues to cool until the container and the water reach thermal equilibrium. The same is true if you were to add an ice-cube to a hot container. The heat-energy from the container transfers to the ice, causing the ice to melt and heat up until the container and water reach the same temperature. Blackbody radiation behaves in a similar manner. If we deposited a closed, empty metal box heated to 100°C into deep space, approaching absolute zero temperature, energy in the form of thermal photons radiate away from the metal (some into the interior of the empty box) until energetic equilibrium is attained. Energy emitted by matter into the space surrounding it (outside and inside) is distributed in a regular and predictable manner. The population of radiated photons appears as one might expect to see in a temperature distribution curve if the momentum of each individual molecule was sampled and plotted on a graph. A peak forms around the average frequency in the spectrum of photons and relatively fewer photons have very high or very low-frequencies. The peak value in the distribution varies according to the temperature of the object. Actual measurements of blackbody energy distributions are shown to precisely fit the curve Planck’s theory predicts.

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(Above): Blackbody radiation curves for stars of different temperature (T). The X-axis represents the wavelength of EM radiation and the Yaxis represents the relative density of photons according to frequency in the EM spectrum. The most innovative aspect of Planck’s theory is that it works on the basis of quantum increments of energy. This is to say that, just like water molecules, fractional increments of energy cannot exist. Rather, the energy distribution is composed of harmonic integers (i.e. whole quanta of energy). The incorporation of Planck’s constant (h) entails that the imaginary energy “oscillators” possess energies of “hv”, “2hv”, “3hv” etc; a condition where a string has “1/5thhv” energy, for example, cannot exist. All this seems quite straightforward and easy to conceptualize until one considers the effects of a single oscillator in a metal box at absolute zero temperature. This is where things get a bit strange and the temperature analogy becomes inapplicable; however, amazing new conclusions emerge by way of this consideration. In a blackbody system the single oscillator spreads out to “fill” the entire box, and does not bounce around inside like a single water molecule would. Remember, photons are also waves and a wave is, by its fundamental nature, required to cycle – otherwise it would cease to be. This point is of vital importance. The photon inside the box is not a “particle” bouncing around, it is a wave. It can never fully come to www.deltagroupengineering.com

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rest because that would imply that the photon had been “destroyed”. Energy can neither be created nor destroyed; hence, the photon perpetually fluctuates around its lowest permissible energy state inside the box. The inevitable emergent conclusion from what we know about QM and Heisenberg’s Uncertainty Principle is that any physical system in the Universe must possess some minimum intrinsic energy which cannot be removed. This perpetual fluctuation of photonic energy in space is termed Quantum-Vacuum-Energy (QVE). QVE exists even when all thermal motions between atoms and molecules has completely ceased. For this reason, QVE is also termed ZeroPoint-Energy (ZPE), emphasizing that the energy comprising the vacuum is present at absolute zero temperature. Throughout this book, we shall refer to the sub-thermal ZPE as Quantum-Vacuum-Energy (QVE) to emphasize its derivation from QM and its reference to the vacuum. Planck’s blackbody radiation principle entails that vacuum energy is intimately tied to mass energy, and that the vacuum energy filling space surrounding matter is just as important as the matter residing within it. All systems possess a ground state of energy attained by equilibration with its environment. For example, many possible sizes of energy-trapping “boxes” may exist in space and many minimum energy states may exist within those boxes. A solitary photon inside each variation of box possesses different QVE parameters defined by the box it occupies. Thus, different vacuum states (i.e. “vacua”) must exist, associated with specific classifications of matter. A single atom, for example, interacts with the vacuum by establishing “its own” boundary condition by equilibration, analogous to the manner in which an empty box floating in space establishes an interactive boundary condition within the QVE33. The prediction of QVE leads to a “foamy” description of space, saturated with frenetic, evanescent fluctuations. If you switch your television to an unutilized channel, you’ll see thousands of dots of static buzzing about like bees in a hive. This imagery is physically reminiscent of what’s occurring at the quantum level in the vacuum of space; a chaotic jumble of fluctuations at all points in the Universe, whether within inter-galactic voids or within the space between subatomic particles! Stranger still, vacuum energy exhibits particle-like attributes, with “virtual particles” instantaneously crackling into existence and 33

This partitioning of space becomes particularly important at the level of subatomic particles.

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abruptly vanishing back into the vacuum. QM permits the creation of virtual particles from pure energy by briefly “borrowing” energy from vacuum fluctuations. Virtual particles34 are invoked to explain the conservation of energy and momentum occurring in particle lifetimes and decay processes. Moreover, they are also applied to explain the electro-weak and strong nuclear forces within atoms via a virtual particle “catch game” between subatomic particles. The mechanism of the electroweak force is generally explained as the result of a subatomic transfer of “virtual photons”. Virtual particles are also utilized to plot the formation and annihilation of intermediate particles that are generated during collisions in accelerators. At research laboratories like CERN and SLAC, particles are smashed together at enormous speeds and the resulting high-energy subatomic particles produced in these collisions are analyzed using a mapping process that often requires the use of accessory virtual particles. Virtual particles are utilized in such mapping processes to “fill in the gaps” where details are lacking in these exceedingly short-lived events. One may then wonder why virtual particles are considered “virtual” instead of “real”. On one hand, since virtual particles cannot actually be seen or detected directly we must consider them to be imaginary, but on the same note, they have real, measurable effects. This is somewhat analogous to the manner in which words convey ideas. Words themselves are the real, objective tools facilitating the conveyance of ideas. However, ideas themselves are incorporeal. This shouldn’t imply that an idea doesn’t exist or have observable effects. An idea may exist as a real force with the power to affect our objective reality as much as anything else. Many wars fought throughout history were wars of ideology, based upon ideas, beliefs, and emotional motivation. Human history has been shaped by our physical requirement to survive and propagate, but also by the forces of ideology and belief. Ideas and beliefs, like virtual particles, have measurable effects even though they, themselves, are not directly measurable. We now understand that the “vacuum of empty space” is, in fact, the opposite; it should more properly be regarded as a plenum. In this way, the Universe is a container which may never be emptied. Rather than a “void”, space represents something far more substantive. By way of QM, we have discovered that energy is the quintessential substance filling the Universe. 34

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4 4.1

Making Something of Nothing Virtual reality

Although QVE is obliged to exist by the rules of QuantumMechanics (QM), our psychological acceptance of the QV appears to be more a suspension of disbelief rather than a sincere conviction. The QV seems a bit too weird to be true. Yet the Casimir Effect has provided substantial physical proof that QVE is real, or at least virtual but with real, measurable effects. The most dramatic insight to be gained through this level of understanding is that space affects matter just as matter affects space. A deep, mutual connection exists between matter, space and energy which cannot be severed. Matter and the QV are two aspects of a fundamental concept, as if two sides of the same coin. The existence of Quantum-Vacuum-Energy (QVE) is revealed by the application of spatial boundary conditions as demonstrated by the Casimir Effect. From such spatial partitions, forces are generated due to the formation of Quantum Vacuum (QV) asymmetry, causing the two parallel metallic plates to be pushed together. If only one plate were utilized, the QV would remain symmetrical and appear identical from either side of the plate, and no force would be generated on the plate. However, bringing two parallel plates close together causes the QV between them to change. Fewer QV photons exist between the plates than outside them due to the boundary the plates establish. All but the smallest wavelengths of energy are excluded from the space between the plates. The field asymmetry between the inner and outer vacua generates a net pressure on the outer surface of the plates, and as the inner and outer vacua attempt to equilibrate to identical energy states, the plates are pushed together in the process as if carried along by an increasingly swift current. However, the Casimir Effect isn’t the only development lending credence to the existence of QVE and its influence upon matter. Professor Stephen Hawking has become one of the most famous theoretical physicists of the late 20th century, and a legend in his own time, yet many people would not be able to say precisely why his has become a household name in our current day and age. If one were to ask the same question about Einstein, one would almost invariably get an answer pertaining to “E = mc2”, something about Relativity or the atomic bomb etc. So what brilliant insight into Nature has earned Hawking the privilege of sitting in Sir Isaac www.deltagroupengineering.com

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Newton’s chair at Cambridge University? For one, Hawking came up with a theory describing how black holes “radiate” by kicking virtual particles out of the vacuum and into the real world. Black holes are referred to as such because they produce a gravitational field so intense that not even light can escape it. When an extremely massive star pulls in matter, it generates an ever-larger gravitational warp in space-time until a threshold is reached. The threshold marks the point at which the gravitational strength of the enormous mass causes the star to collapse under its own weight. The gravitational acceleration becomes so great that not even light can escape; at this point, the object becomes a black hole because the light entering its gravity well can never escape to reach our eyes. When electromagnetic (EM) radiation, is emitted from an object it is said to “radiate” photons. Hence, one expects that if black holes attempted to emit radiation, it would get sucked right back in (analogous to the submarine example described earlier). The signal could be sent, but it would never reach the outside world. If we were traveling in intergalactic space, far from any star or material object, rogue black holes marauding through space might pose a serious threat to us should we happen to fly a bit too closely. Since they are just as dark as the surrounding space, they would be invisible to us. When we attempt to hunt for black holes with a telescope, we run into the same dilemma. Because we cannot see them, we may only infer the black hole’s presence through its gravitational effect on other nearby stars. What Hawking discovered was that there might be a way, theoretically, to detect a black hole in empty space via its subatomic particle emissions. But if light cannot escape a black hole, then how can they “radiate” particles? Black holes are extremely dense, creating a near-infinite depression in space-time. At a certain distance from the center of the black hole, a point exists at which gravitational attraction is low enough so that light may escape. If light crosses this invisible border it will be drawn into the black hole. This dividing line encircling the black hole is termed the “event horizon”; marking the boundary between our Universe and the mystery inside. But again, if a black hole can’t actually emit radiation then how does it release real particles as Hawking maintains? The answer lies within the vacuum. Based upon mathematical prediction, the QV seethes with virtual particles, flashing imperceptibly into and out of existence. Virtual particles form in pairs comprised of a particle and its corresponding anti-particle, as required by charge symmetry, only to dissolve back into the QV just as quickly.

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Virtual photons are ever-present in the vacuum, and are responsible for the Casimir Effect. But they are also responsible for the creation of virtual particle-antiparticle pair formation, as virtual particles are formed by borrowing energy from vacuum fluctuations. Hawking’s revelation came as he wondered what might happen if a pair of particles popped into existence on the razor’s edge of the event horizon. One of the virtual particles would be sliced away and disappear into the black hole, and the other particle would be cut off from its partner and thrust into reality. Thus, the event horizon is thought to be brimming with orphaned particles that were created as part of a virtual particle pair, and then torn apart by the intense gravity of the black hole. These orphaned virtual particles, in turn, should be detectable as “radiation” being “emitted” from the black hole. Even more interesting is the fact that when one particle of the pair becomes “real”, the other member of that pair must account for that addition of mass-energy to our Universe because of the First Law of Thermodynamics35. The particle of the pair falling into the black hole is assigned a negative mass-energy value, while the particle that has been formed on the outside of the event horizon is assigned a positive mass-energy value. As negative mass-energy rains onto the positive mass of the black hole, an infinitesimal piece of it is annihilated. Each of these mass annihilations eats away at the matter contained inside black hole, facilitating a net gain of mass outside the black hole and a net loss inside. Thus the black hole not only appears to radiate particles, it will eventually evaporate away! Hawking’s principle is purely theoretical because we haven’t yet detected “Hawking radiation”, nor have we directly observed a black hole evaporate or emerge back into our Universe as a neutron star. However, it may be possible to substantiate Hawking’s principle by other means. The Equivalence Principle demonstrates how physical laws are maintained for an object accelerating through flat space-time or held fixed in a gravitational field of identical apparent acceleration. Thus, if we produced enough thrust to fix the position of a spaceship just outside the event horizon of a black hole, this produces the equivalent physical condition of accelerating to nearly light speed in free space. It’s somewhat like rowing up stream in a swift current. One may have to expend a lot of energy, rowing swiftly in order to simply keep pace with a stationary point on the shore. One highly noteworthy theoretical prediction made by the physicists Paul Davies and Bill Unruh in the 1970’s lends credence to 35

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Hawking’s theory. Paul Davies and Bill Unruh independently derived a free-space acceleration equivalent of Hawking radiation at approximately the same time Hawking developed his black hole evaporation hypothesis. Although different approaches were taken, Davies and Unruh determined mathematically that if an observer was accelerated at an extreme rate to nearly the speed of light, the observer would perceive themselves as being immersed in a haze of thermal energy, making it appear as though the space outside was heating up. The effect, although exceedingly slight, may be likened to quantum “friction” as the observer tears through the QV while accelerating. This curious effect is known as the “Davies-Unruh Effect”. The Equivalence Principle states that gravitational acceleration is equivalent to mechanically induced acceleration. In either case, a force is experienced when an object attempts to deviate from its geodesic path through curved space-time. When we observe a comet orbiting the Sun, its elliptical path is experienced as being a straight line of least resistance through curved space. The only way that the comet can move out of its geodesic path is if energy is supplied to counteract inertial resistance as it deviates from that path. An alternative way to change the comet’s path would be to place another massive object like a planet nearby, disrupting the space-time curvature and redirecting the comet. In both cases, due to mass-energy equivalence, energy is simply being added to the system either through thrust-energy supplied to the object or by adding mass-energy to a region of space in the vicinity of the object. The Earth may be regarded, in relativistic terms, to reside in a well of space-time curvature. As the space shuttle launches from the Earth’s surface, it gradually climbs “uphill” to get free of the Earth’s gravity well. In the case of a black hole, the space-time curvature at the event horizon is analogous to “the hill becoming vertical”; which means that an infinite amount of energy would be required in order to escape. Similarly, if our spaceship is traveling in a straight line through flat, interstellar space, and we decide we want to change direction, we would need to fire our thrusters in order to change our path. Changing paths always entails accelerating, and by accelerating we are, in effect, curving our geodesic path, and curving our local space-time by adding energy to the system. Just as gravity is discussed in terms of space-time curvature, so is acceleration. As an object is accelerated to near light speed, an apparent “near-vertical” space-time curvature is experienced. To the accelerated object, it would appear as though it were hovering near (but not at) the event horizon of a black hole! At the accelerationinduced event horizon, the object being accelerated perceives space-

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time around it to be “warming up” with thermal radiation as virtual photons are compressed in its vicinity. Since the object cannot actually be accelerated to light speed (as is represented by the event horizon of a black hole), Hawking radiation and Unruh-Davies radiation are not entirely congruous, although both occur by way of the same mechanism. High-energy particle physicists are laboring to find a method of detecting Davies-Unruh radiation in a particle accelerator when subatomic particles are accelerated to near light-speed.xi If this radiation is observed, it will not only provide proof for Davies’, Unruh’s and Hawking’s theories, it will provide further vindication for the importance and physicality of the QV. Gravity and acceleration appear to have an effect on the vacuum, based upon Hawking Radiation and the Davies-Unruh Effect. In both cases, intense gravitational fields or extreme accelerations physically stress and tear the fabric of space-time. Both of these effects are expressly due to mass and its interaction with the vacuum. Mass warps space-time to produce gravitational fields and it experiences inertial resistance upon acceleration. Both of these effects may also be described by evoking Einstein’s concept of space-time geodesics. Since the Hawking and Davies-Unruh Effects deal with gravity and acceleration respectively, one faces a revolutionary and inescapable conclusion: that mass is completely and impartibly linked to the QVE of space! We know from Einstein that mass and energy “curve” spacetime. However, Einstein did not appeal to QM as being the mediator of this process. What Nature has written for us in boldface type is that GR and QM, formerly considered to be disparate aspects of the Universe, are indeed quite capable of being unified. In fact, Relativity and QM must already be unified – the physics community just hasn’t been able to figure out exactly how quite yet . . . or have they?

4.2

Mutually assured construction

If mass directly affects the vacuum through mechanisms such as the Hawking and Davies-Unruh Effects, and the vacuum can affect matter through the Casimir Force, could it also be possible that the properties of mass are attributable to the QV? We have discussed how mass affects the vacuum and vice versa; but in these examples, mass36 remains independently defined. Recently, scientists have begun to

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investigate whether the specific attributes defining mass might actually be physical manifestations of QVE. Matter is comprised of atoms, themselves composed of subatomic particles which may be classified in terms of their energy and described as wave-functions. Particles also possess charge; for example, a proton carries a positive charge while electrons carry a negative charge. Charge is “relativistically invariant”, meaning that unlike mass, length or time, it doesn’t appear to change according to its relative velocity. Charge is more akin to light, in that it is a standard by which other relativistic effects are measured. But what is charge anyway? What does it mean when someone speaks of positive or negative charge? One might consider it to be analogous to the opposite poles of a magnet, where the northern pole emits a field and the southern pole seems to re-absorb it, like a one-way revolving door allowing passage either “in” or “out”. However, this doesn’t describe what charge actually is. The truth is that no one really knows what charge is. Charge is certainly a wellcharacterized attribute, but the question: “what is charge?” is presently unanswerable. Some physicists believe that every charge is akin to a miniature black hole “singularity”, or a dimensionless mathematical point generating or absorbing field energy. Although much debate surrounds the fundamental nature of charge, an electron’s charge is characterized by a rather fascinating key attribute: electrons continually radiate EM waves (photons) and generate “electrostatic fields”. EM force is transmitted via an exchange of photons. The net charge of a single atom is typically zero, as there is a balance between the number of electrons and protons it carries, causing charge effects to be neutralized. The continual exchange of photons is what mediates the attraction and balance between opposite charges. If a localized accumulation of electrons builds up in a substance, an “electrostatic” field is produced. When the repulsive force between electrons becomes too great, the charges arc to a region of lower potential. A bolt of lightning is an example of this release of electrostatic energy. When an electron is in motion, it radiates an EM field, measured as a collection of photons. Whatever an electron may physically be, it is characterized by an EM field propagating into space. Even though photons forming an EM field are mass-less, their interaction with charged matter imparts either repulsive or attractive forces. Magnetic force is produced through the interaction of fields, coupled to the field source (the magnet itself). For example, as one brings two like poles of a pair of magnets together, one finds it increasingly difficult to make the surfaces of each magnet touch. A

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strong repulsive force is being transferred to each magnet via the fields they extend into the space surrounding them. Similarly, the field emanating into the surrounding space is coupled to the magnet, so the magnet experiences the force imparted by the field. Whether it is through the Hawking or Davies-Unruh Effects, or the fundamental connections between electricity and magnetism, a deep connection exists between space and matter, field and particle. A synergistic relationship is at play, enabling the existence of all things. An unceasing, dynamic exchange occurs, which provides structure to the Cosmos. Were it not for the perpetual dance between space and matter, the Cosmos would cease to be. The key to our continued understanding of the Universe is our acknowledgement of the connection between matter and the QV. If we are going to make further progress in science, we need to change our collective perspective and begin thinking in terms of systems and interactive wholes rather than disconnected, singular entities.

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5 5.1

Mass Illusion A matter of terms

It is very easy for us to take for granted this truly strange and mysterious attribute called mass. It is so fundamental to our everyday experience that few people pause to consider it. Of course, scientific progress has yielded a vast working knowledge of matter extending into the furthest depths of scale. We have come to know the inner structure of the atom, and that the atom is the basic building block of matter. This knowledge not only permeates, but also creates the foundation upon which our modern civilization is built. It has enabled the development of the field of chemistry, and through application of this knowledge we can create a seemingly infinite array of useful compounds and materials. Indeed, our modern way of life on Earth is rooted in this deep working knowledge of matter. However, when we talk about matter we aren’t necessarily talking about mass. Mass isn’t so much a thing like matter is; it is an attribute of matter, in much the same way that temperature is an attribute of matter. Temperature may vary due to the amount of thermal energy a given material possesses, but temperature doesn’t define the atomic or molecular structure of matter. Likewise, “mass” is a measure of the energy embodied by matter, and represents a physical attribute associated with all matter at all levels of scale. Matter experiences inertial reaction forces upon acceleration, gravitational attraction to other objects, and is subject to relativistic effects. Not only does it “warp” space-time to generate a gravitational field, but depending on an observer’s motion relative to an object, the mass of that object may appear to change when the observer alters their motion relative to it. Moreover, Relativity states that mass is energy and energy is mass. If mass is nothing more than a synonym for energy and is subject to relativistic effects, then how does it assume the physical attributes we associate with matter? Why does matter resist acceleration and why does it gravitate? Although Einstein and Newton invented marvelous and ingenious methods for modeling and predicting the behavior of mass, their models do little to explain why mass behaves the way it does, or what causes matter to have the particular set of attributes it does. If GR cannot explain the physical origin of the collection of attributes we call mass, then what can? The answer seems to be inscribed within the very fabric of space and time. All we must do to uncover the answer is decipher Nature’s language. www.deltagroupengineering.com

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Matter and energy are locked in a ceaseless dynamic exchange and define one another through this intimate collaboration. In quantum reality, the barriers defining individuality are nebulous and vague. Matter, and the space in which it resides, may no longer be considered separate entities. Einstein states that energy and mass are equivalent, and by way of Quantum Mechanics (QM) we are able to glean literal meaning from this statement. Could the quantum connections between matter and energy be utilized to explain the properties of mass? The answer to this question is beginning to take shape at the forefront of theoretical physics. A fresh understanding of the quantum origins of mass will lead to new discoveries and unparalleled technological advancements so profound, that the course of human history will be radically altered.

5.2

Intrinsic inertia

The connection between the field and the field-source has been explored as a means of describing one way in which an electron might acquire the attribute of mass. This connection provides a possible explanation for why the Equivalence Principle holds true, hinting at the possible mechanism underlying General Relativity (GR). Physicist Vesselin Petkov at Concordia University in Montreal, Quebec describes the historical basis for what he terms “Classical Electromagnetic Mass Theory”xii. Petkov hints at the possibility that physicists may have uncovered the origin of inertia long ago, had they not been so dazzled by the bright lights of Einstein’s “geometric space-time curvature” early in the 20th century. If one considers classical models of the electron proposed by such physicists as Thomson, Maxwell and their successors, a proposed mechanism for inertia and Relativity appears to emerge quite readily through the nature of the electron. What this model proposes is that the force of inertia is simply the result of the charge source interacting with its own field while accelerating. This describes a classical, physical and completely intrinsic model of inertia, helping to explain the observation that inertial force is local to matter, and immediate in action, i.e., it is not a force to be “transmitted” to matter by mysterious means. The model for intrinsic inertia posited by Petkov is based upon the electron model from Quantum Electrodynamics (QED), dealing with recoil forces on the electron charge as it absorbs and radiates virtual photons. As the electron is accelerated, it senses that the surrounding virtual photons it interacts with are asymmetrically red or blue-shifted. However, to make the reasoning behind this

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model amenable to principles described in previous chapters, it shall be interpreted via the Doppler Effect. If we were moving with uniform motion alongside an electron and were able to view it, we would expect it to be perfectly spherical. In this model we shall presume that the electron is a pointlike singularity (the source of the charge), radiating a uniformly spherical electromagnetic (EM) field in all directions. Imagine that the charge is analogous to a tiny ambulance with its siren on. The siren emits sound waves of consistent frequency that we can hear. When we travel alongside the ambulance at the same speed, or if the ambulance is stationary next to us, we hear the siren as undistorted with consistent pitch. If we could view the sound waves emanating from the ambulance, we would see a series of perfectly uniform concentric waves radiating spherically outwards like a rain-drop in a pond. However, if we were able to observe the electron as it accelerates past us, it would appear to be radiating an asymmetrical field. As the charge accelerates, the EM field emitted at the speed of light in all directions becomes compressed in wavelength in the direction of its acceleration, and decompressed (i.e. stretched out) in the trailing direction. The electron and its field now appear eggshaped, with the electron offset in the direction of acceleration. If the electron were an ambulance siren, we would notice the pitch rapidly dropping as it passes by. If we consider the charge source to be coupled to its own field, we begin to understand where the reaction force against acceleration originates. As the EM field is continually compressed to a higher frequency in the direction of acceleration, the energy of the field in the direction of motion increases proportionally. Conversely, the trailing waves are decompressed to a lower frequency and energy37. “E = hν” states that the leading compressed waves possess greater energy than the trailing decompressed waves. The electron charge source is analogous to a ball suspended in a two dimensional (2D) box by two springs attached to opposite sides. As the ball moves in one direction inside the box, one of the attached springs is compressed in the direction of motion while the other is decompressed (i.e. stretched out). The total energy between the springs remains constant, but the energy in the springs is shifted

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asymmetrically, divided between them during acceleration. When one spring increases in energy, the other decreases in energy.

When the electron is accelerating it “perceives” itself to be immersed in an asymmetric field which is more energetic in the direction of motion. However, the electron seeks existence at its equilibrium state, with neither of its springs deformed and sharing its energy equally in all directions. Whenever compression occurs, the electron experiences a counter-force acting to nudge it into a resting state of equilibrium within its environment. The ball, attached by springs inside the box, moves independently from its frame to a certain extent, but the forces acting on the ball and box cause them to co-move, adjusting to each other as they change position. For example, if the box were to enter a region of curved space-time, the box, being defined by the Universe in which it exists, would deform asymmetrically. If the ball inside the box is held fixed, the springs would be forced out of equilibrium and asymmetrically deformed. However, to keep pace with the energy disequilibrium of its surroundings, the ball naturally moves to keep pace, centering itself in the area of lowest energy within the box. The movement of the ball inside the deforming box describes the inertial motion of freefall in a gravitational field. When Einstein developed GR, one of the tools he utilized to develop the theory was an “elevator thought experiment”. An elevator compartment is very handy as a descriptive tool in this regard because it provides a way of walling-off the Universe and considering the laws of physics to exclusively exist in a small, local volume of space-time. The elevator is analogous to the box, ball and spring model previously described. Since there are no windows in the elevator, it is impossible to determine any information about ones location, direction or

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velocity, etc. Einstein imagined riding inside such an elevator compartment in two locations. One involved being held fixed in the Earth’s gravitational field and the other in free space. Let’s start by riding inside Einstein’s elevator in free space. At first we find ourselves floating about freely inside the elevator. We are weightless and do not experience “up” or “down” orientation. However, we have decided that the elevator can only travel in what we, inside the elevator, perceive to be an “up” or “down” direction, so we shall refer to the tiled surface inside the elevator as being the “floor”. Now let’s imagine that we place our feet against the tiled floor to mimic standing upright. To do our experiment, we brought with us a rubber ball to bounce around inside the elevator. In a zero-gravity environment, if we threw the ball in a perfectly straight line to the wall on either side of us, the ball would bounce back and forth several times, striking opposing walls at the same height without ever “falling” to the floor. But what would happen as the elevator started accelerating in what we regard as being the “up” direction? If the elevator began to accelerate upwards fast enough, as the ball bounced back and forth between the walls, the ball would suddenly appear to fall to the floor. The rate at which it would fall would be precisely the same rate of the elevator’s acceleration because the ball isn’t really falling in this case. The ball remains in the same place as the elevator begins accelerating past the ball’s position. However, according to our frame of reference, defined by the interior parameters of the elevator we move along with, the ball appears to accelerate towards the floor. If we traced the ball’s path inside the elevator, it appears to fall along a parabolic trajectory, just as it does after being thrown horizontally at the surface of the Earth. If the elevator sat on the surface of the Earth and we threw a ball at the wall, it would bounce off and fall to the floor along the same parabolic trajectory as it would inside the elevator accelerating in free space at the same rate as Earth’s gravity. The idea leading directly to the development of GR and the concept of “curved spacetime” was that the ball in the elevator may be replaced with a beam of light. The acceleration required would be much, much greater, but if we could accelerate fast enough, a light beam (or photon) propagating from one side of the elevator would appear to bend towards the floor along a parabolic path. Paths of light in accelerated reference frames, such as the frame defined by the elevator compartment, are geodesic paths defining the topology (i.e. “curvature”) of space-time! Inside an elevator floating in free space, the path of light inside will be a straight line from one side of the elevator to the other. www.deltagroupengineering.com

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This tells us that the observed space relative to our reference frame is “flat”. When the elevator accelerates in free space, the path of the light beam bends and our reference frame then tells us that the observed space-time is “curved”. Space-time in a gravitational field always appears to be curved, and curvature defines the “depth” of the gravitational “well” produced in space. The more massive the object, the greater the curvature and the apparent acceleration experienced. Similarly, as acceleration rates increase, the greater the apparent curvature of space will be38. The whole of GR theory is based upon the pathways of light within our perceived reference frame in space. Now, let’s re-visit our model of intrinsic inertia for the electron. Whether the electron is moving in an accelerating elevator in space, or falling to the Earth in a gravitational well, it is always moving in accordance with our perceived view of the space-time around it. To us, an electron may appear to fall to the ground due to gravity, but the electron perceives itself as being in equilibrium with its environment and not experiencing a “force” causing it to fall. Human experience causes us to believe that the “force of gravity” is “pulling” the electron to the floor. No “pull”, no “force” and no “gravity” exists per se; we simply observe an electron moving in equilibrium with the geodesic path of lowest energy encasing it, which happens to be “curved” (i.e. asymmetrical) in this case. If the electron’s field is uniform and it enters a region of space-time asymmetry (such as a gravitational field), it responds to environmental conditions by “falling” in search of an equilibrium state within that asymmetric space-time. Similarly, any imposed perturbation of the electron’s natural path produced by altering its intrinsic energy to an asymmetrical state within a flat space-time background (what we term “acceleration”), requires energy input. When an electron is held stationary in a gravitational well (e.g. the surface of the Earth), ambient space-time appears curved and the object continually responds to it. When the electron falls freely in curved space-time, it feels no force because it adjusts to the background field asymmetry. Utilizing the box and spring example, if the box moves then the ball attached by springs inside is compelled to keep pace and co-move within its frame to equilibrate with the asymmetric energy of the springs. However, when an object is held fixed within a gravitational field, it senses that the immediate spacetime is always asymmetric, and this asymmetry of space-time results in gravity. 38

Based upon curved paths of light in the local frame of reference.

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Objects, no matter how massive, are equally affected by space-time curvature (i.e. asymmetry) because they are immersed in the same gravitational environment. However, the energy required to move objects out of equilibrium within curved space-time depends upon the object’s mass, and this is termed “weight”. The acceleration of gravity is constant and all masses equilibrate to the local asymmetry at the same rate. The mass of an object is only consequential when resistance to the acceleration of gravity is taken into account; a force is required to counter the inertial resistance to the change in an object’s natural geodesic path. The greater the mass an object possesses, the greater the force required to counter inertia. So even though a hammer weighs more than a feather when fixed in the same gravitational field (because it has greater mass) all matter, regardless of how massive it is, responds to the asymmetry of space-time by accelerating downwards at the same rate. In this regard, mass is a measure of the force required to move an object out of equilibrium with its immediate space-time environment. The electron self-energy model not only describes inertial and gravitational effects, it also hints at the deeper meaning behind “E = mc2”. Since inertial resistance is a measure of an object’s mass, the more massive an object is the more inertial resistance it will experience upon acceleration, and the more curvature it will generate in space-time. Similarly, the more intensely an object is accelerated, the more massive it becomes because acceleration generates apparent curvature; this is why mass is relative under GR. Consider the electron self-energy “ball-and-spring” analogy once again. In order to completely compress one spring connected to the ball to zero length, one requires an infinite amount of energy input. This also implies that the leading EM field of an accelerating electron approaching the speed of light approaches infinite energy. The energy required to compress the leading EM field increases because the EM field frequency in the direction of acceleration increases. The inertial reaction force against acceleration becomes greater, which in turn is a measure of mass, thus the mass increases according to the relationship “E = mc2” (or in this case, “m = E/c2”). Simply put, matter cannot attain the speed of light because it would become infinitely massive.

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5.3

Extrinsic inertia

We now understand from QM that we must always consider the notion that space is replete with QVE fluctuations, and that the QV has an effect on matter. So one might wonder what kinds of forces, if any, an electron experiences as it accelerates through the QV. This is precisely what astrophysicist Bernard Haisch and physicist Alfonso Rueda wondered, and when they looked into it in greater detail, they began to find some truly remarkable results! Having a background in astrophysics, Haisch was drawn to the notion that the QV might contribute to inertia because he already knew quite a bit about “radiation pressure”. Everyone has seen pictures of a comet, with its tail streaming elegantly behind it like the train of a bridal gown. However, what some people may fail to realize is that the comet’s tail isn’t necessarily streaming along “behind” it as it moves through the solar system. The comet’s tail is formed by debris blown off the comet’s surface by the Sun’s solar wind and by radiation pressure, so that the comet’s tail always trails in the direction of the solar wind, like a cosmic windsock. The solar wind, of course, always “blows” radially outwards from the Sun. However, the thing to remember in this case is that the solar “wind” isn’t really like the atmospheric wind we have on Earth. Solar wind does have a “material” aspect to it, in that many energetic particles radiate from the Sun. In fact, the solar wind is largely comprised of electrons and atomic nuclei of hydrogen and helium atoms that have been stripped of their electrons (i.e. ionized gas plasma)xiii. But countless numbers of photons are also released from the sun. Even though photons lack mass, they can still pack quite a wallop because they have momentum. All materials exposed to EM radiation experience radiation pressure. The atoms comprising any substance may absorb or reflect radiant photons, and when an atom absorbs a photon, it also absorbs the energy associated with it. When a photon is reflected, energy is transmitted as it “ricochets” off the recoiling atom. James Clerk Maxwell realized this in the late 1800’s, but it wasn’t verified experimentally until the year 1900 by Russian physicist, Pyotr Nikolayevich Lebedevxiv. Luminiferous momentum (i.e. radiation pressure) is at least partially responsible for physically blowing material off the comet’s core, producing the tail we see streaming through the heavens. New spacecraft propulsion technology has even been developed aiming to harness solar wind and the force of radiation pressure. This particular method of propulsion is referred to as a “solar sail”, and poetically, a

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spacecraft could sail on the solar wind, and move through vast distances of space without needing to carry fuel. In 2005, the Planetary Society built and launched a privately funded solar sail spacecraft named “Cosmos-1”. The spacecraft was designed in the form of a giant reflective umbrella, to be unfurled in space and catch the solar wind. The radiation pressure impacting the sail’s surface per unit time is miniscule, but the cumulative force applied to the sail over a long period will produce staggering velocities – perhaps even enough to reach nearby stars. Unfortunately, Cosmos-1 was lost after a faulty launch, so we must continue to dream of sailing amongst the stars on the winds of light … at least for now anyway. It is possible to estimate the force Cosmos-1 would experience from the solar wind by calculating the power associated with light39 as it propagates. This is made possible by utilizing the “Poynting vector”40 developed by the English physicist, John Henry Poynting in 1884. When you switch on your flashlight, you are generating a “beam” of light that propagates from the bulb towards whatever object you wish to illuminate. The Poynting vector is a quantitative measure of the power of flow (i.e. the flux) associated with the combined electric and magnetic wave components of light as it propagates from the flashlight to the object. The QV of flat space-time comprises a near infinite spectrum of photons of various energies and random orientations, meaning there is no cumulative or net direction to the QV. So in flat space-time the QV photons can be disregarded from most calculations. This doesn’t mean that the spectrum of QV photons doesn’t exist; it simply means that the QVE may be considered virtual because a net force does not arise from a random, baseline QV. Thus, in free space, the QV is said to be “isometric” (i.e. equal in all directions). In the early 1990’s, Haisch and Rueda applied the concept of radiation pressure to the QVE derived from QM. They wondered how the QV might appear when viewed from an accelerated reference frame, in much the same way that Einstein wondered how light paths behaved inside an accelerating elevator in free space. What they found was shocking. By applying textbook Electro-Dynamic principles, they determined, by transforming QVE from a stationary to an accelerated reference frame, that it acquired asymmetry. The field was no longer random and isometric, rather, the QVE in the accelerated frame 39

For a photon or a radiation field composed of many photons. By chance, the sound of its name describes what it does. A vector quantity possesses magnitude and orientation (i.e. an “arrow” of varying size and direction).

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appeared to have a net direction to it, and because it had a direction they were able to calculate the Poynting vector associated with it! They determined that the magnitude of the energy flux generated in the local QV was proportional to the magnitude of the applied acceleration. Thus, as the acceleration increased, the QVE flow opposing it also increased. Apply these terms to mass and what do you get? Inertia! EM radiation generates forces on matter. Haisch and Rueda surmised that upon acceleration, the particles and charges comprising matter experience an EM “drag-force” against the local QV, analogous to radiation pressure. The only instance in which an object is affected by the local QV occurs when it appears to possess net direction (i.e. when it is asymmetrical or “anisotropic”). The fact that QV anisotropy appeared to be acceleration-dependent was the ace in the hole – the key reason for believing that they may have discovered the physical basis of inertia. Haisch and Rueda consider the electron to be a classical point-like particle, jostled about by QVE flow impinging upon it, resulting in inertial resistance to acceleration. Here, we are shown a model for inertia which is extrinsic. In this model, inertia arises due to the influence of an external source; similar to that of Mach’s Principle, as opposed to the intrinsic electron self-energy model as described by Petkov. This extrinsic model proposed by Haisch and Rueda is termed the “Quantum Vacuum Inertia Hypothesis” (QVIH). But why does asymmetry manifest in the QV only during acceleration and not uniform motion? In other words, why do objects experience inertial force only when they accelerate? This question may be answered by the electron self-energy model and Haisch and Rueda’s QVIH. Consider the Doppler Effect. The change in pitch we hear as an ambulance siren moves past us is due to the ambulance’s motion relative to the sound waves propagating from the siren. But the ambulance doesn’t need to be accelerating to cause this auditory effect; it just has to be moving past us. However, with inertia, the situation is rather different. Inertial force is only experienced in such cases where a change in velocity is occurring. If the nature of inertia was rooted within Mach’s Principle or a Doppler-like effect, one might conclude that all motion should result in a resistance force. If inertia operated by Mach’s Principle, then a preferred reference frame would exist within the Universe, acting as a backdrop to the motion of all objects moving through it – an idea that is anathema to the tenets of GR. The Doppler Effect may hold “some” value as an analogy, but it cannot be directly applied to inertia because space is quite different

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from a fluid like air or water. Whatever we wish to call it; space-time geometry, the aether or what have you, the nature of space must also satisfy the rules of inertia, and all physical laws that have been experimentally validated thus far. What then, should the vacuum of space be like in order to satisfy the condition of inertia? The answer has to do with the way in which energy is distributed throughout the QV. Unlike the blackbody spectrum of the Sun, for example, peaking in a specific region of the EM spectrum and based entirely on temperature, QVE is predicted by QM to be distributed throughout space in a fundamentally different manner. When we plot the blackbody energy distribution41 for the Sun, we find that it emits photons spanning a wide range of the EM spectrum, peaking in the ultraviolet, visible and infra-red range42. QVE has a rather different distribution along the EM spectrum, however. The QV is predicted to possess a “frequency cubed” energy distribution throughout free space; at low QV frequencies, the spectral energy density of QV photons is minimal and at high QV frequencies it is maximal. The spectral energy density of QV photons follows the cube of the frequency along the EM spectrum, and doesn’t peak at any particular bandwidth as a blackbody radiation spectrum does. For example, let’s say we want to calculate the QVE density in the microwave region of the EM spectrum. Microwaves exist in the “10(GHz)” range (approximately). To simplify matters, we may say that the density of QVE at “10(GHz)” along the EM spectrum is proportional to “10 x 10 x 10”. The frequency cubed distribution of the QV means that moving up the EM spectrum to waves with a frequency of “100(GHz)”, the proportional energy density of QV photons is “100 x 100 x 100”! Thus, the highest frequency ranges of the EM spectrum contain the most QVE, implying that the energy density of free-space is inconceivably energetic. It has been estimated43 that the amount of QVE contained in a coffee cup sized

41

The density and arrangement of photons surrounding an object. A Blackbody spectrum calculator may be found at The Wolfram Demonstrations Project: http://demonstrations.wolfram.com/BlackbodySpectrum/ 43 This is the mainstream view, not the view of the EGM construct in the “Quinta Essentia” series (i.e. QE3,4) where the opposite conclusion is mathematically derived. That is, QE3,4 mathematically demonstrate that “free space” does not contain a near infinite amount of energy in a vanishing volume. 42

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volume of empty space, if converted to heat energy, would be enough to boil away the Earth’s oceans! The frequency-cubed distribution of QVE in a flat space-time manifold explains why an object doesn’t experience a reaction force against uniform motion. Michelson and Morely experimentally verified that an absolute reference frame by which to measure uniform motion does not exist. Thus, for an object to avoid experiencing a resistive force against uniform motion, the QV must appear identical to all observers irrespective of relative velocities44. This necessitates the cubic frequency distribution form of the QV spectrum,xv rendering uniform motion “Lorentz invariant” such that it appears consistent across reference frames. For example, wave amplitude may be small or large, but its form remains unchanged regardless of magnitude. The frequency-cubed QVE distribution ensures that space-time appears flat and isometric for any object traveling in uniform motion. However, during acceleration, the background QVE distribution appears asymmetric. Therefore, the QVIH model remains Lorentz invariant and consistent with GR via the cubic frequency distribution of QVE. GR states that an observer traveling in uniform motion through space-time perceives the Universe as being flat and isometric; however, in an accelerated reference frame space-time appears to be curved. Haisch and Rueda’s classical ElectroDynamics model of inertia asserts a congruent position; during uniform motion the QV appears symmetric. In an accelerated reference frame, asymmetry45 manifests in the QV that is proportional to the magnitude of the applied acceleration. Thus, rather than relying upon the metaphysical, nonintuitive terminology of GR, which describes space-time as being “flat” or “curved”, these terms may now be substituted with the more physically meaningful reference to “symmetrical” or “asymmetrical” QVE densities.

5.4

Bridging the gaps

Einstein relied upon the Equivalence Principle to demonstrate how the geometric space-time of an accelerated reference frame can be equivalent to a gravitational field. The same is true for Haisch and Rueda’s QVIH, which utilizes the Equivalence Principle

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Caveat: applicable to objects traveling in uniform motion, not accelerating. 45 i.e. anisotropy.

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to demonstrate how QVE asymmetry appears in an accelerated reference frames and reference frames held fixed in a gravitational field. The force an object experiences in a gravitational field is due to local QVE asymmetry, producing a net energy flux that, in effect, pushes downwards on the object. The question Einstein was never able to address, and which remains in the QV interpretation is: how, exactly, does matter “curve” space or generate QVE asymmetry? Although the mechanistic particulars have not yet been formally conjectured by Haisch and Rueda, they have been able to replace the “imaginary” four-dimensional geometry of Einstein’s space-time with their own classical, physical modeling of QVE distributions. Their description modestly insinuates one of the most astounding and profound ideas ever suggested in the history of science! QM was largely formulated several years after Einstein developed GR, and he considered the entire field to be rather unpalatable. Einstein modeled inertial and gravitational frames of reference based upon the geodesic pathways light follows in the presence of matter and during acceleration. However, Einstein lacked the tools to offer any potential physical basis for the existence of inertia, or why matter curved space-time. The QV had not yet been conceived at the time he was developing GR, so he lacked a source from which to derive a potential physical basis for gravity and inertia, aside from the “luminiferous aether” which he believed did not exist. The development of QM eventually produced a rift between itself and GR which remains solidly in place to this day. QM, through its prediction of the QV, states that the Universe possesses a specific value of energy density. However, when viewed through Relativity theory, the energy density of the QV should cause a catastrophic gravitational collapse of the Universe . . . but the Universe hasn’t collapsed. In fact, recent observations reveal that the Universe is expanding. This observation has created a major dilemma for physicists, because it means that either QM or Relativity is fundamentally flawed or incomplete, yet QM and GR have both proven to be highly accurate means of representing physical systems. To avoid a seemingly insurmountable incongruity between GR and QM, Einstein left his original interpretation of space-time alone, as a mathematical tool to extend Newton’s laws of motion into the extreme limits of the Cosmos. His theory worked so beautifully that there was little need to worry about precisely how it worked so well or why it didn’t jibe with the emerging quantum view. The beauty and elegance of GR has stood impervious to criticism for over a century and gave birth to modern cosmology. It has directly www.deltagroupengineering.com

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generated some of the most profound questions to be asked and has predicted the existence of otherwise unfathomable objects in our Universe such as black holes. Yet QM has proven to be equally valuable for explaining observations at the subatomic scale which Relativity cannot handle. Therefore, it is only fair to say that both formalisms are equally correct, even though they don’t appear to corroborate. The most important aspect of the QVIH is not that it provides a physical mechanism for inertial and gravitational forces, which GR merely describes, but that it represents the unification of GR, QM and electromagnetism. It takes the first steps at bridging the gap between these formerly incompatible, yet equally valid theories. Since Sir Isaac Newton formulated his postulate “F = ma”, it has remained just that – a postulate. “F = ma” is a tenet in physics; the immutable law governing how objects move. However, the remarkable mathematical feat leading to the QVIH was that Rueda managed to derive Newton’s postulate from QM! If Newton’s first law of motion, and thus GR, may be derived from QM then in principle these formalisms must already be unified. “F = ma” predicts how objects move; Rueda offers an explanation for why objects move in the manner they do by deriving Newton’s postulate from QM. In order to achieve this result, the QVIH model must assume something quite radical: which is that the subatomic particles comprising matter, such as quarks and electrons, are intrinsically mass-less, and it is only through their interaction with the external QVE environment that the property of inertial mass is born. In this model, mass merely arises as a by-product of an interaction between the energy packaged in the form of matter and the QVE surrounding it. The QVIH model likens this interaction to EM interference or scattering that takes place as charges are perturbed by the QV fields they move through, and the energy of this interaction is a measure of the particle’s inertial mass. In this model, the mass of any object may be considered to be a measure of the energy with which fundamentally mass-less particles interact with their quantum environment. Through this interpretation, a (classical) physical explanation for Einstein’s mass-energy equivalence relationship is also revealed. According to Haisch and his colleagues, mass arises as a function of scale. For example, if a large46 vessel floats in fairly calm waters with only small waves on the surface, it remains motionless and unperturbed by the action of the waves. However, if a toy boat is 46

Much larger than the small waves surrounding it.

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placed in the same water, it will be jostled about by the small waves it encounters as if weathering a violent storm at sea. The size of the toy boat is on the same scale as the waves it floats upon, causing it to feel the undulating terrain of the rough and choppy sea surrounding it. On the molecular scale an analogous effect exists, termed “Brownian motion”. Robert Brown was a Scottish botanist who collected and catalogued thousands of plant species in Australia in the early 1800’s. He was highly skilled at microscopy and utilized it as a tool to study plant pollens. In studying pollen grains under the microscope, he noticed that the individual pollen grains appeared to jitter wildly in suspension, yet maintained their overall position within the field of view. He noted that the movement seemed to be an intrinsic quality of the grain itself, resembling a freely moving lifeformxvi. However, he also noticed that particles only slightly larger than pollen grains do not move in this manner. Like the toy boat, pollen grains are of a particular size, which allows them to experience the kinetic motion of the water molecules they are suspended within. As the water molecules impact the pollen grain from all sides, the pollen grain jitters wildly, while larger objects are unperturbed. In Brown’s time, the cause of this effect was not entirely clear, but thanks to his initial observation, this effect has since been dubbed “Brownian motion”. Again, the temperature of any substance is a measure of the average kinetic energy of the molecules comprising that substance. Within fluids like air and water, molecules dart about bouncing off one another; the higher the temperature, the more frenetic the molecular activity. Some molecules possess sufficient momentum such that when they strike the surface of a pollen grain it recoils. Since water molecules are too small to be viewed through a microscope, we may infer their movement because we observe the pollen grains rapidly quivering and jittering in place as they recoil upon impact. Over a period of time, if one tracked the motions of a pollen grain under Brownian motion, one notices generalized movement in some direction; referred to as a “random walk”. This range of motion represents the statistical average of the combined small-scale movements of the pollen grain, resulting in travel from point A to point B. The QVIH was developed utilizing “Stochastic Electrodynamics” (SED). The term “stochastic” refers to a mathematical treatment incorporating random behavior over time. Random stock market fluctuations or the walk of Brownian motion may be modeled utilizing this technique. Haisch and Rueda, in their www.deltagroupengineering.com

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development of the QVIH, modeled the electrodynamics of a moving electron stochastically as though it were a pollen grain jostled about by Brownian motion in the randomly fluctuating sea of QVE. According to Haisch and Rueda, under conditions of uniform motion, the classical, point-like electron is buffeted about by the chaotic fluctuations of QVE. When the electron is forced to accelerate, it appears to the electron that the QVE fluctuations in the direction of acceleration become increasingly energetic. It is this QV asymmetry that is thought to result in the acceleration reaction force of inertia. Since mass is a measure of inertial force, the interaction between the electron and QVE is thought to establish the electron’s inertial mass. QV fluctuations, in this model, are thought to cause the electron to be wildly shaken about while stationary or in uniform motion. The stationary fluctuation of a charge was predicted mathematically by Erwin Schrödinger in the early 1930’s. Schrödinger derived from Dirac’s equations that the electron should be expected to fluctuate at the speed of light in what he referred to as “zitterbewegung”, which in German means “trembling motion”. But if the charge truly is fluctuating at the speed of light, it means that the electron must be intrinsically mass-less. Otherwise, how could it move at light-speed? It is this idea that establishes the basis upon which the Haisch-Rueda interpretation operates. What they propose is that if particles such as the electron are inherently mass-less, then it must be through an interaction with the extrinsic QV field that the property of mass emerges. In other words, the energy of the fluctuation is a measure of the particle’s mass. Thus, in this view, mass and energy are equivalent, and mass cannot exist without the QV of space! Louis de Broglie predicted, by combining the equations “E = mc2” and “E= hν”, that all matter has wave-like properties. Although the de Broglie wavelength of a moving planet or person is imperceptibly minute, the wavelength of a moving electron or subatomic particle is quite large compared to its size. As a direct mathematical consequence of combining the two equations, the restmass of a “stationary” electron may be expressed in terms of wavelength. In other words, the mass of the electron may be expressed as a frequency of energy equivalent to the mass-energy of the electron. This relationship is termed the “Compton wavelength”xvii. However, electrons aren’t the only particles which may be expressed in Compton wavelength form. Other subatomic particles possess characteristic Compton wavelengths because, by

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way of combining the equations, a particle’s mass defines its wavelength. Like Einstein, who used the photoelectric effect to illustrate that light could be thought of as having particle-like attributes, Arthur Compton also contributed to this particulate (photon) model of light by experimentally verifying that photons possess momentum (a characteristic associated with mass). Compton demonstrated this by scattering X-ray photons off atomic electrons. As X-ray photons bounce off electrons, the photon’s momentum diminishes as it knocks the electron out of place (i.e. changes its momentum). Compton found that the X-ray photon loses momentum energy in the form of frequency, and that the frequency lost is limited to double the electron’s Compton wavelength. So not only did Compton help establish the particle nature of light, he also confirmed the physicality underlying the wave nature of matter, revealed by mathematically combining “E = mc2” and “E= hν”. By means of the extrinsic interpretation, Haisch and Rueda propose that the Compton wavelength is established as the electron charge physically interacts with the QV at the Compton frequency. In this interpretation, the Compton frequency is associated with the restmass due to its zitterbewegung energy. However, when the electron is in motion, it gains the attribute of momentum (mass multiplied by velocity). Since the de Broglie wavelength is a measure of a particle’s momentum, Haisch and Rueda decided to investigate whether the Compton and de Broglie wavelengths were interrelated phenomena. In the year 2000, Haisch and Rueda published a manuscript demonstrating how an electron fluctuating at the Compton frequency, as it passes by a stationary observer, appears to be moving at its de Broglie wavelengthxviii. They achieved this by mathematically “observing” the electron’s Compton frequency from a Doppler shifted reference frame in motion. When they superimposed the Doppler shifted frequency from the moving reference frame onto the Compton frequency of the electron, they noticed that the resulting “beatfrequency”47 was precisely equal to the de Broglie wavelength of a moving electron! Beat-frequencies arise when differing wave frequencies overlap and are often readily identifiable in videos of cars in motion, when the wheels (as viewed on video) appear to be slowly rolling backwards as the car drives forward48. We perceive this visual effect 47

The mathematical difference between frequencies. This phenomenon is referred to as “temporal aliasing” or “the wagon-wheel effect”.

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due to the difference between the frequency with which the video frames are captured by the camera (in frames per second), and the frequency at which the wheels of the car rotate (in revolutions per second). Video cameras typically capture approximately thirty still frames per second, which during play-back are blended together by our visual cortex to re-produce the effect of motion. If the wheels of the car were turning at a rate of “25” revolutions per second as the car is captured on video, the wheels will not have revolved completely by the time the next video frame is captured; the wheels would only have turned about “85%” of the full cycle. If a marker were placed on the wheel to keep track of its position with time, it would show that the wheel shifts about “55°” counter clockwise with each captured frame of video. Thus when the video is played back, the wheel will appear to be rotating backwards at roughly four revolutions per second. By changing either the frequency of the video capture or the speed of the car, the effect may be run faster or slower in the clockwise or counter clockwise direction. If the revolutions per second and frames per second are equally matched, the wheel will appear motionless as the car drives along. In this regard, Haisch and Rueda have “filmed49” the Compton frequency of an electron against the background frequency of the QV in a moving reference frame. In doing so, the electron’s wavelength appears to an outside observer to be the de Broglie wavelength. Here, Haisch and Rueda suggest that the de Broglie wavelength is ultimately derived extrinsically from the QV. However, this particular example represents just one of many suggestions for how the QV might help us understand the deep mysteries of the quantum Universe. The QVIH suggests the possibility that the property of inertial mass, and other quantum phenomena such as the de Broglie wavelength, arise extrinsically through an interaction between the subatomic “particle” and QVE. This stochastic modeling system yields quite profound results, but not without stirring some controversy, because it represents a very literal way of approaching the problem. But if we are ever going to fully understand gravity and inertia, we must be open to innovative interpretations like Petkov’s intrinsic model and the Haisch-Rueda extrinsic model. Creative interpretations of reality are commonplace in contemporary physics, and we are quite accepting of them because we are cognizant of the fact that they are merely human rationalizations 49

Analogous to the wheels of the car in the preceding example.

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of purely mathematical concepts. However, these mental models sometimes forge bias in our thinking, and cause us to form preconceived notions about matter and space which obfuscate our intuition and our ability to observe the obvious. One such bias is the notion that space-time is literally curved or that space should be interpreted as a purely geometric manifold. It is of vital importance that we not confuse the abstract mathematical description of space for space itself. The other cataract clouding the lens of truth is the notion that gravity is one of the primary forces in nature, or a force in its own right. We know that the action of gravity on matter is equivalent to inertial force, and arises by way of apparent curvature, or asymmetric energy distribution in space-time. The root of our problem is that we have defined separate terms (gravity and inertia) for a single phenomenon, and find it necessary to cling to such misguided dogma. Einstein’s work explicitly states that gravity and inertia are equivalent, and “E = mc2” tells us that energy and matter are equivalent. Perhaps if it weren’t for the atomic bomb, we would have just as much difficulty with the notion of mass-energy equivalence as we seem to have with the idea that gravity and inertial forces are, in fact, one-and-the-same phenomenon. GR is as brilliant and elegant as it is effective, yet on the same note, it is also one-sided and incomplete because it disregards the demands of the quantum Universe. When we view mass only in terms of GR, or only in terms of QM, we limit ourselves to a partial and incomplete description of the Universe, and this inevitably leads us in the wrong direction. However, by viewing the problem from both perspectives simultaneously, a wondrous and limitless horizon begins to unfold before us.

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6 6.1

The Polarizable Vacuum Blind-sighted

General Relativity (GR) is a geometric model of gravity such that space-time is represented as a four-dimensional manifold yielding a topological map of space in the presence of matter. This space-time landscape, in turn, guides the paths of light and the motion of objects passing through it. We interpret this motion as “gravity”. On one hand, GR is a marvelous achievement which has profoundly enhanced our understanding of the Universe. On the other hand, it is not at all amenable to technological applications, in that it would require huge amounts of matter or energy to modify or manipulate gravitational forces. GR yields highly accurate predictions, yet makes no assumptions as to why the Universe is as it is. It doesn’t explain why matter produces a gravitational field, or the specific mechanism by which matter experiences inertial forces upon acceleration. Einstein’s space-time manifold is a vacuum – a void. If this is indeed the case, then the obvious question remains: how can nothing possess a curved four-dimensional geometry? And how is it that objects “know” whether they are passing through a region of curved or flat space? It is of critical importance to remember that GR is merely a highly effective descriptive tool – a mathematical representation, not a literal explanation of Nature. Bernard Haisch and Alfonso Rueda introduced a model describing matter as being immersed within and wholly dependent upon the quantum medium of space for its existence. Their model does away with the notion that matter rests suspended in a vast, inert nothingness while exerting gravitational force on other objects from afar. Throughout the history of physics, it is almost incomprehensible that we have virtually ignored the question of why an object experiences a force upon acceleration, and have yielded without protest to the notion that this force emerges from nowhere! Perhaps this is due to the way in which our brains are wired. Our ability to function as human beings relies upon our capacity to selectively tune-out superfluous input like the sound of a ticking clock, the buzz of fluorescent lighting, or the background murmur of conversation in a crowded room. At every moment of every day throughout the course of our lives we sense the weight of our own body as we sit or walk, and the tug of inertia whenever we change direction or velocity. It is a constant and consistent experience; so consistent that we scarcely think of it. It is human nature to ignore the www.deltagroupengineering.com

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obvious so that we may focus on things that seem important, aberrant or threatening. We seem content to nod vacantly in agreement to any suggestion, no matter how bizarre or disconnected from our intuitive knowledge and everyday experience, as long as it satisfies our need to predict the patterns of Nature. We are apt to swallow contradictions such as the idea of “geometric nothingness” hook, line and sinker in lieu of other, perhaps more rational explanations. Twentieth century physics has merely replaced the notion of “action at a distance” with the equally abstract concept of “curved space-time”. Many physicists are quite comfortable with this contradiction, insisting that the relativistic tensor mathematics beautifully describing the space-time manifold actually is space-time – substituting the abstraction for the phenomenon! This may be suitable for those who are highly adept and well versed in the language of applied mathematics, but it leaves little for the more pragmatic mind to chew on. GR was developed by “mapping” the trajectory of light as it passes alongside massive objects. The extent to which gravitational fields bend light allows us to trace the contours of the otherwise invisible space-time manifold. The physicist John Wheeler is noted for one of the most succinct and concise descriptions of GR in stating: “matter tells space how to curve, and curved space tells matter how to move”. But is matter actually curving space, and in so doing causing rays of light to bend as they propagate along a curved manifold? Ask an engineer to bend light and they won’t attempt it by curving spacetime; if you want to bend light, shine it through a lens!

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6.2

Optical gravity

If you dip a long stick into a swimming pool, you will notice that it appears to bend as it enters the water. The same is true if you happen to be spear fishing – you would need to aim your spear at a slightly different place than where you see the fish if you wish to hit your target. This phenomenon arises because in both cases you are seeing light (an image) which has been refracted (i.e. bent) by the water. Light is refracted as it passes from one substance through to another of different density. A substance like water possesses a specific index of refraction based upon its density. When light transits from air into water, it moves from a medium of lower to higher density. As photons of light move through substances such as air, glass, or water, they don’t simply pass through unaffected – light interacts with the atoms and molecules comprising it; the light might be absorbed and re-radiated, or reflected. When light passes from air into water, it takes longer for the photons to interact with the water because it is more densely packed with molecules than air; as this occurs, the light slows down, causing it to bend. It’s a bit like the difference between running on land and trying to run in a swimming pool. You can’t run as fast in water as you can in air because water is denser. The degree to which a beam of light is bent depends not only on the density of the medium it passes through (its index of refraction), but also the angle of approach (i.e. “angle of incidence”). The science of optics is based upon the principles of refraction and angle of incidence. Thanks to optics, we have eyeglasses, telescopes and a whole host of other magnificent technologies which improve our daily lives. Sir Isaac Newton worked extensively to create the science of optics. Newton studied the manner in which lenses of different shape and density bend and refract light in various ways, and how curved mirrors reflect and focus light. However, the foundations of optics are based upon interactions occurring at the quantum level, which Newton knew nothing of. The theory fully describing the fundamental interaction between light and matter is termed Quantum Electrodynamics (QED), and is one of the most accurate theories in physics. The application of optical principles to those of GR as led to an alternative and more intuitively appealing interpretation of the space-time manifold referred to as the “Polarizable Vacuum (PV) www.deltagroupengineering.com

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Approach to General Relativity (GR)”xix. Harold “Hal” Puthoff introduced the PV model in 2002, having drawn upon earlier work by physicists Harold Wilson, Robert Dicke, and famed Nobel laureate, Andrei Sakharov. The PV model utilizes optical principles to define the topological features of space-time via the application of a variable “Refractive Index”50 rather than “curvature”. As a beam of light propagates through space, passing nearby a massive object, its path is not bent due to the curvature of “the nothingness” it happens to be transiting through; it is bent by passing through a region of variable energy density which in turn, generates a variable Refractive Index affecting the path of the beam. According to the PV model, all matter establishes an energy density gradient in the QV surrounding it, acting as a space-time lens. This results in the formation of a changing Refractive Index within the Quantum Vacuum (QV) surrounding matter. Consider the use of a magnifying glass to focus light from the Sun. The magnifying glass bends the parallel beams passing through it to a single focal point. It is the tapered shape and varying lens thickness which causes the light to bend to differing degrees as it passes through. A similar effect also occurs in space. Einstein predicted that a strong gravitational field should cause the trajectory of light to bend in much the same way as it does when passing through a lens. This effect is referred to as “gravitational lensing”, and astronomers have obtained direct photographic evidence of this phenomenon with the Hubble space telescope. Given the right set of circumstances, light from a distant quasar may be bent around the intense gravitational field of a galactic cluster positioned between the Earth and the quasar, so that it may be seen even though it is located directly behind the cluster. Hubble images of distant lensed objects appear warped and stretched as though having been reflected off the back of a polished spoon. Within the context of GR, the space-time geometry of a gravitational field surrounding a galactic cluster is depicted as a depression in the fabric of space. As light passes by this curved region of space-time it bends, resulting in a gravitational lensing effect. Substituting the concept of “variable index of refraction” within the QV in place of “space-time curvature” yields a congruent interpretation of gravity to that of GR. The key distinction between the PV and GR models is that the PV interpretation explicitly describes a physical manner in which space-time may, in effect, be 50

Denoted by the symbol “KPV”.

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“curved”. However, it doesn’t completely address the precise mechanism by which this occurs. That is to say, the PV model doesn’t explicitly describe how matter physically changes the Refractive Index of the space-time manifold surrounding it.

6.3

Shaping the lens

The PV model asserts that matter polarizes the QV into regions of variable energy density that, in turn, generates regions of variable Refractive Index in the space surrounding an object. To visualize this concept, one might consider a common magnet. If you sprinkle iron filings onto a piece of paper and place a magnet underneath, the filings rapidly align themselves with the magnetic lines of force produced by the magnetic field. The magnet’s influence polarizes (i.e. enforces direction and order) to the random scatter of filings. A precedent for the existence of vacuum polarization comes from the generally accepted model of the electron. In previous chapters, a highly simplistic model of the electron was utilized to describe “Classical Electromagnetic Mass Theory”; the electron was described as a point-like charge in a pure vacuum, radiating an electromagnetic (EM) field. To further simplify this concept, the electron was treated as a ball held fixed inside a frame by springs which expand or compress as the ball moves within its frame. The contemporary model of the “bare electron” stems from QED51. The QV is effervescent with virtual particle pair formation and annihilation; thus, we must consider the effect this has on the dynamics of all elementary particles, including the electron. The effect an electron has on the QV is termed “vacuum polarization”. In a volume of space devoid of all matter, the QV is comprised of a chaotic and equally distributed mix of virtual particle pairs popping into and out of existence. However, drop an electron into the mix and all that drastically changes. Its presence attracts the virtual positrons present in the vacuum, forming a cloud of positive charges surrounding the bare electron. The QV becomes biased as

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virtual particle pairs are segregated into clusters of positive and negative charge. In this state, the QV is no longer neutral or uniform – it has been polarized52. One possible explanation accounting for the formation of gravitational fields is that all material objects are composed of atoms which are themselves composed of charges and elementary particles generating their own localized polarizations within the QV. The cumulative effect of these densely packed particles and charges generates a large-scale, synergistic polarization in the QV extending into space. Taking vacuum polarization into account, the PV interpretation combined with the Quantum Vacuum Inertia Hypothesis (QVIH) provides a physical explanation for why matter experiences inertial force and generates gravitational fields. GR offers little in this regard; it describes the manner in which energy moves in gravitational fields but doesn’t offer a physical explanation for why objects gravitate, or experience weight and inertia. According to the PV model, matter generates a polarized gradient in the QV resulting in a change in the Refractive Index of space-time. In such cases the QV appears asymmetrical, thus inertial and gravitational forces are experienced. When the optical effect of an asymmetrical energy gradient is considered, the manner in which the polarized vacuum affects light propagation becomes apparent53. As a ray of light enters an area of vacuum polarization, it is affected by the change of Refractive Index and bends towards the polarization source as if it were passing

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http://physics.nist.gov/cuu/Constants/alpha.html: according to QED and relativistic Quantum Field Theory (QFT) describing the interaction of charged particles and photons, an electron is considered to emit virtual photons which, in turn, may become virtual electronpositron pairs. The virtual positrons are attracted to the “bare” electron while the virtual electrons are repelled from it. The bare electron is therefore shielded due to polarization within the vacuum. 53 The paths of light altered by the presence of matter define spacetime “curvature”.

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through a lens. The bending of light in this context is congruent to the curved path of light predicted geometrically within GR. GR states that inertial force and gravitational weight are defined by the geodesic paths of light in curved space-time. Any deviation from the natural geodesic topology requires energy input. When an object accelerates or is held fixed in a gravitational field, space-time appears curved and the object experiences a force. For an object moving with uniform motion in free space, or falling along the natural geodesic in a curved manifold, space-time appears flat and no force is experienced. Likewise, to an observer held fixed on the surface of the Earth, space-time appears asymmetrical, thus constant acceleration is experienced. Similarly, from the perspective of a uniformly accelerating observer in free space, the QV appears asymmetrical and one experiences a force. In both cases, the Equivalence Principle is preserved and we are equipped with a framework for understanding its origin.

6.4

Conflux

What of the other strange predictions made by GR, such as time dilation, mass scaling, length contraction and mass-energy equivalence? In order for the PV model to robustly challenge GR, it must satisfy all competing predictions which have thus far been experimentally verified. The solution and answer to “the challenge” pertains to the Refractive Index “KPV”. When light passes from air into water, it moves from media of lower to higher density and slows down. In terms of an optical model of gravity, relative to a distant observer, if “KPV” increases, the speed of light “c” appears to slow down54. GR is based upon the trajectories of light through curved space-time relative to an observer; this implies that the propagation of energy within the QV is the basis of gravity. Thus, descriptors such as mass, size and time are also subject to “KPV”. Energy is the currency of the Universe and can neither be created nor destroyed, it may only be exchanged or transformed; all mass-energy influences its environment and is itself affected by

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environmental conditions. One such phenomenon illustrating the interaction between an object and its environment is “buoyancy”. Consider a helium balloon near the surface of the Earth. The helium gas inside the balloon is less dense than the encapsulating atmosphere of heavier gasses (nitrogen and oxygen). The balloon possesses buoyancy because atmospheric density is greater than inside the balloon; the density differential forces the balloon upwards as it seeks environmental equilibrium55. Equilibrium marks a point of neutral buoyancy such that the pressure inside and outside the balloon are equalized. Because the balloon is elastic, it expands during ascension. Higher atmospheric pressure near the surface of the Earth acts uniformly on the balloon, confining the helium inside to a particular volume. However, with increasing altitude, the atmospheric pressure decreases and less environmental energy is available to contain the gas inside and the balloon expands. A similar concept sustains the PV model of GR such that mass-energy equilibrates to the local Quantum Vacuum Energy (QVE) environment56. Hence, objects appear to shrink upon acceleration to near light-speed while equilibrating, as perceived by a distant observer; from the object’s perspective the Universe appears to increase in energy, however its own size does not seem to change. From the distant observer’s perspective, the situation is analogous to watching a helium balloon being pulled to Earth from high altitude. At high altitude, the balloon is stretched to a size determined by environmental equilibrium. As the balloon is displaced from its initial equilibrium state by moving into a region of higher pressure, the increase in atmospheric density compresses the balloon. In terms of the PV model, because “E = mc2”, we must consider that mass is a measure of energy and the energy density of the encapsulating space directly affects mass as it equilibrates to the local QVE environment. An object accelerating away from us at near light speed57 appears red-shifted because the frequency of emitted light is subject to the “KPV” value. Regardless of the energy density (i.e. “KPV” value) of 55

All physical systems seek stabilization, marked by the lowest permissible energy state. 56 Analogous to the manner in which a helium balloon is affected by the atmosphere. 57 The speed of light in a vacuum is a definition, not a measurement. This is why it is listed as “exact” by the National Institute of Standards and Technology (NIST); http://physics.nist.gov/cgi-in/cuu/Value?c|search_for=Speed+of+light

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the local space-time encapsulating you in a vacuum, the light you emit always propagates away at “c”. However, to a distant observer, the light you emit appears refracted by the space-time you move through. The “tone” of the light appears to shift because the observer views the light source as moving into a region of “KPV” which is different from the observer’s local value. The spectral shift of the light emitted from an accelerating source is solely dependent on the relative difference between the “KPV” values of the observer and the source. Consider a light source moving naturally into a region of variable “KPV” (a gravitational field). To the source object, nothing appears to change in terms of its own size, the way light moves, or the way time flows. However, to a distant observer, light from the source appears to refract as it moves into the gravitational field. An object moving naturally within a region of variable “KPV” experiences no external forces because natural motion in such a case requires moving along a geodesic path in “curved space-time”. Thus, the geodesic path of GR may be expressed in terms of “KPV”, rather than explicitly in terms of space-time curvature. The primary advantage of the PV model over GR, in this regard, is its conceptual simplicity. An observer might presume that a force acts on a naturally moving object causing it to shift into a curved trajectory around a planet or star, but the object itself doesn’t experience any force. It is only when the object is displaced from equilibrium within its local environment that it experiences a force. All objects seek the lowest energy equilibrium state within an environment; this is why acceleration requires energy input and inertia is experienced during acceleration. Thus, energy input is required to maintain disequilibrium and once the energy input ceases, the object resumes a state of uniform motion, in equilibrium. No matter where uniform motion occurs or how fast an object may appear to be moving with respect to its environment, a uniformly moving object will be in equilibrium with the energy configuration of its environment. It perceives the Universe as being flat even though it may appear curved to a distant observer. Therefore, we may summarize equilibration in terms of the PV model of gravity and GR as follows; “uniform motion” is synonymous with “QV equilibrium” and “acceleration” is synonymous with “QV disequilibrium”. From Relativity theory we know that an object can never accelerate to the speed of light because it becomes infinitely massive; in order to accelerate an object to the speed of light, an infinite amount of energy is required to push it that fast. This is truly one of the most bizarre predictions of Relativity and one of the most difficult www.deltagroupengineering.com

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to understand intuitively. It also presents one of the most formidable boundaries limiting our hopes of finding an efficient means of interstellar space travel. As mass accelerates, it encounters inertial resistance due to disequilibrium, becoming a “sink” for the increasingly energetic environment it perceives. To achieve greater acceleration (i.e. QV disequilibrium), more energy must be dumped into the mass from the environment in order for the system to equilibrate. Since energy is equivalent to mass, the mass increases with the addition of thrust energy. As an object is accelerated to near light speed, its mass becomes nearly infinite. Consequently, infinite force would be required to accelerate an infinite mass to the speed of light. Haisch and Rueda’s QVIH demonstrates that as matter accelerates through space, it perceives the QV as being asymmetrical. The PV model advances this approach by assigning form in terms of a “KPV” value. As an object moves into a region of space with an apparent asymmetric vacuum energy density58, a force is required to counteract the resistance induced by QV asymmetry. When an object is held in a gravitational field it experiences constant acceleration; this is what we have come to call the “force of gravity”. In actuality, due to the Equivalence Principle, the object is actually experiencing an inertial force. No unique force of “gravity” exists per se, only a disequilibrium stress between matter and the QV. All points in a gravitational field exist in a constant state of asymmetrical energy polarization; thus, all material objects in the field continually attempt to equilibrate to the asymmetry. However, equilibration is impossible while any object is held fixed and not permitted to fall along its natural geodesic trajectory (i.e. path of energetic equilibrium). The only means to equilibrate with environmental asymmetry is to “go with the flow” and fall with gravity. This is why objects are weightless during free-fall. An object’s weight is a function of its mass and the acceleration of gravity. If we travel to the Moon, we weigh less than we do on Earth because our weight is a product of our mass (which remains the same) and the acceleration of gravity, which is lower on the Moon. If Jupiter had a solid surface we could stand upon, we would expect to weigh more than we do on Earth. Held fixed in a stronger gravitational field, the force required to counter the acceleration of gravity is much greater.

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i.e. a region of space with a “KPV” value greater than unity.

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In a weak gravitational field such as the surface of the Moon, the QV possesses a lower Refractive Index59 than on the surface of the Earth. One may relate Refractive Index (QV asymmetry), to the slope of a curve, such that greater asymmetry induces a steeper slope. The higher the “KPV” value, the steeper the slope and greater the gravitational acceleration will be. Because mass is a measure of the force required to counter QV asymmetry, mass scales according to the local “KPV” value as it does under GR due to the intensity of spacetime curvature. Thus, when optical principles from the PV model are applied to GR, physical processes are easier to comprehend. One of the most fascinating aspects of GR is the notion that time is enmeshed with space. GR not only states that mass and energy must be considered “mass-energy”, it also states that space and time are a singular phenomenon termed “space-time”. In the fourdimensional matrix of space-time, an object has a precise position within 3-D space, and it has a coordinate or “position” in time as well. When an object moves to different coordinates in 3-D space, it will take a certain amount of time to do so. We define “time” as the interval between linked events. In Relativity the speed of light is constant, thus the most appropriate means of representing the passage of time is to base it on the duration of the interval required for light to traverse a particular distance in space. However, the consequence of holding the speed of light constant is that mass, length and time will all appear to change relative to it. Let’s consider Einstein’s elevator again. In this case, we decide to quantify time by measuring how long it takes for a photon to bounce between the walls of the elevator from side to side. Let’s also imagine that we have two identical elevators moving parallel to one another through space. At first, they move at the same rate with no difference in velocity between them. The photons bounce back and forth inside each elevator in unison, hitting each wall at exactly the same moment. However, when one of the elevators begins to move at a faster rate than the other one, the vertical movements of the elevators must be considered when measuring the total distance each photon travels between each wall. Not only is the distance travelled by each photon measured in terms of the horizontal distance inside the elevator, the vertical distance the elevator travels within that period must be added to that distance. This causes the photon’s path to stretch into a zigzag rather than a horizontal line.

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As one elevator moves faster than the other, the photon has a greater distance per unit time to travel between each wall. A photon propagates in a vacuum at the speed of light; thus, the modified factor between each elevator is the time required for the photon to bounce between the walls60. In the slow-moving elevator, the photon has a shorter overall distance to cover, but in the fast-moving elevator the photon travels a greater distance overall, taking into account the larger vertical distance it has to travel. If we are measuring time as the interval between photons striking each wall, time in the fast-moving elevator appears to an outside observer to slow down. However, if we were inside either elevator, we would not notice any difference in the passage of our own time; we would only be aware of photons bouncing from side to side. Likewise, if we examine the behavior of the slow-moving elevator from inside the fast one, it appears that time has slowed down for the other elevator while ours remains the same; from inside the “slow” elevator, time in the fast-moving elevator also appears to have slowed down. Time is thus relative, not only because it is relative to an observer’s motion, but because it is relative to the constant speed of light in a vacuum. If we were riding in a space ship headed towards a black hole, we would observe that we move towards it and “fall” in61. However, to an outside observer watching the scene unfold, we first appear to shrink62 and the light we emit begins to red-shift, but we would never actually appear to fall into the black hole! This is because, to the outside observer, our time first appears to slow down and then stop at the moment we reach the event horizon! Within GR, these strange effects are due to the propagation of light in a curved space-time manifold. In the context of the PV model, the same effects occur but they are a function of “KPV”, not curvature. Imagine that a region of flat space-time was analogous to a large rug laying flat on the floor. Let’s say an ant is walking from one end of the rug to the other, moving at the maximum speed its legs permit (the ant represents a photon traveling at light speed). If we scrunch up the rug and measure the time required by the ant to traverse a distance relative to the bare floor, the distance per unit time the ant travels appears to be less than if the rug were lying flat. When the “KPV” value increases, QVE density increases. This is analogous to “scrunching up” the fabric of space-time. Even 60

The relativistic mass effects discussed previously do not apply because the photon is considered to be mass-less. 61 Not withstanding the tidal forces ripping us apart beforehand. 62 Before being stretched apart by gravitational tidal forces.

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though the speed of light does not appear to change locally within a region of varying vacuum polarization63, to a distant observer in flat space-time, light appears to slow down64 and the distance between two points decreases65. By considering the difference between local and observed vacuum polarization states of space-time, it becomes obvious why an object appears to behave as though its time was slowing down, its length was contracting or its emitted light was being refracted and shifted in frequency. It’s like spear fishing in a tide pool; the image of the fish we see is refracted, and if we aim for what we see we will miss the target. However, if we aim for where the fish should be after refraction is considered, we have a much better chance of hitting it. The PV model demonstrates the manner in which the “KPV” value of the QV is congruent with the concept of “curved space-time” which Einstein invoked to explain acceleration and motion through gravitational fields. Most importantly, the PV model leaves us better equipped to understand the physical basis for the perplexing conclusions of GR. Mathematically, the laws of motion elegantly unfold through the implementation of GR but the basis for these laws remains difficult to grasp from the perspective of relativistic “curvature”. However, when we replace the concept of “curvature” with the principles of optics, the consequences of relativity make intuitive sense when viewed through the “lens” of the PV.

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e.g. at the surface of the Earth. Appearing to refract towards the region of higher “KPV” value. 65 As measured in accordance with the ambient energy density condition in the observer’s local environment. 64

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7 7.1

The Harmony of Nature Ancient wisdom

The Universe is an ever-changing system in motion. All of its parts; the stars and planets, the galaxies and nebulae, are all linked in a marvelously intricate dance. If a single attribute characterizes the Cosmos, it is movement. The Universe flows and evolves – forming whorls and spirals like eddies in a flowing river; it appears at once chaotic yet profoundly ordered. We see order in the regular orbits of planets around the Sun and the quantum jumps of electron energy levels in atoms. Science rests upon our ability to mathematically predict these regularities in a seemingly chaotic Universe. But why is there order in the first place? What is the organizing principle upon which order arises in our Universe? Our innate appreciation of music and harmony affords us a singular distinction in the animal kingdom, and it is by way of this principle that we may gain a more thorough understanding of order in the Cosmos. The Universe is built upon the foundation of harmonic relationships. Harmony is stability, and stability is order. The Cosmos exists through a sympathetic balance of forces; a dynamic equilibrium binding its inner workings in perpetual dance. Nothing exists independently and all things find order and stability through harmonic concordance. The supreme clockwork order of the Cosmos is regulated and overseen by an almost musical harmony. Without this harmonic imperative acting to govern the existence of matter and motion, chaos would ensue and the Universe would cease to be. This is not simply a philosophical exhortation – it is a physical fact. The concept of harmony permeates virtually every culture and philosophy, and has been a pervasive theme throughout recorded history. The ancient Babylonians, whose civilization thrived some four thousand years ago, are reported to have defined their cultural and philosophic identity according to the principle of harmony. The Hellenistic philosopher, Philo of Alexandria (20BC – 50AD), described the ancient Babylonians as having “… set up a harmony between things on Earth and things on high, between heavenly things and earthly. Following as it were the laws of musical proportion, they have exhibited the Universe as a perfect concord or symphony produced by a sympathetic affinity between its parts” xx. The Father of Numbers, Pythagoras of Samos (582 – 507BC) was a scientist, a mystic, but foremost, a mathematician. Pythagoras is known primarily for his “Theorem”, utilized to calculate the www.deltagroupengineering.com

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dimensions of right triangles. However, he is also known for having formulated the Laws of Cosmic Harmony. Similar to the ancient Babylonians, Pythagoras adopted a world-view founded not only on the order that harmony implies, but the physics of harmonic relationships. His harmonic philosophy was not merely a poetic and idealistic notion – it was an idea forged from mathematical logic. The Pythagorean philosophy arose from the study of musical and tonal relationships. Pythagoras was the first to formally describe the manner in which our human appreciation of musical tone and pitch rests upon a solid a mathematical foundation of harmonic proportions. The notes in a scale are not arbitrary. The spectrum of all possible tones is delineated into distinct divisions, forming scales of whole notes which we naturally discern as being evenly defined increments of a larger whole. Most people can immediately identify whether a note sounds flat or sharp. We sense upon hearing a note sounding flat or sharp that it is mathematically discordant from other notes in the scale. Western music is based upon the “diatonic scale”, defined by Pythagoras; thus, originally known as the “Pythagorean scale”. Certain notes of a scale may be produced on a single string of a guitar, for example, if the string is held fixed at fractions of its fixed length. The “octave” marks a complete cycle of the tonal scale. Two tones separated by eight full tones, termed the octave, is actually the same tone, just higher or lower in pitch. The harmonic ratio describing the octave is “2:1”; meaning, a string vibrating along half its length produces the same note as the whole length but at a higher pitch66. If a string is held fixed at a point one-third of its whole length, a note five tones above the fundamental67 will sound. The ratio for this tone is “3:2”. The ratio producing a sound four tones above the fundamental is “4:3”. All of these even ratios produce sounds in tune with the others. However, when two different notes not mathematically concordant with this harmonic ratio are played simultaneously, the tones sound dissonant. Musical notes are not arbitrarily chosen from a spectrum of tones, they are increments in tone derived from geometric ratios of a fundamental tone. The frequency of vibration is what we hear as a tone and the physics describing the musical scale is defined by the harmonic relationship between the tones. “Harmony” means to be in concordance with, or having parts joined in sympathetic union; connoting congruence, compatibility and 66

The high-tone octave is double the frequency of the low-tone. “Fundamental” refers to the lowest tone (i.e. frequency) in a harmonic series. 67

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stability. The Pythagoreans interpreted numeric harmonic relationships as being implicit in Nature such that the Cosmos owed its existence to a mathematical imperative. Pythagoras believed that numbers were the only real things in the Universe and that divine numerical ratios caused all order to arise. Harmony, in the Pythagorean Universe, begets order and influences all forms in Nature. Pythagoras was also the first to apply the term “Cosmos” to characterize the Universe. To us, the “Universe” is abstract – something out there. However, the term “Cosmos” encompasses everything that is the Universe, from galaxies to planets, from people to plant life; everything. The word “Cosmos” that we now colloquially apply interchangeably with “Universe” is an ancient Greek expression describing a state of perfect order – the antithesis of chaos. That Pythagoras so carefully chose to assign this word to describe the Universe is quite telling because in doing so, he implies that the Cosmos is far more than a void in which we are suspended; it is a supreme manifestation of perfect harmony, permeating all facets of existence.

7.2

Music of the spheres

“Harmony” is not merely a poetic philosophical concept; it is also physical and literal. Assuming harmonics represented the basic nature of the Cosmos, Pythagoras developed a mystical model of planetary motion known as “the Music of the Spheres”68. He surmised that the planets, the Earth and Sun included, were organized and set in place according to a divine rule of harmonic proportions. Although this was a purely mystical philosophy, based upon a mathematical concept, some literal truth remains in its core. We have come to discover that the planets do not orbit the sun in arbitrary paths of their own design; the gravitational fields of the other bodies in the solar system directly affect their orbits. This gravitational network is a key factor in the formation and evolution of our entire solar system. Jupiter’s moon Europa, for example, is tugged by the gravitational influence of all other moons in the Jovian system, and this acts to “align” and stabilize the orbital period of each moon. This stable gravitational arrangement that evolves over time is known as “orbital resonance”69.

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Musica Universalis. Orbital resonances may be stable or unstable. www.deltagroupengineering.com

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Orbital resonance was the key driver in the formation, evolution and order of our current solar system. Early in its evolution, our own solar system is thought to have possessed many more planets than exist today. However, resonant instabilities caused these early planetoids to congeal into larger ones, or nudged them out of their precarious orbits and into the Sun. Some planetoids ejected from their solar orbits were “captured” by planets and became moons. The substantial masses of gas giants such as Jupiter and Saturn provide a source of protection and stability for our solar system – acting as grand matriarchs of the solar family, reigning in rebellious rogues and ejecting uncooperative dissidents. Over the course of many millions of years, the solar system eventually evolved more stable orbital resonances as it settled into the configuration that exists today. These stable resonances act to hold our solar system together. For example, the Earth’s period of rotation around the Sun is one year and Saturn takes nearly 30 years to complete its orbit. The closest planet to the Sun, Mercury, takes roughly three months to complete its orbit. Considering the orbital periods in relation to one another, we notice a marked regularity amongst them. For every orbit of the Earth, for example, Mercury orbits the Sun approximately four times and for every five orbits of Jupiter, Saturn orbits twice. Quasi-uniform ratios are found amongst the orbital periods of the planets and moons, and these alignments stabilize and balance the solar system. A rhythm and synchronicity exists, as if the planets are engaged in a grand, cosmic waltz. To illustrate this point, we shall examine the orbital resonance ratios of Jupiter’s moons Ganymede, Europa and Io. The harmonic ratio of these three moons is “1:2:4” respectively; for every orbit of Ganymede, Europa orbits twice and Io orbits fourfold. Harmonically ordered orbits evolve because all objects and systems seek the condition of greatest stability, marked by the state of lowest energy. For example, a ball rolling back and forth in a U-shaped well eventually stabilizes as it comes to rest at the lowest point in the well, achieving a state of least energy. Moving the ball up the side of the well requires energy input and represents an unstable energy state. Resonant orbital arrangements are self-reinforcing because they often represent the lowest permissible energy configuration of the system.

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The orbits of other planets in our solar system have selforganized and evolved over the eons into highly regular harmonic ratiosxxi, and though not all planets in the solar system possess highly regular orbital resonances, our solar system continues to evolve into a state of increasing stability as time progresses. Harmonization in the orbital periods of planets in our solar system has been recognized and appreciated since ancient times. This clockwork syncopation mesmerized early philosophers and physicists such as Johannes Kepler. In his 1619 treatise entitled Harmonice Mundi,70 Kepler sought to explain the arrangement of the planets according to an organizing principle stipulated by the Pythagorean model and the geometric conventions of Plato’s five perfect solids. Kepler believed that the circumference of each planetary orbit was prescribed by the ratio resulting from nesting the five perfect solids inside one another. In Kepler’s model, a cube with a sphere fitting snugly inside indicated the orbital circumference of an arbitrary planet. Within that sphere fits another solid such as a tetrahedron, and the sphere nested within the tetrahedron indicated the orbital circumference of another planet. Within the orbit defined by the tetrahedron another perfect solid would fit, thus defining another planetary orbit and so on, until all the planets were accounted for.

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Needless to say, Kepler’s speculative model ultimately proved to be incorrect. However, his deep conviction that a divine, harmonic order regulated Natural laws inspired him to develop the famous Three Laws of Planetary Motion. These laws not only maintain their rank as the gold-standard of celestial mechanics to this day, they laid the ground-work for Newtonian Mechanics and provided undeniable evidence for a heliocentric model of the solar system.

(Left): Kepler's planetary model of the solar system as nested Platonic solids. Mysterium Cosmographicum (1596).

7.3

The quantum-harmonic axiom

Harmony implies stability. This is not only true in philosophical terms; it also applies to physical systems. Matter exists in the Universe because elementary particles71 are products of an inherent harmonic order. Atoms are composed of three particle constituents; the proton, neutron and electron. The proton and neutron are themselves composed of three quark subunits. The structural composition of atoms is never arbitrary; symmetry and uniformity exists at every level of scale. Simple and consistent mathematical rules of symmetry always apply, giving rise to the existence of matter. A simple rule, such as the number of electrons in an atom, dictates how an individual element reacts and combines with others to form a varied array of molecules which, in turn, form all substances in the Universe. The stability and homogeneity of matter and its predictable chemical behavior is a manifestation of the underlying mathematical order upon which it is constructed.

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The building blocks from which atoms are constructed.

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The energy levels of electrons surrounding the atomic nucleus are harmonically defined. Atomic electrons may be considered to exist as three-dimensional probabilistic standing waves surrounding the nucleus. Sometimes the probability of finding an electron at a specific point in an atom is unlikely, while in other places the presence of an electron is very likely. The electron probability distribution is proportional to the size of the atom itself. One may consider the atom as being trapped inside a box containing the electron-wave, analogous to the orbit of a planet in Kepler’s model. The boundary imposed upon the electronwave limits its existence to harmonic multiples of its ground-state72, not unlike a guitar string held fixed at both ends. The fixed string may only vibrate in harmonic increments of its fixed length. Similarly, atomic electrons exist as harmonic intervals of their fundamental frequency. In the electron’s case however, instead of vibrating like a string in two dimensions, the electron exists as a standing wave encompassing the three-dimensional volume of the atom. These harmonic frequency intervals are termed “Eigenfrequencies”, derived from the German word “Eigen”, meaning “same”. The electron Eigen-frequencies (i.e. “Eigen-states”) are quantum and discrete73; representing whole harmonic multiples of the ground-state energy. It is this harmonic organization principle that led to the development of Quantum Mechanics (QM), and it is also the reason it is called “quantum” in the first place. (Right): Eigen-states of the electron in a hydrogen atom74. In order to better explain this concept, we shall turn to the model of blackbody radiation. Max Planck demonstrated that thermal radiation may be described by a spectral relationship. The distribution pattern of the blackbody radiation spectrum is characterized as a skewed 72

The lowest permissible whole-integer frequency within the parameters set by the atomic boundary. 73 Intermediate energy states do not exist. 74 Image credited to the Florian Marquardt, Theoretical Condensed Matter, department of physics, University of Munich (LMU), Germany. www.deltagroupengineering.com

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bell-shaped curve; the majority of photons surrounding a hot object possess roughly the same energy, and the prevalence of photons with higher or lower energy diminishes on either side of the spectrum. Planck treated each photon as a harmonic oscillator, analogous to a tiny string in space; each one vibrating at a specific frequency. Planck concluded that the range of permissible oscillation frequencies was not continuous, but limited to integer multiples of “hν”, i.e., the frequency multiplied by “Planck’s Constant”xxii. Thus a blackbody radiation spectrum is not randomly defined; it represents a distribution of discrete frequencies with variable prevalence along the spectrum. In other words, photon energies surrounding a hot object cannot oscillate at random frequencies; they may only exist at precise sub-harmonics of the Planck Frequency, implying that the energy associated with any material object is harmonically defined. For example, the majority of radiant energy from the Sun occurs in a relatively narrow bandwidth of wavelengths. When graphed, the prevalence of photons in a given energy range forms a skewed bell-shaped distribution termed a “blackbody radiation curve”. Planck determined that the only manner in which to accurately depict the distribution of energy in a blackbody curve was to “quantize” the field. He partitioned the spectral energy into discrete “bits”; each “bit” being harmonically related to others by Planck’s Constant, analogous to the manner in which various Eigen-states of an electron are delimited by its ground-state energy. Thus, the quantum model not only applies to energy, it also applies to matter. In quantizing electron Eigen-states and dividing the electromagnetic field into photons, the underlying structure and order of the quantum Universe is revealed. QM states that matter and energy are literally built upon the foundation of harmonic relationships.

7.4

Fourier’s legacy

If we delve deeply enough into any physical phenomenon, it seems that nearly all physical processes are governed by “some kind” of harmonic statute. But what is the reason behind all this order and structure we find in the Cosmos, and how does it naturally arise? Order governs the balance of energy and forces. An unstable, disordered system is like a boulder precariously balanced on the tip of a mountain peak. A boulder that has come to rest on the valley floor after having tumbled down the mountainside denotes a stable system at its lowest energy state.

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Analyzing orbital resonance in planetary motion, we find that configurations evolve75 to represent the most energetically stable and efficient arrangement possible. Each planet contributes gravitational influence to the system such that the resulting tidal forces provide a positively or negatively reinforcing effect upon the elements76 of the system. A complete cycle of a planet around the sun is termed an “orbital period”. Orbital periods and cyclical motions of any kind, such as the swing of a pendulum, may be represented as sine waves possessing frequency and amplitude. To increase the amplitude (height) of the pendulum’s swing, energy may be added in the form of a push to the pendulum’s direction of motion. When pushing in syncopation with the motion of the pendulum77, the amplitude of the swing increases. Similarly, to decrease the amplitude of the swing, a push may be applied which is out of phase78. Doing so saps the kinetic energy of the motion and the pendulum will eventually come to a stop. The energy dynamics of this process may be represented mathematically by the simple addition and subtraction of waves. Adding79 two waves of equal length and amplitude peak-to-peak80 forms a resultant wave possessing the same length, but double the amplitude of the initial waves; this is termed “constructive interference”. Conversely, if two identical waves are added peak-totrough81, the waves cancel each other out. This is termed “destructive interference”. This scheme for adding and subtracting waves has been greatly elaborated upon in the world of mathematics to encompass all manner of wave interactions. Many different waves may be combined to produce a single composite waveform. Conversely, a composite waveform may be decomposed into a set or spectrum of individual waves. The decomposition process is a bit like defining the number 100. Many individual numbers may be added together to obtain “100”; alternatively, “100” may be decomposed into sets of lesser numbers equaling “100” when summed. Waves are analogous to numbers in this regard. Each wave is analogous to a number which may be added 75

Over long periods of time. i.e. celestial objects. 77 The addition of energy is “in phase” with its natural swing. 78 Opposing the swing of the pendulum. 79 Superimposing. 80 The two waves are said to be “in phase”. 81 The two waves are said to be “out of phase”. 76

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or subtracted from the others to create a final number, denoting a “constant function”. This process of summing harmonic modes of a fundamental wave may be used to mathematically re-construct any waveform or constant function by applying the rules of constructive and destructive interference. The reverse is also true, as one may readily decompose any constant function into a cognate spectrum of discrete harmonic frequencies. The process of waveform dissolution is termed “spectral analysis”. Spectral analysis has broad applications and is commonly utilized in electronics, optics, acoustics, image processing, computer data compression and more. It may even be used to model gravitational acceleration82. In fact, the use of spectral analysis to characterize gravity forms the basis of what we refer to as “space-time engineering”. The early 19th century French mathematician and physicist, Joseph Fourier, founded the field of spectral analysis through his development of a mathematical process for compiling harmonic waves. This method is nowadays termed “Fourier series”83, and the mathematical operation facilitating spectral decomposition is termed “Fourier Transformation”84. Sir Isaac Newton learned that if he shined white light through a glass prism, it spread into a rainbow of colors. This experiment demonstrated that sunlight is composed of many distinct wavelengths of light, spanning all visible colors of the spectrum. In terms of spectral analysis, sunlight is analogous to a “constant function” compiled from the superposition of a spectrum of light waves. Spectral analysis may be utilized to characterize electromagnetic 82

The harmonic representation of gravitational acceleration is thoroughly demonstrated in Quinta Essentia Part III (QE3). A brief summary of this process is also available in the EGM Technical Summary. 83 http://mathworld.wolfram.com/FourierSeries.html 84 The Fourier Transform defines a relationship between a signal in the time domain and its representation in the frequency domain: http://www.see.ed.ac.uk/~mjj/dspDemos/EE4/tutFT.html

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(EM) fields85 such as “sunlight”, for example, by mathematically compiling the individual wavelengths that make up the visible spectrum.

The Fourier summation of waves may be utilized to construct a constant function by the mathematical superposition of the harmonics associated with a fundamental wave. For example, a periodic square wave86 may be represented as harmonic multiples of the fundamental frequency utilizing Fourier series87. The following illustration depicts a Fourier series summation of a small number of harmonic modes, demonstrating that as the number of summed modes approaches infinity, the Fourier representation utilizing sine waves becomes (in this case) a perfect square wave of unit amplitude.

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EM energy is typically represented as a span of radio, microwaves, visible light, x-rays or gamma rays. Gamma rays possess shortwavelengths (i.e. high frequencies) and are highly energetic, whereas radio occurs at long-wavelengths (i.e. low frequencies) and are low in energy. All possible energy values of EM radiation fall along a continuum called the “EM spectrum”. EM waves are spectrally organized according to wavelength, representing a range of possibilities. “Bandwidth” refers to a range or sub-set of wavelengths within the spectrum such as “visible light”. The bandwidth of white light lies between the UV and infrared EM limits. 86 http://www.falstad.com/fourier/ 87 Each harmonic, relative to its lowest permissible frequency value in the applied mathematical spectrum, is termed a “mode”. www.deltagroupengineering.com

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The ground-state of any system represents its lowest permissible energy value, and is synonymous with stability. Whether it is the orbital period of Jupiter’s moons, the quantum shifts of electrons in a hydrogen atom, or a drop of oil spreading upon the surface of water, stability (a constant energy state) is a direct consequence of environmental equilibrium. In terms of spectral analysis, any ground-state system we wish to consider represents a summation of inputs and outputs resulting in a constant function; the system’s most stable configuration. It is possible to mathematically visualize the difference between stability and instability, in terms of symmetry and asymmetry, utilizing Fourier series. Let’s look back to the orbital resonances of Io, Europa and Ganymede. If the harmonic orbital periods of these moons are superimposed upon one another as periodic functions, the wave summation forms a regular and symmetric pattern. If the orbital period of Europa happened to be “2.765” per orbit of Ganymede rather than “2”, the resulting waveform will be asymmetric.

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The same is true for musical tones as well. When we hear multiple notes played in unison, which denote even harmonic intervals in a scale, (termed a “chord”) it sounds pleasing. However, if one of the notes possesses a wavelength which is not an exact harmonic increment in that scale, the chord sounds dissonant. Mathematical and harmonic symmetry is often congruent with aesthetic value. Mathematically, the dissonant interaction of sound waves generates a composite asymmetrical waveform which sounds unpleasant. However, harmonic sound waves combine elegantly, yielding an ordered and symmetric waveform which sounds pleasant. Our aesthetic appreciation of harmony, symmetry, music, order and beauty defines our humanity. Pythagoras and the ancient Babylonians reasoned that this was due to an underlying mathematical symmetry in Nature; a harmonic sympathy amongst all things which enables and establishes structure in the Cosmos. We intrinsically appreciate Natural order because we innately understand that all things are drawn to, or tend towards this end. We readily appreciate the difference between free-flow and interference, harmony and dissonance. The fact that we may apply Fourier’s techniques to analyze systemic symmetry affords us a unique opportunity. Through this perspective, we may view the processes of Nature in a deeper and more enlightened manner, and easily identify the common threads and underlying principles of action driving natural processes in all their forms.

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8

Electro-Gravi-Magnetics (EGM)

“Controversy is the first step towards reformation.” • Riccardo C. Storti

8.1

Introduction

Gravity is an electromagnetic phenomenon. Many physicists in the scientific community today might deem this to be a rather bold, even heretical statement because gravity has traditionally been treated as a unique and distinct force in and of itself. Electricity and magnetism, which were once thought to be entirely disparate entities, are now unified into a single set of interactions termed “electromagnetism”. The weak nuclear force, which helps keep the subatomic particles of atoms bound together, was shown to be mediated by photons, and thus we now call this combined interaction the “electroweak interaction”. Nature has placed many conspicuous clues pointing directly to the notion that gravity and inertia are electromagnetic in origin. We have chosen to use this argument as the starting point of our investigation into the nature of gravity, simply because it is the most logical and obvious place to begin. The science of physics has long considered the development of an all-encompassing “Theory of Everything” to be its greatest and final purpose – to unify gravity and all the other forces of Nature into a single, elegant equation. Despite the fact that by the turn of the 21st century there was still no single theory which could successfully unite gravity with electromagnetism, there is good reason to suggest that gravity has always been unified with electromagnetism, in principle at least. If one rationally considers the tenets of General Relativity (GR), one is forced to conclude that gravity must operate, at least in part, through some component of electromagnetism. According to GR, matter generates “curvature” in space-time, and this imaginary curvature directly affects the propagation of electromagnetic (EM) energy and the motions of material objects. As a beam of light enters a gravitational field, its trajectory is curved in direct response to the gravitational field it passes through. However, the dynamic behavior of EM energy in proximity to matter defines “space-time curvature”, which in turn defines how material objects interact gravitationally. This means that one may remove the concepts of “space-time curvature” and “gravitational force” entirely and substitute them with the refraction of EM energy in the presence of matter. www.deltagroupengineering.com

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We use the term “electromagnetism” because we now understand that the forces of electricity and magnetism go hand-inhand. This is connection is empirically proven because magnetic fields may be applied to induce electrical currents in conductors, and vice versa. Each force has the ability to directly affect the other. By this logic, we must also conclude that because gravity is the result of energy displacement due to the presence of matter (i.e. what Einstein termed “curvature” of space-time) gravity must act through some deep and fundamental connection between matter and EM energy. This fundamental connection may be described in exquisite detail utilizing the Electro-Gravi-Magnetics (EGM) method. EGM has been developed through a synthesis of observation and application of time-tested principles of engineering, physics and mathematics. No ad hoc theories are required and no “new physics” has been conjured up in order to develop the EGM method. EGM doesn’t require the invocation of multiple dimensions or universes to yield highly accurate results which are fully consistent with observation and proven theory. EGM simply and elegantly reveals mathematical patterns and relationships in Nature which form the basis of all physical phenomena involving matter and energy – including gravity. More specifically, EGM models the manner in which mass-energy behaves in the milieu of Quantum Vacuum Energy (QVE). Most importantly, this interaction between matter and the Quantum Vacuum (QV) constitutes a system which not only defines the properties of mass, but also reveals the primary canonical rule governing the existence of matter. The first principle which must be acknowledged and accepted to fully understand how the EGM method works is that matter doesn’t exist as an autonomous entity floating inertly in space. EGM models mass-energy as a dynamic interaction process in which energy in the form of mass establishes equilibrium with the energy of the QV surrounding it. Matter and EM radiation follow geodesic paths of least resistance through space-time as they seek equilibrium within the ambient vacuum-energy environment.

8.2

Similitude

If we wish to investigate gravity as being a function of electromagnetism, we must assume that gravity and electromagnetism are already unified. Furthermore, if we wish to implicate the QV, and therefore Quantum Mechanics (QM) as the binding link, we must additionally assume that QM is also unified with gravity and electromagnetism. However, prior to adopting this perspective, we

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must identify the common thread relating these outwardly divergent concepts. This was the first step in the development of the EGM method, and the reason why it is referred to as a method and not a theory. Buckingham “Π” Theory (BPT) is a well established fundamental engineering principle which has been widely utilized since its formulation in the early 1900’s. In fact, much of what we know today about thermodynamics has been gained through the implementation of this theory. Buckingham’s technique is applied to simplify the representation of complex physical systems. In doing so, BPT determines which components are necessary (or unnecessary) in order to adequately represent the dynamics of a system. The Greek letter “Π” (Pi) in BPT doesn’t refer to the ratio “π”, but instead denotes dimensionless variables arranged according to like terms in order to describe the components of a system. It is somewhat analogous to the manner in which words are arranged according to the rules of grammar and sentence structure. In this regard, the dimensionless “Π” groups are the words of the sentence, whereas the grammatical structure and choice of words in the sentence are analogous to the equation best describing the system being analyzed. For example, a single event may be described in many different ways, utilizing different words, different combinations of words, placed in various order, and yet still yield an adequate description of that event. No right or wrong sentences exist per se, only ones adequately describing the event being observed. One may choose to recount a single event quite differently from another person, or rephrase the details of one event in various ways, yet the desired result is the same: that the information is communicated adequately. BPT formalisms afford an engineer the ability to phrase the dynamics of an experimental prototype in multiple ways, with the end result being an equation describing the system mathematically. Syntax in language provides the structural framework upon which ideas are communicated. The basic rules of syntax allow a limited number of words to be arranged into an almost limitless number of expressions. Syntax provides structure and meaning to language so that ideas are conveyed. BPT, in a sense, provides the mathematical syntax upon which an equation may be constructed. An engineer designs and selects a mathematical expression, in accordance with syntactic guidelines, yielding the most complete depiction of the prototype. Variables may be added or removed from the equation until a model is constructed which best predicts the outcome of a simulation.

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BPT is utilized to model the behavior of a whole system88 without requiring precise knowledge of all components within the system. For example, it is not necessary to calculate the movements of every water molecule in the ocean to adequately model or predict the movement of a wave passing through it. BPT operates within the framework of Dimensional Analysis Techniques (DATs)89, demonstrating the scaling relationship between similar systems90. For example, in modeling a wave in water, DATs demonstrate that the size of a wave may be irrelevant in many cases. A wave may be several meters high, or a mere ripple on the surface; however, the wave dynamics of the system are geometrically scalable. Likewise, the dynamics of a vortex of water going down a drain may be described in the same terms as a tornado in the atmosphere. If we wish to design a computer simulation of a new submarine prototype, BPT and DATs allow us to select the proper physical parameters affecting the real submarine, such as the tensile strength of the hull, the pressure of the water acting on the hull and so forth, and it also allows the researcher to reduce or eliminate variables and parameters which are unnecessary. This dramatically increases the efficiency of the prototype design process by reducing the number of experiments and simulations necessary in order to test it adequately. These methods also provide a framework for understanding and analyzing problems, and a means of assessing the overall quality and usefulness of the model itself91. Generating an equation utilizing BPT is quite straightforward. All the factors involved in the system being analyzed are considered, then the experimenter judges which variables92 are expected to be physically important, such as energy, time, mass, length, gravity, pressure, etc. The variables are then grouped as a set of parameters influencing the system, in accordance with the standard methodology developed by Edgar Buckingham.

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Particularly when scaling physical relationships to the size of bench-top experimental prototypes. 89 Primarily enforcing dimensional homogeneity across mathematical and physical representations. 90 Indicating that they may be described in like terms. 91 Norwegian University of Science and Technology, http://www.math.ntnu.no/~hanche/kurs/matmod/1998h/ 92 Each possessing units of physical measure; for example, mass is a fundamental unit (e.g. “kg”) which cannot be reduced nor expressed as a combination of units.

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An important consideration involving DATs and BPT is the rule of “similitude”. In order to compare a mathematical model to a physical system, certain criteria must be satisfied. The model must have dynamic, kinematic or geometric similarity to the real-world system (any of, or all of these if applicable). “Dynamic similarity” relates forces, “kinematic similarity” relates motion93 and “geometric similarity” relates shape94. Once the design principles of similitude are satisfied, the mathematical model is considered applicable to the realworld system95. The famed English physicist, Sir Geoffrey I. Taylor, masterfully demonstrated how dimensional analysis could be applied to predict the energy generated by the first atomic bomb, detonated outside Alamogordo, New Mexico in 1945, utilizing declassified high-speed camera images of the explosion. Taylor surmised that the five physical factors involved in the explosion were; the energy of the explosion, the radius of the shockwave, the atmospheric pressure and density acting to contain the shockwave, and the time interval of the shockwave’s expansion. These five physical terms possess three fundamental units between them (i.e. length, mass and time). The number of dimensionless groups96 equals the number of physical factors involved in the system, minus the number of fundamental units. Five physical factors are involved in the system yielding three fundamental units, therefore two dimensionless “Π” groupings are required to solve for the energy released by the detonation. Energy, exerted as atmospheric pressure, acts to partially contain the explosion as it occurs. The dynamic interaction between the energy released in the blast and the energy exerted by atmospheric pressure generates the shock wave. This interaction is similar to the manner in which the size of an air bubble in the ocean is defined by the ambient pressure of the water. Thus, the shock wave is utilized as a measure of the total energy of the system. High-speed cameras were utilized to film the explosion and each still image provided Taylor with precise time intervals to measure the size97 and rate of the shockwave’s expansion. This information facilitated the determination of the energy released by the 93

Synonymous with the time domain. For instance, the topology of space-time curvature within the context of GR. 95 Refer to a standard Engineering text for worked examples of DATs and BPT. 96 i.e. “Π” groups. 97 i.e. the spherical dimensions of the expanding explosion. 94

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blast, without foreknowledge of the amount of explosive used in the device itself. The rate and size of shockwave expansion is proportional to the energy released by the explosion and representative of the energy exerted by the surrounding atmosphere acting to contain the blast-sphere as the system moves towards a state of energetic equilibrium.

8.3

Precepts and principles

The EGM method is so named because it was initially developed as a means of representing, based upon DATs and BPT, how a gravitational field might be described solely in the mathematical language of electromagnetism. EGM is not a theory; it is a modeling approach – a method of mathematically simulating a real-world system. Standard engineering techniques such as DATs and BPT are typically applied to simulate common engineering problems such as those involving aerodynamics, thermodynamics or load stress; however, in this case they have been applied to find solutions to problems in GR and QM. EGM is not “new physics”. EGM is based entirely upon tried-and-true mathematical and physical principles. The original intent of EGM was to determine, via mathematical modeling alone, whether it might be possible to modify the gravitational force acting on a test object, or to potentially generate artificial gravity by utilizing electromagnetic energy to alter the state of the QV surrounding the test object. However, the result proved to be of far greater scope and significance than its developers originally anticipated, or could have possibly imagined. The EGM method has unveiled a universal principle which may be applied to virtually all physical systems involving matter and energy. To any properly skeptical scientist, this may seem either too good to be true, or even impossible to believe. Yet, when EGM is applied to physical systems, it consistently yields highly accurate and astonishingly precise results, whether one is investigating the microcosm of subatomic particles or the largest astronomical objects in the Universe. EGM was formulated with the intent of providing a tool with which engineers and physicists could not only understand, but possibly even modify gravity and inertia. Theoretically, this can only be achieved by somehow modifying the space-time manifold surrounding a test object. Gravity is often erroneously referred to and treated as a “force”, that is said to “pull” on other objects. This is an entirely inaccurate and misleading portrayal. Gravity is the result of

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an interaction between matter and the space-time manifold surrounding it. GR interprets gravity as being due to curvature within the space-time manifold98. The space-time manifold is thought to control how objects and radiation move through it, in accordance with the local index of curvature in a region of space. In effect, GR allows us to study the physics of gravity through a geometric interpretation of space-time. Hence, the original purpose of EGM was an attempt to determine how one might go about physically modifying the spacetime manifold in order to alter gravitational and inertial geodesics. We also know from Einstein’s famous equation “E = mc2” that matter and energy are equivalent. Simply put, this means that matter is energy – the energy is merely “condensed” in the form of matter. However, “matter” is an inadequate term to use in physics and is better represented by its physical attribute termed “mass”. Mass is a mathematical term describing the amount of energy embodied by matter, and is thus referred to as “mass-energy” to reflect Einstein’s equivalence relationship. GR states that mass-energy generates curvature in the fabric of space-time, resulting in “gravity”. However, we must always remember that “space-time curvature” is physically meaningless; that is to say, it is only a mathematical construct allowing us to describe a physical phenomenon. Believing the space-time manifold to be pure vacuum leads to a logically defiant position99. Although GR describes the motions of matter and EM radiation, it may only be regarded as a mathematical interpretation of reality because Einstein was never able to adequately demonstrate the exact physical mechanism by which matter generates curvature in space-time, or the physical attribute of space-time capable of being curved. EGM models the matter–manifold interaction as a physical system such that energy, in the form of mass, does “work” on the space-time manifold in order to directly affect (i.e. curve) it. However, in order for this to be a physical interaction, the space-time manifold must be treated as though it is something rather than nothing – there must be something for mass-energy to exert its influence upon. EGM presumes physicality of the space-time manifold and that the currency of this exchange is electromagnetic (i.e., mediated by photons, or more specifically, by “gravitons”). Presuming gravity is the result of a matter–manifold interaction, the EGM construct may be

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implemented via the application of control-systems engineering philosophies100 in accordance with the following precepts: i. ii. iii. iv.

An object at rest polarizes the QV surrounding it. An object at rest is in equilibrium with the QV surrounding it. The QVE101 surrounding an object at rest is equivalent to “E = mc2”. The frequency distribution of the spectral energy density of the QV surrounding an object at rest is cubic.

In other words, EGM methodology commences by mathematically expressing the mass-energy value “E”, from “E = mc2”, in terms of an EM spectrum by Fourier Transformation. This mass-energy spectrum is then superimposed upon the frequencycubed QV spectrum of “flat” space-time, derived from QM. Expressing mass-energy in spectral terms facilitates the coalescence of these two spectra mathematically, creating a new spectrum. This new spectrum, in turn, depicts an EM energy equilibrium gradient formed between the center of mass and “infinity”. The energy gradient produced is entirely congruent to the attribute of “spacetime curvature” derived from GR. However, it is important to emphasize that EGM is a mathematical construct only. EGM does not propose that mass is literally comprised of spectral modes interacting with the QV, it is merely a tool by which to distil and deconstruct the fundamental energy dynamics of GR, EM and QM; combining like characteristics in order to solve a problem.

8.4

Space-time engineering

In 1939, physicists Lise Meitner and Otto Frisch published an article in the journal Nature entitled “Disintegration of Uranium by Neutrons: a New Type of Nuclear Reaction”xxiii. Meitner and Frisch studied the physics of nuclear fission occurring when the nuclei of uranium atoms are bombarded with neutrons. This causes the nucleus

100

Commonly invoked to design cruise control devices in cars or tracking systems, and in general, any automated technology utilizing feedback to maintain a steady-state. 101 i.e. gravitational field energy.

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of the atom to split in two, forming barium isotopes and releasing a large amount of energy in the process. However, Meitner and Frisch were initially stumped in their investigation of this phenomenon. The mass of uranium and the absorbed neutrons yielded fission products lower in total mass than that of the starting materials, and they could not account for the mass lost in the reaction, until they took Einstein’s mass-energy relationship into consideration. Their breakthrough in finally understanding fission came from the realization that the missing mass-energy is equivalent to the amount of photon energy released by the fission process. Similarly, when a massive star explodes as a supernova, some of its mass is lost as energy102 while some is “fused” into heavier elements such as carbon and iron. Any loss of the star’s original mass must be accounted for, and this “missing mass” takes the form of an equivalent amount of photonic energy. The combined energy of a collection of photons is often expressed mathematically as a spectrum of EM frequencies. The EGM method commences by mathematically representing any mass as an equivalent localized density of photonic energy. Properties of Fourier harmonics are subsequently utilized to mathematically decompile the mass-energy into a spectrum of EM frequencies. The total mass-energy of a celestial object is analogous to a “white light” composite which may be separated by a prism into a spectrum of frequencies103. This mathematical conversion process is somewhat similar to the manner in which a blackbody radiation spectrum is derived. An object radiates thermal photons into its environment (or absorbs them104), such that their spectral distribution may be expressed as a Planck blackbody radiation curve. Similarly, EGM transforms a value of mass into a value of energy, expressed in terms of a spectrum of energy modes (i.e. photons). Mathematically translating an expression of mass into energy is not the only task required to adequately model the matter-manifold interaction; additionally, we must treat our collection of mass-energy “photons” as though they were being confined (i.e. contained) by an external energy density.

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i.e. thermal photons, X-rays and other high-energy radiation. This is not to imply that the material properties of a celestial object may be separated by a prism, it is simply a method of conceptually and mathematically representing mass in standard units of energy. 104 Depending upon the ambient temperature. 103

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Mass-energy105 may be represented through principles of similitude in much the same manner that Sir Geoffrey Taylor modeled the energy of an atmospheric atomic bomb detonation. Sir Taylor treated the physical parameters of the atomic blast as an actionreaction system between the energy released by the blast and the surrounding pressure and density of the atmosphere acting to contain it. Although space-time curvature is representative of this energy relationship, a “pure vacuum” cannot be utilized as a physical means of establishing equilibrium because “nothingness” is non-physical. At this juncture, we must rely on Quantum Mechanics to provide us with the proper tools. The existence of the QV is predicted and required by QM and Quantum Electro-Dynamics (QED). QM and QED are arguably the most precise and accurate theories ever developed in physics. QM and QED dictate that “virtual” energy must be embedded within the fabric of space-time. The origin and physical constitution of virtual energy is too complex to describe in brevity, but we know for certain that truly empty space does not exist. Space is teeming with energy fluctuations. This energy, in a manner of speaking, is the thread from which the fabric of space-time is woven. The energy of free space, originally derived from QM, is thus termed QVE; also known as Zero-Point Energy (ZPE). The QV is represented as a sea of “virtual” photons which may be expressed spectrally by mathematically divvying up the “Zero-Point Field” (ZPF) into individual units (photons) of energy. Any collection of photons is referred to as an EM field. This is conceptually similar to the manner in which we may characterize the surface of the ocean as a spectrum of waves. The ocean possesses many waves of different size and direction, and all the individual waves combined form the surface of the ocean. Each photon comprising the QV is analogous to a single wave on the ocean. The energy of any EM field may be represented as a spectrum of waves; thus, the QV may also be represented as a spectrum of EM energy. Moreover, since mass is equivalent to energy, it follows that we may also represent matter as a precisely defined spectrum of EM energy. Now that matter and the vacuum have been expressed in like terms (as spectra), it becomes possible to model their interaction utilizing Fourier techniques106. This approach enables the construction 105

Mass is contained within a volume of space; thus, it follows that the energy density of the object should be related to the energy density of the field surrounding it. 106 Derived in QE3.

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of a matter-vacuum system engineering prototype, which may be analyzed and manipulated mathematically to simulate gravitational force acting on a test object, and to model potential ways of modifying the gravitational field. Since gravitation is engendered by curvature of the space-time manifold, we employ the term “spacetime engineering” to describe the prototype. The EGM construct treats the interaction of matter with the QV as an equilibrated system. In this way, an object may no longer be considered to exist as a discrete entity floating inertly in the empty vacuum of space. The energy of the QV interacts with the energy packaged as mass (i.e. matter), and these two forms of energy act in concert as part of a dynamic system. EGM works by mathematically superimposing the spectral “signatures” of matter and the QV upon one another utilizing Fourier harmonics. It is through this mathematical superposition of spectra that we might better understand where the “forces” of gravity and inertia come from. This is not to suggest that a precise physical mechanism for gravity has been discovered, because it doesn’t take into consideration the behavior of every particle of matter as it interacts with virtual particles of the QV. Nor does it imply that gravity is the result of energy strings interacting in multi-dimensional space-time as String theories suggest. It simply demonstrates how, by mathematically combining the spectral energy forms of mass-energy and the QV107, a change in Poynting vector108 (∆P) results to produce the effect we associate with gravity.

8.5

Gravity

The universal principle driving the EGM construct is equilibrium. All matter in the Universe109 seeks a state of greatest stability, which is synonymous with its point of lowest energy (i.e. its ground-state). The expression “E = mc2” depicts a relationship of equivalence rather than one of transformation, and it is through this principle that EGM operates. Since mass and the QV are embodiments of energy, we may treat the energy condensed as matter as existing in a state of dynamic equilibrium with the Universe surrounding it. Consequently, EGM asserts that the properties of mass 107

The superposition of the QV and mass-energy spectra results in a new spectrum termed the “Polarizable Vacuum (PV) spectrum”. 108 In the displacement domain. 109 Including the fabric of the Universe (i.e. the space-time manifold). www.deltagroupengineering.com

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are relativistic because mass adjusts to the ambient energy conditions in its local environment. It is by way of these principles that EGM may be considered congruent to GR. The EGM construct yields a precise determination of the mass-energy equilibrium point of an object with the QV110 surrounding it. EGM models the presence of matter immersed within the QV as an interactive system, suggesting an alternative interpretation of space-time “curvature”. Geodesic paths of matter and energy define the topology of space-time curvature under GR. However, EGM provides a rather more heuristic framework for investigating how space-time manifests “curvature” in the presence of matter through the principle of equilibrium. As equilibrium is established between an object and the QV surrounding it, a gradient in the energy-density is formed within the vacuum. This gradient, in turn, is congruent to what Einstein termed “curvature”. However, instead of interpreting gravity as functioning through geometric imperatives, the EGM interpretation demonstrates that gravity operates according to optical principles. EM energy moves in accordance with any local gravitational potential it may encounter. The way light (energy) moves through energy-density gradients within the vacuum is analogous to the manner in which light refracts when passed through a lens. This optical interpretation of gravity was first suggested approximately three hundred years ago by Sir Isaac Newton in his treatise entitled Opticks. Newton describes how gravity may be regarded as a manifestation of density variations in the “aether”, which he presumed surrounded and permeated all objects. These density variations should, as Newton thought, directly affect the motions of light and matter passing through them. Newton theorized that the aether should be most dense far away from an object like the Earth, and conversely, more subtle and rarefied nearby or within an object. Two passages from Newton’s Opticks demonstrate the optical model of gravity exceedingly well:

110

Facilitating a “reverse engineering” approach to gravity if a region of space-time on a laboratory test bench is considered to be the Experimental Prototype (EP) for the mathematical model produced by the application of DATs and BPT. Subsequently, the mathematical model may be applied to the EP for scaling purposes, leading to gravity control experiments.

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Qu. 20. Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies into empty spaces, grow denser and denser, by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curved lines? And doth not the gradual condensation of this medium extend to some distance from the bodies, and thereby cause the inflexions of the rays of light, which pass by the edges of dense bodies, at some distance from the bodies? Qu. 21. Is not this medium much rarer within the dense bodies of the Sun, stars, planets and comets, than in the empty celestial spaces between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great bodies towards one another, and of their parts towards the bodies; every body endeavouring to go from the denser parts of the medium towards the rarer? For if this medium be rarer within the Sun’s body than at its surface . . . and rarer there than at the orb of Saturn, I see no reason why the increase of density should stop anywhere, and not rather be continued through all distances from the Sun to Saturn, and beyond. And if the elastic force of this medium be exceedingly great, it may suffice to impel bodies from the denser parts of the medium towards the rarer, with all that power which we call gravity.xxiv [sic] Newton’s optical model of gravity has a modern counterpart known as the Polarizable Vacuum (PV) Representation of GR – a title originally coined by physicist Hal Puthoff in 1994, based upon an earlier body of work introduced by the physicists, Harold Wilson and Robert Dicke in the 1950’s. The PV model replaces the concept of “space-time curvature” with a variable “Refractive Index” caused by the polarization of the QV surrounding an object. Newton wrote that a gradually changing density in the aether results in gradually curving paths of light. A changing Refractive Index induced by gradual changes in the polarized QV surrounding matter also results in the refraction of light, as though it were passing through a lens. This “bent” EM radiation follows a geodesic path congruent to that predicted by GR according to the “space-time curvature” interpretation. EGM similarly interprets the PV model’s www.deltagroupengineering.com

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Refractive Index as a region of variable vacuum polarization surrounding a mass-object. However, EGM matures this concept by demonstrating that the variable polarization is a product of the mathematical superposition of the QV and mass-energy spectra described earlier. A key distinction between QVE and mass-energy is that the energy contained within matter is highly localized, whereas the energy of the QV is distributed homogeneously throughout the vast regions of free-space. The differences between these energy distributions may be expressed in terms of spectral characteristics. Haisch, Rueda and Puthoff (HRP) were able to ascertain that the QV spectrum possesses a “cubic frequency distribution”; i.e., the spectral energy density increases proportionally to the cube of the frequency. Therefore, the peak spectral energy density of the QV is predicted to occur at maximum frequency. However, this presents a rather formidable dilemma because it implies that the energy density of empty space is nothing short of staggering. Calculating the total energy of the QV in this form suggests that every cubic centimeter of empty space is so energetic that it should cause the Universe to collapse in on itself. According to GR, energy and mass generate curvature in space-time. Thus the energy distribution predicted by HRP should cause the space-time manifold to curve acutely inwards, causing the Universe to implode111. In fact, it has been estimated that the amount of QVE contained in a coffee cup volume of empty space, if converted to heat-energy, would be enough to boil away the Earth’s oceansxxv. Because of these theoretical results, many physicists discount the existence of the QV in cubic frequency form, believing that “something” must be fundamentally wrong with the derivation, despite the fact that this form originates from standard QM. However, the theoretical prediction of an imploding Universe does not preclude the frequency-cubed spectral distribution of QVE. In other words, the distribution of the QV spectrum may remain frequency-cubed, yet not result in a catastrophic collapse of spacetime, as long as the maximum frequency in the spectrum is low enough. To better illustrate this point, all we must do is state the First Law of Thermodynamics; energy can neither be created nor 111

This is the mainstream view, not the view of the EGM construct in the “Quinta Essentia” series (i.e. QE3,4) where the opposite conclusion is mathematically derived. That is, QE3,4 mathematically demonstrate that “free space” does not contain a near infinite amount of energy in a vanishing volume.

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destroyed. The total energy of the Universe is, and always has been, constant. Neither more nor less energy existed in the early Universe, during the first few trillionths of a second after the Big Bang than exists today. The energy of the Universe hasn’t gone anywhere; it has only become more diffuse112 over time as the Universe expanded. As this occurs, energy isn’t conjured from nowhere to fill the everwidening gaps – the energy of the Universe merely becomes “diluted” with cosmological expansion. Precise measurements of the Hubble constant and Cosmic Microwave Background Radiation (CMBR) temperature allow us to quantify the expansion of the Universe since the instant of the Big Bang. We calculate the Hubble constant by measuring the red-shift of light from galaxies moving away from us as they are pulled apart by the expanding fabric of space. Thus, the Hubble constant is a measure of the rate of cosmic expansion and the CMBR temperature is a measure of the EM energy left over from the Big Bang – only now, the once high-frequency radiation filling the young Universe has been “stretched out” into the microwave frequency range as a result of cosmic expansion. Utilizing EGM to analyze the energy dynamics of Hubble expansion spectrally, we may model the primordial spectrum of the “seed-Universe”113 as a single, high-frequency wavefunction containing the total energy of the Universe. At the moment of the Big Bang, this single wavefunction rapidly began to decompose114 into a broad spectrum of lower-frequency waves, forming localized energy gradients within the QV where matter condensed. This spectral decomposition model is a mathematical representation of the energy dynamic which occurs due to expansion, and is not intended to be a literal interpretation. The many modes of lower-frequency waves in the present-day QV spectrum115, when summed, must contain the total energy present at the instant of the Big Bang (excluding the energy condensed as matter).

112

i.e. red-shifted. i.e. prior to the Big Bang. 114 i.e. bifurcate. 115 In “flat” space-time. 113

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However, the total energy value of the present-day spectrum is spread out and divvied up amongst many modes, each with a lower energy (frequency) per mode. The composition of the vacuum at present constitutes a near-infinite number of modes, but the majority of these are low-frequency because the sum of the spectrum must equal the observed energy present in the vacuum. To suggest otherwise would imply that the energy of the Universe had increased since the time of the Big Bang. For the purpose of conceptual demonstration, let us assume that the size of the Universe is almost infinite, such that we may assign low and high-frequency limits to the QV spectrum of flat space-time incrementally above zero Hz and precisely one Hz respectively. Under such conditions, a near infinite number of harmonic modes, relative to a fundamental frequency value, may exist within the QV spectrum, obeying a cubic frequency distribution between “0” and “1” Hz. In this context, the QV contains many modes of low energy and avoids the “infinite energy in a vanishing volume” problem encountered by standard QM because the countless numbers of low-energy modes sum to a finite QVE density value. Moreover, the significant majority of energy contained within flat space-time (in our example) occurs at the one Hz limit. Similarly, if we assume that the Universe is infinitely large, the fundamental frequency of the QV spectrum would be exactly zero Hz, with an infinite number of low frequency harmonic modes existing within the range of zero Hz and a high-frequency spectral limit, arranged in a frequency-cubed distribution. EGM demonstrates that the high-frequency spectral limit approaches zero Hz because the bulk of the total energy of the QV is comprised of a large number of

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very low-frequency modes, each containing a relatively small amount of energy. Therefore, EGM116 produces a QV spectrum in cubic frequency form, low enough in energy density to prevent collapse under its own weight, and without violating GR or QM. Within the EGM construct, the cubic frequency distribution of the QV is probabilistic. This means that, although the upper QV spectral limit is permitted to tend to infinity, the probability of detecting a photon decreases as the spectral limit increases. In other words, it is increasingly likely that a measurable QV photon exists at low rather than high frequency because: (a) QV photons have been “stretched-out” since the instant of the Big Bang and (b), Nature seeks conditions of lowest energy. Although the probability of detecting a high-frequency QV photon in a gravitational field of non-zero strength117 is greater than a field of zero strength118, the probability of detecting a low rather than high-frequency QV photon remains greater in both cases. Detection probabilities are based upon photon populations119 at specific harmonic modes, denoting an important characteristic of the EGM spectrum. In summary, the “QV spectrum” of flat120 space-time derived by EGM is characterized as possessing a cubic-frequency distribution with a cut-off frequency which is quite low. The EGM derivation does not contradict the cubic-frequency distribution form of the spectrum; it merely disputes the cut-off frequency value assigned by HRP. Setting the QV spectrum temporarily aside, we shall now define and describe the energy spectrum associated with matter; termed “the EGM spectrum”. In contrast to the QV spectrum, the EGM spectrum of a mass-object is comprised of a narrow bandwidth of extremely high-frequency modes121. Here, the “E” from the equation “E = mc2” is expressed in the same terms as the QV spectrum; i.e. as a wavefunction representation of mass-energy obeying a Fourier distribution such that the number of modes decreases as energy density increases.122 (see: QE3).

116

Without contradicting any principle of QM or thermodynamics. i.e. in curved space-time. 118 i.e. flat space-time. 119 See: QE2,3,4 for derivations. 120 “Empty” space, containing no matter. 121 This is a simplified reference to the EGM spectrum. Please consult the proceeding chapter for further information. 122 i.e. the number of modes is inversely proportional to the energy density of the space-time manifold. 117

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When the QV and EGM spectra are superimposed upon one another using spectral analysis, the resulting spectrum is termed the “PV spectrum”. This hybrid spectrum represents the energy equilibrium state between the QV and EGM spectra123. It is important to note that the QV and EGM spectra are purely theoretical constructs, because mass and the vacuum never exist in isolation. The QV spectrum represents a theoretical Universe without mass-objects, while the EGM spectrum represents only the mass-energy of an object in isolation. However, mass-energy is invariably found within the milieu of QVE, so the only relevant spectrum is that of the PV. The PV spectrum upholds the HRP cubic-frequency distribution form, with a spectrum extending into very high-frequency ranges, but only in the immediate presence of matter. The PV spectrum, formed by the superposition of the QV and EGM spectra, resolves the HRP “cosmic collapse” problem because the only instance in which the PV spectrum extends into very high-frequency ranges is in the immediate presence of matter. Flat space-time, on the other hand, far from any matter, is comprised of very low-frequency modes and thus does not contain enough energy to cause a catastrophic collapse of space-time. The high-frequency contribution to the PV spectrum does not come from empty space, but rather from energy that is “locked-up” in the form of mass, which is distributed in highly localized points throughout the Universe. For example, consider the action of adding a single star to an empty Universe. Within the EGM construct, the entire mass of the star is represented as a single point (a “point mass”), radiating the totality of its mass-energy into the space surrounding it. This action superimposes the EGM spectrum of the point mass onto the QV spectrum of the empty Universe; doing so forms the PV spectrum.124 Surrounding the point mass, a mode population gradient is established in space-time between the mass and the “edge” of the Universe. The mode population gradient modifies the Refractive Index “KPV” value of the vacuum such that it changes at the same rate as gravitational acceleration “g” from the center of the point mass. Thus, the gradient is congruent to the concept of space-time “curvature” within GR.

123

The EGM spectrum is mass-energy based. Since a maximum mass limit does not exist within contemporary physics, the EGM spectrum is infinitely broad. However, mass-density is theoretically limited to the Planck scale; thus, the EGM spectrum is bounded (in this regard) by the Planck Frequency. 124 i.e. a quantized representation of the gravitational field.

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The obvious question arising from the formation of the PV spectrum is; what induces the modal population gradient?125 The nature of the Universe is to expand such that the energy within it becomes “stretched out”. The Universe continually strives to reach its lowest energy state and greatest stability. As this occurs, the highfrequency modes present shortly after the Big Bang are bifurcated into a larger number of low-frequency modes as the Universe expands. Mass may be modeled as doing work126 on the surrounding vacuum by “curving” it. The presence of a point mass “pushes” the vacuum around it “uphill”, against its natural flux of expansion. The nature of the Universe is to expand, and upon encountering resistance to its normal flux from high to low energy, the Universe “pushes back” as it strives to reach a state of equilibrium. The mass-associated spectrum represents “condensed” energy, which causes the QV spectrum surrounding matter to locally re-compress to fewer modes of higher-frequency. Hence, it follows that the more massive the object, the “steeper” the gradient (change) in mode number between its center of mass and the edge of the Universe, resulting in gravitational acceleration proportional to mass. Compression of the vacuum modes requires energy input, and it is precisely this re-compression of QVE which results in gravity. This model also provides an answer to the question of how and why matter “curves” space.

125 126

i.e. why does the vacuum become polarized? i.e. expending energy. www.deltagroupengineering.com

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The tendency of the space-time manifold is to expand; however, the presence of matter interrupts this movement, polarizing the QV. Energy is required to alter its state to fewer modes of higher frequency, counteracting the thermodynamic tendency of any system to move towards a state of lowest energy and greatest stability. Subsequently, an observer held fixed within a QV gradient senses that the mode energy is asymmetrical127 and based upon the Quantum Vacuum Inertia Hypothesis (QVIH), vacuum asymmetry results in an apparent acceleration force on the observer which is perceived as gravity. Rather than a geometric curvature of nothingness, the manifestation of “g” is better represented as back-pressure from the vacuum as mass-energy exerts its influence upon it. Anything caught in the inward flow of space-time, so to speak, is pulled along with the current. EGM represents this process as the superposition of two distinct spectra utilizing Fourier harmonics, resulting in a mathematical description of “g”. Thus, it may be stated that the EGM construct yields a quantized description of gravity. EGM mathematically represents matter as radiating a spectrum of conjugate EM frequencies. However, if we consider matter to radiate a spectrum of “gravitons”128, the EGM construct may be represented in quasi-physical form,129 such that gravitons emerge as a vehicle for the feedback of information between the EGM spectrum of matter and the QV spectrum of the local space-time manifold. 127

i.e. higher in the direction of the center of mass of an object and lower out in space. 128 i.e. elementary particles presumed to mediate gravitational force. 129 Science has yet to detect or rigorously define gravitons; consequently, sufficient latitude exists to interpret the graviton in a manner suitable to the EGM construct.

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EGM considers the spectral energy of a gravitational field to be equivalent to the mass-energy of the object generating the field, expressible in terms of a PV spectrum and analogous to space-time curvature within GR. It models each of the conjugate EM frequencies as two populations of “conjugate photon pairs”, i.e., each population is “180°” out of phase with its conjugate, consistent with a Fourier harmonics representation of a constant function in complex form (see: QE3). A conjugate photon pair constitutes the definition of a graviton within the EGM construct. The density of gravitons surrounding a mass-object is maximal in close proximity to an object, and gradually decreases with radial distance; thus, the greater the population density of gravitons, the stronger the gravitational field will be. These factors are consistent with the manner in which the PV spectrum is defined via Fourier harmonics, resulting in a spectrum which increases in mode number with radial distance from the mass-object130. The EGM interpretation of gravity is analogous to Newton’s conceptualization of optical gravity as well. According to Newton, the aether was presumed to be “denser” farther away from a mass-object and “less dense” nearby. The change (i.e. gradient) in the density of the aether causes light and the movements of objects through it to follow trajectories characteristic of gravitational attraction. The increasing density of Newton’s aether may be substituted with the analogous concept of increasing mode population in the QV, proportional to the distance from a mass-object.

The physical basis for gravity, within Newton’s optical framework, is similar to that of a long-range Casimir Effect. The Casimir Effect demonstrates that when two neutrally charged parallel metal plates are brought very close together, photons in the QV with 130

i.e. QV mode number decreases with “graviton” density. www.deltagroupengineering.com

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wavelengths too large to fit between the plates are excluded. The reduced energy density between the plates biases the QV131, pushing the plates together with increasing force as the separation distance decreases. Gravity, in this regard, is akin to a long-range Casimir Effect because EGM describes gravity as being the result of a change in mode population across a region of the QV. In fact, EGM derives the Casimir Force from first principles, demonstrating that it differs depending on the gravitational field strength of the location in which it is measured. For example, EGM asserts that the strength of the Casimir Force on Jupiter will be smaller than on the surface of the Moon (see: QE3). The gravitational effect on the Casimir Force is due to the population of modes comprising the PV spectrum. The denser the mass, the fewer modes it has in its PV spectrum because each mode within it possesses higher energy (i.e. frequency). The modal bandwidth of the PV spectrum for a very dense object is narrower than that of a less dense object. Thus, at the surface of Jupiter, fewer low-frequency vacuum modes exist than at surface of the Moon, resulting in a smaller Casimir Force on Jupiter than the Moon. What Sir Isaac Newton originally envisioned over three hundred years ago in his speculations regarding optical gravity is mirrored in the PV model of GR. EGM doesn’t merely elaborate on PV theory, it puts real numbers to it, allowing one to precisely quantify and define the PV. The variable Refractive Index of the PV model acts as a replacement for the metaphysical concept of “spacetime curvature” under GR. EGM models the changing gradient of the PV as a summation of harmonic modes via Fourier series to represent a “constant function” (i.e. “g”) at any position in space surrounding a mass-object. However, it is important to re-emphasize that EGM is a mathematical construct only. EGM does not propose that mass is literally comprised of spectral modes interacting with the QV, it is merely a tool by which to distil and deconstruct the fundamental energy dynamics of GR, EM and QM; combining like characteristics in order to solve a problem. The EGM method provides a unique framework for understanding the physics of gravity. The vacuum of space, as we now understand, is an embodiment of energy, and so is mass. The problem with previous interpretations of gravity has to do with the 131

Casimir experiments (to date) have only been performed in a gravitational field. Thus, it is more accurate to refer to the PV rather than the QV; however, “QV” has been applied for conceptual simplicity in order to assist the reader.

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notion that matter is “something” and space is “nothing” when, in fact, matter and space are actually two mutually dependent forms of energy: one subtle and impalpable, the other objective and concrete.

8.6

Elementary particles

Although the EGM method is ideally suited for modeling the structure of gravitational fields surrounding large objects such as planets and stars, it may also be utilized to model properties of atomic and subatomic matter. Moreover, applying the EGM method to elementary particles has led to some rather startling and profound results! A deeper level of order has been uncovered at the subatomic level that follows as a natural extension of the QM paradigm, which governs the order and structure of the atom. As we have already seen, the atomic system is reliant upon the principle of harmonic symmetry. The discovery that electron energy levels in atoms only exist as stable “quantum” frequency intervals gave rise to the discipline of QM. EGM demonstrates that the electron energy-level isn’t the only instance where this quantum paradigm applies. The QM model doesn’t state what the electron is, precisely, but it does show that when it exists as part of an atomic system, it can only exist in harmonic energy states defined by the parameters of the atom-system. Each quantum change in an electron’s energy level is induced by the absorption or emission of a photon. EGM demonstrates that the properties of subatomic particles are not defined arbitrarily in Nature, and that this harmonic principle of action extends into the furthest depths of the atom. EGM has revealed a QVE equilibrium ratio relationship amongst all subatomic particles, forming a quantum-harmonic canon governing the inner structure of matter. Particle physics research often involves the act of smashing subatomic particles together at near light-speed velocities and analyzing the bewildering array of debris formed in the collision. This process is commonly described as being similar to smashing two cars together and attempting to determine how they worked by analyzing the shattered debris. The discipline of particle physics is also referred to as High-Energy Physics (HEP). This term is applied because the particles resulting from such collisions are only able to exist in extremely high energy environments. Subatomic particles often only exist as interlinked components of another greater particle system and not as free entities in and of themselves. They often exist only when we cause them to www.deltagroupengineering.com

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exist. At the instant of a particle collision, for example, the subatomic particle products generated in the collision may only be measured (or even be generated in the first place) by having increased the energy of the environment in which the parent particles are smashed together132. For example, a proton is composed of three quark subunits; however, quarks themselves are not known to exist as free quarks. The configuration of the proton system acts as a boundary condition, containing the quarks in a composite form called the “proton”. Extremely high energies are thus required to smash protons into their individual quark constituents and the quarks released in the collision can only exist freely for an extremely brief period of time133. The energy of any object, whether particle or otherwise, is equilibrated by the ambient energy in its local environment. However, only when equilibrium is artificially shifted, as occurs in a high energy collision, is the energy balance destabilized sufficiently to allow high-energy quarks to exist autonomously for a brief moment. Quarks generated in a collision, as it turns out, are each more massive (in energy terms) than the proton they originate from! How can it be that the free subunit of a parent particle possesses greater mass-energy than its source? This is analogous to a baby weighing more than the mother at the time of birth! However, this happens to be the case because we release quarks by increasing the mass-energy density of the proton system at the time of the collision. Shortly after the Big Bang, the Universe was a soup of free quarks in a hot and dense environment. In the first moments after the Big Bang, the total energy of the early Universe was much more densely packed than it is today. Quarks could exist freely in the early Universe because the ambient energy density allowed them to exist in this more energetic form. When particles are accelerated to extremely high energies in a collider we are, in effect, re-creating the dense, high-energy conditions of the early Universe, and allowing free particles to exist. As the Universe rapidly expanded and cooled, its energy density decreased, subsequently permitting the condensation of composite particles such as the proton and neutron (termed “Big Bang 132

Relativity describes why tremendous energy is required to accelerate even the tiniest particles like protons and neutrons to near light-speed. It also states that mass scales proportionally with the rate of change of velocity and that accelerating objects (whether it’s a person or a particle) to anything closely approaching the speed of light requires enormous amounts of energy. 133 i.e. until energy conditions return to normal.

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Nucleosynthesis”xxvi), followed by the formation of even more complex, low-energy composites (hydrogen and helium atoms) as the energy density decreased further. This manner of energy-density dynamics is exquisitely modeled by the EGM method, which has been specifically designed to simulate the environmental interaction of such systems where massenergy is affected by the energy density conditions surrounding it. The existence of a particle is wholly and completely based upon the mutual, indissoluble interaction between itself and the environmental energy conditions it strives to equilibrate within. However, the question remains as to why particles posses distinct energies, and why they are not arbitrarily defined in Nature. In other words, photons may possess a wide range of possible frequencies, while elementary and subatomic particles in the atom have well defined and discrete energies. What governs the formation of distinct subatomic particles and their pattern of organization within the atomic system? In elementary particle physics, a particle’s mass is expressed as an energy equivalent via “E = mc2”, which means that the more energy a particle possesses, the more “massive” it will be. The energy of a photon is frequency based (via “E = hν”), meaning the higher in frequency (shorter in wavelength) a photon is, the more energy it possesses. Thus, the EGM construct asserts that “mass” is inherently frequency-based as well, because it is an expression of a particular EM frequency bandwidth. EGM models the energy-density environmental equilibrium dynamics of systems, where matter is affected by ambient conditions, by mathematically decomposing a value of mass-energy into an “EGM spectrum” of frequencies utilizing Fourier harmonics. This is a mathematical construct only, utilized to model the system as a whole, and must not be interpreted as being physically descriptive of reality. Nevertheless, the process of mathematically translating units of mass into spectral information elegantly articulates the equilibrium established between matter and the QV. The resulting equilibrium state, in turn, defines the physical properties and characteristics of any mass-object, including subatomic particles. The physical characteristics of all fundamental particles are born of equilibrium and are a manifestation of Einstein’s principle of mass-energy equivalence. EGM models mass-energy equivalence as a condition of energetic equilibrium within the QVE environment. This energy relationship is expressed in terms of the PV spectrum, and as we shall see, yields a natural harmonic relationship between all subatomic particles.

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In order to fully comprehend the manner in which EGM derives particle characteristics, it is first necessary to derive the EGM spectrum of a particle. Even though a proton is a composite particle composed of quarks, it is still possible to accurately model it with EGM in spectral form as a singular entity. Here, the experimentally measured mass of the proton may be utilized to derive its EGM spectrum. The proton is the easiest place to begin in this analysis because its mass is precisely known and experimentally validated to high precision. EGM methodology commences by mathematically representing the proton’s mass-energy in spectral form. However, this process doesn’t only convert the mass of the proton into a PV spectrum of EM energy; it develops the concept that the mass-energy of an object is contained within a finite volume of space-time, defined by environmental equilibrium. Thus, the free proton isn’t solely described by its mass-energy value, its mass-energy is also associated with density because it occupies a limited and finite volume of spacetime. The PV spectrum of an object is thus derived as a representation of an objects mass-energy density, not just by the quantity of massenergy it carries. For example, stars and planets take spherical form because they are compressed by gravity into their lowest-energy configuration. Under ideal conditions, a gas bubble in water is compressed to a spherical shape by the balance in pressure between the air and the water encapsulating it. The same principle applies to stars as well; the expansion pressure of hydrogen fusion in a star is balanced by the gravitational force acting to hold the hydrogen densely packed together. The equilibrium point established between the two forces confines the star to a particular size and density in space, and also establishes the surface parameters of the object. In Nature, the sphere is generally the most efficient shape for packaging energy or matter. This is because the sphere has the lowest surface to volume ratio of any shape. A cube requires more total surface area than a sphere in order to contain an equal volume. The same is true for a pyramid, or any other three-dimensional shape for that matter. The spherical form is so commonly found in Nature because systems seek the most stable and efficient configuration possible within any given set of circumstances; efficiency is synonymous with stability.

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Note: the sphere represents the equilibrium boundary between the mass-energy of an object and the QVE of the environment acting to contain it. This principle of spherical energy density configuration directly affects the fundamental and harmonic cut-off frequency of the proton’s PV spectrum134. The PV spectrum is derived as a representation of mass-energy density equilibration such that spectral characteristics differ from object to object. For example, the proton possesses fewer harmonic modes and a higher harmonic cut-off135 frequency than that of a star. We may utilize EGM to spectrally model any particle’s mass-energy in precisely the same manner as is done for a star or planet; by assuming that Nature utilizes the most efficient form of packaging and distributes the mass-energy of a free particle spherically. It may or may not be physically true that a singular particle is spherical. However, we may assume that the energy of a free particle is spherically distributed in order to maintain geometric similitude between all mass-energy systems, whether that system is a particle or a planet. At first glance, it may seem like a rather complicated exercise to mathematically treat matter as though it were a spectrum of frequencies. Translating a simple expression of mass into an ostensibly more complicated spectral form is essential, however. There is a way to simplify things a bit though, and it is by way of this simplification process that the aforementioned harmonic relationship amongst particles is established. For all practical purposes, we may 134

Possesses specific characteristics such as a low and high-frequency end-points (i.e. “cut-off’s”). Within the EGM construct, the low and high-frequency limits are termed “the fundamental” and “the cut-off” frequency respectively. Between these, a range of harmonic frequency modes exist comprising the spectrum. 135 Spectral limit. www.deltagroupengineering.com

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disregard all low-frequency modes of the PV spectrum and describe a particle explicitly in terms of its cut-off frequency, because the highest harmonic frequency in the spectrum is representative of the significant majority of the particle’s total energy. Each particle type possesses a particular mass-energy value such that it may be characterized by a unique harmonic cut-off frequency value, derived from the free particle’s rest mass. For example, the proton will have a different cut-off frequency than an electron or neutron because their massenergies are different136. Thus, the harmonic cut-off frequency denotes the equilibration “signature” of a given particle type. Moreover, EGM demonstrates that the harmonic cut-off frequency signatures of all subatomic particles are uniquely related to one another. The EGM construct reveals that particle mass-energies (expressed spectrally) are naturally established according to a distinct and highly precise harmonic pattern. For example, the relationship between any pair of particle types, such as an electron and a proton, may be represented as the ratio of their harmonic cut-off frequencies, demonstrating that all fundamental particles exist as though they were musical “notes” played on the same “string”. Each particle “note” is but one harmonic in a scale of notes, and each note is defined by the particle’s harmonic cut-off frequency. Because the harmonic cut-off frequencies of particles are direct representations of the particle’s mass-energy, and because those harmonic cut-off frequencies are only found in whole, quantum-harmonic increments, it means that the mass-energies of all subatomic particles are strictly ordered according to a quantum rule. Thus, we may consider all particles to be harmonic multiples of another particle like an electron, for example. Based upon this harmonic principle of order, a periodic table of subatomic particles may be formulated mirroring the hierarchical basis upon which the chemical elements are arranged. 136

The harmonic cut-off frequency of the neutron is extremely close to that of the proton. Thus, where appropriate, the ratio of the harmonic cut-off frequency of the proton to neutron is usefully approximated to unity.

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EGM decomposes the energy value of any object into a spectrum of harmonic EM frequencies – mathematically representing its mass as a collection of photons. Each photon in the resulting spectrum is dependent upon the value of the mass from which it is derived. Since frequency relationships are best described in harmonic form, it comes as no surprise that subatomic particles should exhibit harmonic relationships as well. Thus, the mass-energy of any particle may be defined as a harmonic (or sub-harmonic) increment of a common EM frequency. Within EGM, the fundamental particle masses (expressed in frequency terms) exist in harmonic increments (i.e. quanta) in a similar manner to the way in which electron energy levels are defined harmonically in atoms. This is why the EGM model acts as an extension of the QM paradigm. It is not currently possible to derive a precise mathematical pattern or relationship amongst the masses of fundamental particles by any other known method. More importantly, we may utilize the EGM method to predict the mass and operative size of any particle with unprecedented precision, and obtain values orders of magnitude more accurate than may be achieved utilizing the Standard Model of particle physics. One of the most valuable features of EGM is that it demonstrates how GR and QM are interrelated. In this regard, EGM is a unique method, derived from a single paradigm demonstrating the cross-fertilization of the central pillars of physics. It has uncovered not only the framework underpinning the stability, order and coherent inner structure of the atom; it also reveals how this order and stability arises in Nature. Perhaps the most profound insight to be gained from EGM is that the harmonic pattern of organization amongst subatomic particles arises based upon a particle’s relationship to all other fundamental particles. Could this perhaps imply that the common particle “ancestor” from which all atomic elements, all molecules and all material forms are constructed is the photon – energy itself?

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8.7

Cosmology

EGM is “universal”. It is a single concept – a single paradigm which may be applied to sub-atomic particles, planets, stars, galaxies – even the Universe as a whole may be evaluated utilizing EGM methodology. In fact, EGM not only allows the researcher to model all these things independently, it reveals how all of matter and space is interconnected, because the same equation revealing the harmonic relationship amongst particle types may also be applied to precisely derive cosmological measurements such as the present values of the Hubble constant and Cosmic Microwave Background Radiation (CMBR) temperature (“H0” and “T0” respectively). Moreover, EGM demonstrates that “T0” may be derived from “H0”, meaning that these two phenomena are interrelated. The EGM “particle equation” even serves to validate and substantiate the evolutionary epochs of our Universe, as science has come to understand them, since the time of the Big Bang. A “mass-object” may be defined as any interacting collection of material objects, such as an atom or galaxy, and it may also be defined as a single, indivisible unit of matter such as a free elementary particle. This is because EGM models any object as a feedback system between the mass-object itself and the QVE surrounding it. For example, we know that it is not necessary to calculate the movements of every individual water molecule in the ocean in order to adequately predict the dynamics of a wave passing through it. All we must do is model the dynamics of the wave itself. In the same manner, EGM treats any object or collection of objects as a whole entity, whether it

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is a whole proton, a whole atom, a whole star, a whole galaxy, or even the whole Universe. EGM is a method permitting one to mathematically represent a mass-object in spectral form. Although EGM doesn’t purport this interpretation to be literal or physical, it is a computationally accurate means of representing matter within the context of the QV. In place of standard (and often highly complex) differential equation formalisms used to solve for the dynamics of a two body system, such as a binary star system, EGM models this dynamic by way of the constructive and destructive interference resulting between the PV spectra of each mass-object. EGM can model the gravitational dynamics between galaxies, stars or even particles for that matter, in a far simpler manner than may be achieved utilizing relativistic differential equations. The Planck blackbody radiation phenomenon demonstrates that matter radiates a spectrum of EM radiation based upon its temperature, and that the modes comprising that spectrum may be described as harmonics of the Planck Frequency. This principle of spectral distribution is mirrored by EGM because the PV spectra of mass-objects are generated utilizing Fourier harmonics. That is to say, each PV spectrum is a mathematical decomposition of the gravitational energy of a mass-object into a cognate spectrum of harmonic frequencies. Thus, the PV spectrum is analogous to a “gravitational blackbody spectrum”. “Wien’s displacement law” describes the relationship between the temperature of an object and its blackbody radiation spectrum. Comparing hot and cold objects, we see that the blackbody spectrum for each object type possesses a similar shape; depicting peak photon prevalence in a specific frequency range, trailing off at the high and low spectral limits. Differences in peak emission frequencies obey a scaling factor relationship defined by Wien’s displacement law. This principle demonstrates that the spectrum is analogous to the representation of temperature. When we directly measure the temperature of empty space, we are in fact measuring the residual energy from the Big Bang as red-shifted (i.e. stretched-out) photons present in the early Universe; the EM waves we observe today are a snap-shot of the once extremely high-frequency photons present when atoms first formed137. Billions of years later, those photons have become stretched by cosmic expansion to such a degree that now they are approximately “1(mm)” in wavelength, falling within the microwave frequency range of the 137

As asserted by the Standard Model of Cosmology (SMoC). www.deltagroupengineering.com

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EM spectrum. This background radiation filling space is referred to as the Cosmic Microwave Background Radiation (CMBR). We find that this wavelength corresponds to a temperature of approximately “2.725(K)”: the present CMBR temperature, “T0”. At Bell Laboratories in 1964, while working with a large horn antenna designed for Radio Astronomy and satellite communications, Arno Penzias and Robert Woodrow Wilson discovered a ubiquitous white-noise falling within the microwave frequency range that could not be eliminated. It was audible day and night and in all directions. What Penzias and Wilson detected with their antenna was the CMBR radiation left over from the birth of our Universe! The discovery of CMBR earned Penzias and Wilson the Nobel Prize in 1978. The physical detection and measurement of CMBR, and thus “T0”, was momentous because, at the time of its discovery, the Big Bang model of cosmic history was merely conjecture. The Big Bang theory emerged from Hubble’s observation that the Universe was apparently expanding in all directions. It was presumed that it should be possible to trace this expansion back in time when all the matter and energy in the Universe was packed together in a much denser form. However, in the intervening decades between the time Hubble expansion was discovered and “T0” was actually measured, the Big Bang model was by no means on solid ground. The favorable pairing of prediction and observation meant that, as strange as it may seem, our Universe must have suddenly burst into being as if from nowhere. The Universe could no longer be considered an eternal, “steady-state” Universe; it was instead finite – having a beginning and perhaps an end in time. When the Universe burst into existence, it didn’t explode into some pre-existing space. It is not as if matter erupted into a void that was already there. This is a very common and equally grave misconception of what the Big Bang theory actually asserts. The Big Bang model instead suggests that space itself erupted into existence, carrying matter and energy along with it. It is the space-time manifold which expands, not matter expanding into pre-existing space. Thus, the Big Bang happened everywhere. Many people assume that because we measure the accelerated recession of galaxies, we can also trace the motion of those galaxies back to some “origin” in space, and that a particular point marks the location of the Big Bang. What we actually find is that every point in the Universe was the original “location” of the Big Bang, because all galaxies (except those whose gravitational attraction has overcome cosmic expansion) are moving away from each other. The fabric of space is expanding between

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galaxies, in all directions, and all points within space are becoming further separated from all other points – not moving away from a common origin. Similarly, all points in space would converge to a single point if traced backwards, but this “point” would not be located at some particular coordinate in space because every point in the Universe may be considered the “center” of the Universe. The expansion of the space-time metric (not the ejection of matter into static space) provides the reason for why the ultra highenergy photons of the early Universe are now detectable as lowenergy microwaves filling space. All energy and matter are part and parcel of the fabric of space-time, and as space-time expands, matter and energy are also subject to that expansion. In this regard, we may consider Hubble expansion to be intimately tied to “T0”. The current temperature of space defines the blackbody radiation spectrum of the Universe, and vice versa. The radiation comprising the spectrum is composed of far red-shifted photons that were present in the blackbody spectrum of the early Universe shortly after the Big Bang. At that time, those photons were much higher in frequency (energy) because the temperature of the early Universe was extremely high. There was no more energy in the early Universe than there is today, however. To state otherwise contradicts the First Law of Thermodynamics. The total energy of the Universe remains the same, but the energy is now spread out across a much larger volume. Consequently, the energy density of the Universe has changed, not the net amount of energy it contains. This relationship between energy-density and temperature is a well characterized principle of fundamental astrophysics. As a star forms, clouds of hydrogen condense into a massive sphere of gas, similar to the planet Jupiter. A pressure threshold must be achieved before this dense ball of hydrogen (the “protostar”) is hot enough to initiate hydrogen fusion. Increasing gravitational pressure on the hydrogen gas of the protostar causes an increase in temperature. When the pressure and temperature of the protostar reach the threshold required to fuse hydrogen into helium, the protostar ignites and the star is born. The temperature of an active star, which is established as a function of pressure, also determines the star’s blackbody radiation spectrum. All these factors are completely reliant upon a common state of equilibrium. Stars between ten and twenty times more massive than our sun meet their end in the form of a gargantuan explosion termed a “supernova”. As any star fuses its store of hydrogen into helium, an enormous amount of energy is released from the star, resulting in explosive outward pressure. The outward force of the energy released www.deltagroupengineering.com

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from hydrogen fusion is counteracted by the inward pressure of gravity. The balance struck between outward and inward pressures establishes the spherical dimensions of the star. However, as the star’s store of hydrogen becomes depleted and less energy is produced by fusion, the outward pressure begins to wane and gravitational collapse takes over. Gravity places added pressure on the remaining hydrogen, causing it to heat up further. As the star becomes crushed under its own gravitational weight, it heats it up to such an extent that the helium begins to fuse into heavier elements such as oxygen and carbon. The inward pressure continues to build until the star implodes and the resulting shock-wave causes the star to be ripped apart in a massive explosion, expelling the heavier elements just forged in the stellar crucible out into space. The remnants of supernova explosions form neutron stars – stellar cores that are roughly as massive as our Sun but only about 20 kilometers in diameter138. Normal atoms possess a nucleus composed of protons and neutrons, with electrons buzzing around at a relatively vast distance from the nucleus. In fact, atoms are really mostly made up of empty space. However, in neutron stars the atoms are compressed so tightly that they become crushed into a compact ball of atomic nuclei. This form of matter is so dense that just one cubic centimeter of it measures in the billions of kilograms! Similarly, the neutron star’s gravitational field is so strong that in order to escape its gravitational field, one must achieve an escape velocity of roughly forty-percent the speed of light139! If a star larger than twenty times the mass of the Sun begins to burn out its hydrogen supply and collapse under gravity, its matter compresses into a state so dense that it disappears entirely within the fabric of space! This, of course, is a “black hole”. Instead of being compressed into a ball of atomic nuclei, matter gets squeezed by gravity into a point. The black hole is “black” because gravity is so great that the escape velocity exceeds the speed of light. Light attempting to flee the confines of the black hole can never reach escape velocity – it will forever push against the current of gravity in vain, like a fish trying to swim up a waterfall. Whether a massive star explodes as a supernova to become a neutron star, or a super massive star collapses to form a black hole, the outcome ultimately depends upon the equilibrium established

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Encyclopedia Britannica online: http://www.britannica.com/eb/article-9055410/neutron-star 139 Vescape = √(2GM/r).

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between the expansive pressure of the energy of the star and the contractive gravitational pressure. The life cycle and destiny of most stars may be determined utilizing a straight-forward relationship born of the principle of equilibrium. The Sun is a middle-aged star that has fused about half of its hydrogen supply into helium, and still has about 4.5 billion years left before its hydrogen is depleted. As hydrogen becomes depleted, and the outward pressure from helium fusion overcomes the compression of gravity, our Sun will swell into a “red giant”. Eventually the outer layer of the red giant, composed of helium and other freshly-formed elements, will slough away from the core leaving a ring of gasses referred to as a “planetary nebula”. The core of the Sun will remain as a “white dwarf” star at the center of the nebula, continuing to burn the remaining carbon from helium fusion until it is also depletedxxvii. The active hydrogen-burning phase of a star’s life cycle is termed its “main sequence”. As a star like the Sun becomes a red giant, it moves from its main sequence phase into its red giant phase. During a star’s main sequence, its brightness (luminosity), mass, size (radius) and temperature are established as a function of equilibrium. For example, the Sun is “G2V” class star140, which means that it is a main sequence star whose temperature is “5,700(K)” at its surface. Wien’s displacement law demonstrates that the peak of the Sun’s blackbody spectrum occurs in the “yellow-white” photographic light range. The star Rigel in the constellation Orion is seventeen times more massive than the Sun and six times its radius, with a temperature of “11,000(K)”. The mass-density equilibrium of Rigel relates to its temperature, and the temperature relates to its apparent color, which is in the blue range. The color blue is higher in frequency than yellow, and this difference in frequency between Rigel and the Sun is a function of Wien’s displacement law. As temperature increases, the peak emission of the blackbody spectrum shifts upwards in energy. This is termed “color temperature”. It’s just like a flame: the blue part of the flame is the hottest, whereas the yellow and orange parts of the flame are relatively cooler. This tangential foray into astrophysics has been for the purpose of conveying a crucial point, which is that seemingly independent physical parameters of the star are intimately connected, and a change in one will affect the others. The mass-density and radius of a star in its main sequence relates to the star’s temperature. From the temperature we may predict the star’s color which, in turn, 140

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is derived from the star’s blackbody radiation spectrum. As massdensity increases, so does temperature. This causes the star’s blackbody spectrum to shift to a higher-energy and narrower peak frequency bandwidth according to Wien’s displacement law. This example from fundamental astrophysics reinforces the concept that objects are systems – they are neither static nor inert. This is the fundamental premise of EGM and the basis upon which all EGM calculations are performed. As discussed earlier, any mass-object may be described by its PV spectrum, which is a direct function of mass-energy density. The equilibrium point of the star affects its radius, temperature and blackbody spectrum. The PV spectrum of a star depicts a very similar relationship. As the mass-energy density of any object increases, its harmonic cut-off frequency increases and the modal bandwidth is compressed. Thus, the PV spectrum of a neutron star, for example, possesses a higher harmonic cut-off frequency and a narrower modal bandwidth than our Sun, which is less massive. This is why the EGM principle is universal. We may model any object, whether it’s a galaxy, a cluster of galaxies, a black hole, a neutron star, the Sun, a planet or a subatomic particle using the same fundamental equation. However, the real value of the EGM method lies in its ability to relate mass equilibrium states to one another, as demonstrated by the subatomic particle harmonic relationship. It is by way of this harmonic relationship that we may extrapolate cosmological parameters like the Hubble constant and the CMBR temperature as well. Because EGM models a mass-object as existing in equilibrium with the QV, the local energy state of the vacuum may be considered to be equivalent to the mass-energy of the object it encapsulates. For instance, this equivalency relationship is mirrored by the stable equilibrium state of a star, such that the outward energy produced by fusion is equal to the inward gravitational energy acting to contain it. One may also conceptualize this by considering a “seesaw” or lever with a fulcrum placed at its center. The lever may be balanced horizontally if objects of equal weight are placed on each end. The weight of object “A” on one side must be exactly the same weight as object “B” on the opposing side for the lever to remain stable and horizontal. In this regard, the mass-energy of an object must be equivalent to the vacuum energy encapsulating it in order for it to rest in equilibrium.

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EGM is based upon dimensional analysis, which permits the researcher to model real-world systems by similitude. Employing similitude, EGM derives “H0” and “T0” by relating the PV spectrum of an imaginary particle possessing the energy density of the Universe at the instant of the Big Bang to its present-day value; utilizing the mass-energy density of the Milky Way galaxy as a basis for the comparison. We may apply the EGM method to model the difference in energy density between the early Universe immediately after the Big Bang and the present moment by presuming that the seed of the Big Bang was a particle of maximum permissible energy density, i.e., a “Planck Particle” – representing a state in which all the energy in the Universe is compacted into a single point141. Like Sir Geoffrey Taylor, who calculated the energy of the atomic bomb explosion knowing only the difference in blast sphere radius at given intervals in time, we may extrapolate “H0” and “T0” by comparing the analogous “Planck Particle Universe” at the instant of creation with the present-day Universe because of the First Law of Thermodynamics. The derivation process is executed by utilizing the “EGM harmonic representation of fundamental particles” equation to relate the primordial-Universe Planck Particle to a present-day equivalent of known mass. However, instead of a proton or electron, the arbitrary particle we elect to apply as a base-line reference particle is imaginary, possessing the mass of the Milky Way galaxy. If we were to use a proton, it would reflect its local equilibrium boundary within the atomic system, not the energy-density state of the Universe. The PV spectrum of this Milky Way particle, referred to as the “Galactic Reference Particle” (GRP), possesses a harmonic cut-off frequency which is very high, but less than the Planck Frequency, and represents 141

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the mass-energy density and vacuum equilibrium state of the presentday Universe. The Universe is quite isometric142; we observe that all galaxies are, on average, evenly distributed throughout the Universe, and that they are all roughly in the same stage of evolution. Thus, we may assume that the evolution of all galaxies has been subject to the same ground rules and has followed roughly the same time-line as our own. Because of this, our own Milky Way galaxy acts as a “reference particle”, yielding an average present-day value of the gravitational intensity throughout space-time. Astronomers have been able to produce a fairly good estimate of the total mass of the Milky Way, and have been able to calculate the distance of our sun to the center of the galaxy. We may mathematically represent total galactic mass as being contained within a single “particle”, placed at the galactic center. This reference particle (the GRP) may be represented as radiating gravitational energy equivalent to its total mass. The intensity of gravitational energy at any radial position, such as the Sun’s mean distance from the galactic center, may be calculated from the PV spectrum of the GRP. Thus, the GRP is proportionally representative of the total mass-energy density and QV equilibrium state of the Universe at the present time. Pressure, as it has recently been described within this chapter, is directly related to temperature. Temperature, as we also know, is directly related to the blackbody spectrum. A mass-object of any type may be represented by its PV spectrum, which may also be physically interpreted as a spectrum of gravitons. The parameters of the PV spectrum directly relate to the gravitational intensity of the mass-object. In other words, the modes comprising the PV spectrum indicate the gravitational intensity present at any point from the center of the mass-object. As one moves away from the center of mass, the gravitational intensity decreases, and the number of PV spectral modes increases. This equilibrium gradient denotes a balance of field pressures between the QV and the mass-object. “H0”, in a sense, is a measure of the “expansive pressure” of the space-time manifold. Thus, we may utilize the GRP to determine the average cosmological matter-space-time equilibrium value and derive “H0”. In this regard, “H0” describes the observed energy condition of the vacuum in its entirety, as does “T0”. Deriving “H0” in this manner provides the required input for the derivation of “T0”. Once again, we shall commence by stating that 142

i.e. the same, no matter where you may be measuring it.

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pressure is related to temperature. Relating the current average “pressure” of space-time (i.e. “H0”) to the “pressure” of the primordial-Universe Planck Particle at the instant of the Big Bang (via Wien’s displacement law) yields a scale by which the Planck mode decayed into its current spectrum. Gravitons143 radiated at the instant of the Big Bang have red-shifted144 at the scale defined by the ratio between the GRP and Planck Particle equilibrium end-points. This red-shifted frequency may, in turn, be converted to cosmological temperature, producing an estimate surpassing the precision of the most accurately measured value of “T0”145. This level of accuracy is due, in part, to the natural derivation of the cosmological inflationary epoch under the EGM construct146. It is also possible to utilize the primordial-Universe Planck Particle and GRP end-points to thermodynamically model the change in “H” and “T” since the instant of the Big Bang, forming a complete historical record of the evolution of the Cosmos! This is accomplished by relating the Planck Particle and GRP via the “harmonic representation of fundamental particles” equation, yielding a dimensional scaling factor which fills the gap between creation and the present-day in terms of volumetric expansion. Immediately after the Big Bang, as energy began condensing to form matter, the gravitational energy radiating from matter formed equilibrium gradients within the QV. Hence, the formation of matter is a vital component for determining the average expansive pressure of the Universe following the Big Bang and the manner in which “H” has changed over time. The influence of matter upon the expansive pressure of the space-time metric is automatically factored into the model by incorporating the gravitational energy state at the Sun’s relative position to the GRP. We may extrapolate the evolution of “H” and “T” by assuming that the number of space-time modes has bifurcated exponentially since the Big Bang, taking into account the effect of matter condensation on the modal spectrum. This facilitates the determination of scaling factors based upon the intensity of gravitational flux between the instant of the Big Bang and the presentday; the scaling factors are then applied over the Hubble and 143

i.e. conjugate photon pairs. Into the microwave range. 145 EGM predicts “2.7248(K)”. 146 The SMoC does not naturally derive the inflationary epoch or consider gravity to be an EM phenomenon; thus, the residual radiation measured as “T0” is assumed by contemporary physicists to be the result of the formation of atoms. 144

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temperature domains. The result of this calculation is truly astonishing! Based upon the EGM method, the epochs of cosmic evolution are mapped out in extraordinary detail. The resulting history of “H” and “T” corroborate with all epochs of cosmic evolution as asserted by the Standard Model of cosmology. The theory of early “cosmic inflation” is reinforced and the recently measured “accelerated expansion” is derived. Cosmic inflation is an epoch thought to have occurred within the first fractions of a trillionth of a second after the Big Bang. This burst of rapid acceleration was followed by a reduction in the acceleration rate, continuing throughout the life-time of the Universe. Of particular interest in this case is that the inflation epoch emerges spontaneously as a result of the EGM calculation, and isn’t presumed or “placed” there a priori as part of the modeling process. Alan Guth introduced the cosmic inflation hypothesis to the Standard Model of cosmology as a requisite so that the Big Bang theory “fits” observation. Without this inflationary epoch, the Universe would not exist in present observational form. It would be flat and featureless, with no clumps of matter or galaxies, and would be so small today that the Universe, even after billions of years, would only fit on the head of a pinxxviii. The inflationary epoch has been added to the Standard Model of cosmic history because it is required. Without it, the Big Bang theory flounders. However, the EGM construct generates the inflationary epoch from first principles, and is ultimately derived from a particle physics equation. The latest scientific measurements demonstrate that the expansion of the Universe continues to accelerate. Previously, scientists wondered whether there might be enough matter in the Universe to halt cosmic expansion. In the fullness of time, it was thought that perhaps there was enough matter present to suck spacetime back in, causing the Universe to meet its end in a reverse of the Big Bang termed the “Big Crunch”. However, when the data was assembled, it vexed some astronomers to discover that the Universe is actually accelerating at a rate exceeding predictions, based upon the best estimate of the total amount of matter in the Universe. The discrepancy between prediction and observation (within the Standard Model of cosmology) is so vast, in fact, that cosmologists were forced to invent the concepts of “dark energy” and “dark matter” in order to make sense of the findings. Our best measurements of expansion are so far from the predicted value that theorists presently estimate that “72(%)” of the Universe must be composed of dark energy and “23(%)” must be dark matter, meaning

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that a whopping “95(%)” of our Universe exists in an unknown, unobservable form147! According to observationxxix, it is thought that a substantial portion of matter comprising galaxies is “missing” because of the peculiar manner in which galaxies rotate. Instead of rotating fastest in the center and slower on the periphery, as occurs in a vortex of water, or a cyclone in the atmosphere, stars located in the spiral arms of galaxies rotate around the central axis at the same rate as the stars near the center. One might naturally expect that individual stars in the arms of a galaxy would gradually spiral into the center, moving slowly at the edge and then faster and faster as they spiral in towards the center of the vortex. Surprisingly, however, the entire galaxy rotates uniformly like a giant pin-wheel in space. In order for an entire galaxy to rotate uniformly it would require much more mass, in the form of stars, planets and gasses, than is actually found to be present. Therefore, it is thought that matter must be present in some undetectable form in great halos surrounding the visible part of a galaxy. The concept of “dark matter” has been manufactured in order to make up for the “missing mass”, and explain why entire galaxies rotate uniformly like a wheel, rather than spiral inward like a vortex. Similarly, “dark energy” is also a contrivance invoked to explain why the Universe continues to expand at an accelerated rate, despite the addition of dark matter. Notwithstanding dark and visible matter, the remainder of the Universe is thought to be in the form of an energy field which generates a negative pressure in space, counteracting gravity on a cosmological scale, causing intergalactic voids of space-time to expand like giant balloons. Although the CMBR spectrum is not entirely smooth and uniform, its overall smoothness necessitates that a certain critical density of matter exists in the Universe. Unfortunately, the derived value contradicts measurement when the expansion rate of the Universe is applied to calculate the density value. In other words, the CMBR and acceleration rate measurements are in direct conflict with current theory, which means that either something is fundamentally wrong with the Standard Model of cosmology, or we must come to terms with the notion that a mere “4.6(%)” of our Universe is composed of matter and energy that we may observe and measure. Even though the cosmic inflation epoch is also a contrivance introduced to fit a theory, EGM substantiates its existence because the inflation epoch emerges spontaneously as a natural consequence of 147

NASA JPL PlanetQuest news: “SIM PlanetQuest to predict date of cosmic collision” by Bob Silberg. www.deltagroupengineering.com

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the calculation deriving “H0” and “T0”. However, EGM calls into question the existence of dark energy and dark matter. This is due to the fact that the EGM method not only predicts “H0” and “T0” with extraordinary precision, it predicts the inflationary epoch and current measures of accelerated expansion without invoking dark matter or energy. In fact, based upon the EGM method, the contribution of dark matter and energy to the cosmological model is negligible. The EGM method requires no contrivances or fudge-factors in order to produce results which are substantially more precise than those provided by the Standard Model of cosmology (and particle physics). Astonishingly, EGM allows one to derive “T” from “H”, demonstrating that they are intimately related phenomenon. As a consequence, the entire history of the Cosmos is revealed such that key evolutionary epochs are clearly and precisely defined without the need for dark energy and matter. After the Big Bang, an “inflationary epoch” ensued, followed by phases leading to the condensation of matter, the formation of stars, heavy elements and large-scale structures such as galaxies. Cosmological epochs arise due to the energy density conditions present in the Universe during each phase. Just like the formation of subatomic particles in a collider, each cosmic phase transition was induced by the epoch-specific energy density parameters of the Universe which existed at that particular time. These epochs in the lifetime of the Universe are not unlike the main sequence lifetimes of stars. The fate of a star is preordained by consequence of its physical state of equilibrium. The characteristics of the star; its temperature, color, size and even the duration of its life hinge on a dynamic balance between the star’s thermal energy and gravity. When a giant star transitions between its main sequence and its death as a supernova, the phase transitions brought about by shifts in equilibrium forge heavy elements and disperses them throughout the Universe. The formation of these elements provided the starting material for planet formation, and ultimately, the emergence of life. We owe our existence to the principle of equilibrium and the harmonic paradigm that EGM describes. The fact that it is possible to utilize the EGM “harmonic representation of fundamental particles” equation to solve for cosmological problems such as “H0” and “T0”, as well as describing in fine detail the timeline of cosmic history means that the Cosmos is beholden to the same harmonic imperative begetting the existence of matter. The EGM principle is more than “universal”, it is cosmological.

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We have come full circle, from alpha to omega, having substantiated a mathematical philosophy once fervently espoused by Pythagoras and the ancient Babylonians over two-thousand years ago. We now hold substantive evidence authenticating the philosophical beliefs of our ancient scientific predecessors, who contemplated and understood the Cosmos to be much more than a “void” in which matter merely resides. Their depiction of the Cosmos encompassed all forms in the Universe, from the miniscule to the immense, living and inert. Their Cosmos was an expression of Musica Universalis – the harmonic affinity connecting all things and giving rise to all forms in Nature.

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EGM Technical Summary Written by Riccardo C. Storti

“Brevity is the sister of talent.” Interpretation: revolutionary statements in science should be simple. • Russian proverb “Brevity can be the enemy of comprehension.” Interpretation: recognition and comprehension of simple and revolutionary scientific statements depends upon the skill-set of the audience. • Riccardo C. Storti

9.1

Overview

The following section outlines the method developed within QE2-4 to describe “g” in harmonized terms, yielding new predictions and highly precise experimentally verified results beyond the Standard Models (SM’s) of particle physics and cosmology. The EGM construct derives (see: QE3): i. A harmonic representation of gravitational fields at a mathematical point arising from geometrically spherical objects of uniform mass-energy distribution using modified Complex Fourier series. ii. Characteristics of the amplitude spectrum based upon (i). iii. Derivation of the fundamental harmonic frequency based upon (i). iv. Characteristics of the frequency spectrum of an implied ZPF based upon (i) and the assumption that an EM relationship exists over a change in displacement across a practical bench-top test volume. The derivational procedure obeys the following hierarchy: v. A harmonic representation of “g” is developed. vi. The frequency spectrum of (v) is derived by application of Buckingham “Π” Theory (BPT) and dimensional similarity. vii. The ZPF energy density is related to (vi) based upon the assumption that engineered EM changes in “g” may be

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produced across the dimensions of a practical bench-top test volume. viii. Spectral characteristics of the PV are derived based upon (vii). ix. A description of physical modeling criteria is presented. x. A set of sample calculations and illustrational plots are presented. Applicable definitions: • • •

• • •

Quantum Vacuum (QV): a quantum representation of the space-time manifold within GR. Quantum-Vacuum-Energy (QVE): the spectral energy associated with the QV. Zero-Point-Field (ZPF): the QV field associated with globally flat space-time geometry. However, such a configuration cannot physically exist; thus, the ZPF takes the form of a generalized reference to the QV field throughout the “Quinta Essentia” series (i.e. QE2-4). Zero-Point-Energy (ZPE): the spectral energy associated with the ZPF. Polarizable Vacuum (PV): a polarized representation of the ZPF. Electro-Gravi-Magnetics (EGM): a theoretical relationship between EM fields and “g”.

Fourier series148 may be applied to represent a periodic function as a trigonometric summation of sine and cosine terms. It may also be applied to represent a constant function over an arbitrary period by the same method. Since the PV model is (historically) a weak field isomorphic approximation of GR and the frequency spectrum is postulated to range from negative to positive infinity, it follows that Fourier series represent a useful tool by which to describe gravity.

148

A Fourier series representation of a constant function involves the hybridization of amplitude and frequency spectra (i.e. a Fourier distribution contains two embedded spectra).

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Utilizing Fourier series in complex form149, the square wave is constructed by summing modes. The manner in which the function to be approximated is articulated influences its harmonic characteristics150.

Figure 1.1, A constant function is termed even due to symmetry about the “Y – axis”; subsequently, its Fourier approximation need only contain certain terms at odd harmonics151, presenting the added advantage of mathematical and energetic efficiency152. Thus, the preceding periodic square wave may be reconstructed utilizing the symmetry characteristics of a constant function as depicted by the proceeding graph153 such that “g” is physically measured as a constant function at the surface of the Earth. A Fourier series approximation of “g” may be obtained by computing the magnitude of the preceding / proceeding periodic square waves154 as the number of harmonic modes tends to infinity.

149

The preferred representation in the Quinta Essentia series, possessing Real (Re) and Imaginary (Im) parts; however, the “Im” contribution mathematically sums to zero. 150 i.e. it may contain exclusively cosine or sine terms; alternatively, it may contain both trigonometric forms. 151 i.e. “1st, 3rd, 5th …” etc. 152 i.e. the system is modeled as existing at its lowest energy state. 153 i.e. for demonstration purposes only, up to the “21st” harmonic. 154 i.e. computing the magnitude acts to enforce full wave rectification; http://en.wikipedia.org/wiki/Rectifier www.deltagroupengineering.com

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Figure 1.2, Therefore, “g” (i.e. a constant function) may be mathematically characterized as a fully rectified periodic square wave composed of odd Fourier harmonics. Due to symmetry (as illustrated above / below), “g” may be constructed utilizing half the period of the fully rectified square wave155.

Figure 1.3,

155

i.e. the complete square wave cycle is not required to describe the system.

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Time domain modeling may be applied over the displacement domain of a practical bench-top test volume by considering the relevant changes over the dimensions of that volume. Constant functions may be expressed as a summation of trigonometric terms; subsequently, it is convenient to model a gravitational field utilizing modified Complex Fourier series according to an odd number harmonic distribution. Hence, “g” may be usefully represented by the magnitude of a periodic square wave solution as the number of waves utilized to describe it, approaches infinity. It is demonstrated in QE3 that dimensional similarity and the equivalence principle may be applied to represent the magnitude of an acceleration vector such that an expression for the frequency spectrum is derived in terms of harmonic mode. This is achieved by assuming that electromagnetically induced acceleration is dynamically, kinematically and geometrically similar to “g” as constructed by Fourier series wave summation. The gravitational field surrounding a homogeneous solid spherical mass may be characterized by its energy density. If the magnitude of this field is directly proportional to the mass-energy density of the object, then the field energy density of the PV may be evaluated over the difference between successive odd frequency modes. The reason for this is due to the mathematical properties of Fourier series for constant functions. For such cases – as appears in standard texts, the summed contribution of all even modes equals zero. Subsequently, only odd mode contributions need be considered when modeling a constant function. Utilizing the approximate rest mass-energy density of a solid spherical object, an expression relating the terminating harmonic cutoff mode may be derived by assuming that the equivalent quantity of mass-energy within an object is also stored in the gravitational field surrounding it. Subsequently, the upper boundary of the frequency spectrum, termed the harmonic cut-off frequency, may be calculated; the derivation is based upon the compression of energy density of the “random ZPF form” to one change in odd harmonic mode while preserving dynamic, kinematic and geometric similarity in accordance with BPT. The compressed “random ZPF form” is subsequently decompressed over the Fourier domain (assigning structure), yielding a highly precise reciprocal harmonic representation of “g”; preserving dynamic, kinematic and geometric similarity to the Newtonian, PV and GR representations. The cross-fertilization of the amplitude and frequency characteristics of a constant function described by Fourier series with the ZPF spectral energy density distribution derived by www.deltagroupengineering.com

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Haisch and Rueda, is a useful tool by which to determine the spectral characteristics of the PV representation of GR (proposed by Puthoff) at the surface of the Earth (for example) by assuming, xi. The PV physically exists as a spectrum of frequencies and wave vectors. xii. The sum of all PV wave vectors at the surface of the Earth is coplanar with the gravitational acceleration vector. This represents the only vector of practical experimental consequence. xiii. A modified Complex Fourier series representation of “g” is representative of the magnitude of the resultant PV wave vector. xiv. A physical relationship exists between electricity, magnetism and gravity such that “g” may be investigated and modified. Therefore, we may summarize the solution algorithm constituting the harmonically based EGM construct by five simple steps as follows: xv. Apply Dimensional Analysis Techniques (DAT's), BPT and similarity principles to combine electricity, magnetism and resultant EM acceleration in the form of “Π” groupings. xvi. Apply the equivalence principle to the “Π” groupings formed in (xv). xvii. Apply Fourier Harmonics to the equivalence principle. xviii. Apply ZPF Theory156 to Fourier Harmonics. xix. Apply the PV model of gravity to the ZPF. Within the EGM construct, the Poynting Vector “P” represents the propagation of energy (i.e. conjugate photon pairs, see: QE3), radially outwards from the center of mass; however, “g” is the result of the change in “P” (i.e. “∆P”) between two points in the displacement domain. This may appear counter-intuitive since “P” propagates away from the center of mass, but “g” is a consequence of “∆P” not “P”. A “∆P” arises due to the superposition of the “P” field upon the ZPF. The ZPF acts to constrain the “P” field, yielding “g” as predicted by Newtonian mechanics and GR. This principle may be demonstrated by a simple example; let the value of “P” at positive radial displacements from a mass-object “r1” and “r2” be given by the positive values “P1” and “P2” respectively. Hence, if “r2” is greater than “r1” then “P2” is less than 156

See also: ZPF equilibrium as described in QE2 (i.e. the chapter titled “The Natural Philosophy of Fundamental Particles”).

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“P1” because “P2” tends to zero as “r2” approaches infinity such that the difference between “P1” and “P2” is negative, indicating that “g” acts towards the center of mass and opposite to the direction of propagation of “P”. “P” represents the propagation of spectral mass-energy equivalence in the form of populations of conjugate Photon pairs. An equilibrium gradient in the displacement domain arises due to the mathematical interaction between the mass-energy and ZPF spectra, equivalent to space-time curvature under GR because the intensity of “P” varies congruently with “g”. Hence, the radial gradient in “P” is analogous to variations in the Refractive Index of the space-time manifold in an optical model of gravity.

9.2

The QV spectrum

Historically, the QV has been considered to be composed of a near infinite spectrum of randomly orientated wave functions, each of specific frequency and amplitude, analogous to the static one observes on a dead television channel. However, the EGM construct disagrees with this historical conception as it implies the existence of a near infinite quantity of energy in a vanishing volume (i.e. free space contains a near infinite amount of energy). EGM asserts that the QV is more appropriately described as a finite spectrum whose wave function population is determined by the quantity of mass-energy occupying a specific volume (i.e. free space contains a near zero amount of energy). Subsequently, the QV spectrum may be characterized by the following statements: xx. It is a generalized reference to a quantum description of the space-time manifold. xxi. In flat space-time geometries, it transforms to the ZPF spectrum. xxii. In curved geometries (i.e. gravitational fields), it transforms to the PV spectrum.

9.3

The EGM spectrum

The EGM spectrum is a harmonic description of mass-energy represented as conjugate EM wavefunction pairs; incrementally above “0(Hz)”, tending to the Planck Frequency and obeying a Fourier distribution. Key generalized spectral features are: xxiii. It is discrete and harmonically continuous.

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xxiv. The terminating frequency is a harmonic multiple of the fundamental (i.e. lowest freq.). xxv. Each wavefunction represents a population of photons such that each conjugate photon pair constitutes a graviton. xxvi. Where appropriate, due to the principle of mass-energy equivalence and the law of conservation of energy157, it may also be referred to as the PV spectrum.

9.4

The ZPF spectrum

The ZPF spectrum may be partially described by its contrast to the EGM spectrum. The EGM spectrum relates the mass of an object to the gravitational field surrounding it utilizing Fourier harmonics; hence, it is “somewhat localized”. However, the energy of the ZPF is dispersed homogeneously throughout the Universe. The historical conception of the ZPF implies the existence of a near infinite quantity of energy in a vanishing volume (i.e. free space contains a near infinite amount of energy). Fortunately, EGM resolves this conflict such that a vanishingly small volume of flat space-time does not contain an infinite amount of energy. This is achieved by merging the continuous cubic frequency characteristic of the ZPF with a discrete and finite Fourier distribution such that, xxvii. The number of harmonic modes approaches infinity. xxviii. The highest frequency tends to zero. A determination of available ZPF energy throughout the observable Universe is demonstrated in QE2,4 and the gradient of the Hubble constant in the time domain is shown to be presently positive158.

9.5

The PV spectrum

The PV spectrum may be formulated by merging the EGM and ZPF spectral distributions. Energy condensed as mass is finite; representing a small fraction of the total energy in the Universe. The finite parameters of matter dictate the form that the mass-energy spectrum will take. The resulting harmonic description is termed the PV spectrum. 157

i.e. the mass-energy within an object is energetically equivalent to the gravitational field surrounding the object. 158 Facilitating an explanation of the “accelerated cosmological expansion” phenomenon.

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PV spectral formation may be conceptualized by considering a Universe populated by a singular spherical object of homogeneous mass-energy density. When such an object is added to an empty Universe, the EGM spectrum of the object is superimposed upon the background ZPF spectrum. Merging the EGM and ZPF spectra results in the cross-fertilization of characteristics; the complete mathematical derivation is contained in QE3. Descriptions of the specific mathematical events required are as follows, xxix. Integrate the Haisch-Rueda-Puthoff (HRP) spectral energy density equation over the frequency domain “ω”. xxx. Recognize that, for any Fourier summation resulting in a constant function, only odd harmonic modes are required due to the null summation of even modes. This is a fundamental property of Fourier mathematics and should not be dismissed159. xxxi. Formulate an expression for the change in energy density with respect to odd harmonics, in terms of “ω”, utilizing the integrated HRP spectral energy density equation. xxxii. Substitute the harmonic frequency “ωPV” relationship into the integrated HRP spectral energy density equation. xxxiii. Solving appropriately, one obtains the harmonic cut-off mode and frequency (i.e. “nΩ” and “ωΩ” respectively). “nΩ” denotes the highest harmonic mode contained in the merged spectra (i.e. the PV spectrum) and “ωΩ” represents the terminating spectral frequency relative to a fundamental value (i.e. its lowest permissible magnitude). Hence, all required attributes have been derived to completely describe “g” in harmonic terms. The next step is to understand how the EGM method produces a PV spectrum such that the “infinite energy” dilemma of ZPF Theory (derived by contemporary QM methods), is averted. The deductive reasoning may be articulated as follows: xxxiv. The HRP derivation implies that the majority of ZPE exists at the spectral limit160. xxxv. Assume that the ZPE at an arbitrary mathematical point in the space-time manifold is constant such that the associated spectrum may be described harmonically relative to the

159

Refer to any standard text for further information regarding Fourier techniques. 160 i.e. low frequency energy contribution is comparatively trivial. www.deltagroupengineering.com

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xxxvi.

xxxvii.

xxxviii.

xxxix.

magnitude of “some” fundamental frequency at the point under consideration. The Fourier characteristics of a constant function demonstrate that only odd harmonic modes are required for summation. Principles of equivalence and similitude imply that the highest spectral transition of odd harmonic mode may be utilized in the representation of the total localized ZPE. Assume that the mass-energy density of an object is equal to the spectral energy density of the gravitational field surrounding it. Integrating the HRP spectral energy density relationship yields the total ZPE, which may be expressed locally as a narrow high-frequency bandwidth of equivalent energy. Equating this result to the mass-energy density of an object yields the PV spectrum surrounding it, preserving similitude.

Therefore, when the EGM and ZPF spectra are merged, the continuous ZPF spectrum is compressed and equated to the Fourier distribution of the EGM spectrum such that the resulting PV spectrum is a decompressed form of the merged spectra and the properties of its spectral limits may be determined. This process mathematically transforms the continuous ZPF spectrum to a discrete and finite Fourier distribution of equivalent energy. Thus, as radial displacement “r” at a mathematical point from a mass-object increases; xl. Gravitational field strength decreases. xli. Spectral energy density decreases. xlii. The number of harmonic modes increases (i.e. bifurcation). xliii. Greater numbers of modes are required to be summed for energetic equivalence. The EGM interpretation of gravity is similar to Newton’s thoughts of an optical model such that the aether was presumed to be “denser” farther away. The gradient in aether density causes light and objects to follow trajectories characteristic of GR. EGM demonstrates that the increasing density of Newton’s aether is analogous to increases in mode population in the PV spectrum. Hence, the PV is an EM frequency spectrum obeying a Fourier distribution at displacement “r” describing a mass “M” induced gravitational field such that; xliv. It denotes a polarized form of the ZPF spectrum161. 161

Mass pushes the ZPF surrounding it “uphill”, against the natural flux of space-time manifold expansion.

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xlv. The population of spectral modes decreases as mass increases. xlvi. Maximum spectral frequency increases as mass increases. xlvii. The fundamental spectral frequency increases as mass increases. xlviii. Spectral frequency bandwidth162 increases as mass increases.

9.6

The EGM, PV and ZPF spectra

The difference between the EGM, PV and ZPF spectra is that the EGM spectrum commences incrementally above “0(Hz)” and approaches the Planck Frequency. The PV spectrum is mass specific and represents a bandwidth of the EGM spectrum commencing at a non-zero fundamental frequency. The EGM and PV spectra follow a Fourier distribution, whereas the ZPF spectrum possesses the same frequency bandwidth of the EGM spectrum, but does not follow a Fourier distribution. Thus, the EGM spectrum is the polarized form of the ZPF spectrum, while the PV spectrum is an object specific subset of the EGM spectrum following a Fourier distribution.

9.7

The Casimir Effect

The Casimir Effect163 demonstrates that when small distances separate two flat neutral metal plates, photons in the PV field with wavelengths larger than the plate separation distance are excluded from the spatial cavity, resulting in an attractive force between the plates due to the bias in vacuum energy across the system164. Gravity, in this regard, is analogous to a long-range Casimir Effect because EGM asserts that mass induced gravitational effects may be described by changes in mode population across a region of space. The EGM construct was applied in QE3 to derive the Casimir Force from first principles, demonstrating that it differs depending upon ambient gravitational field strength! For example, the Casimir 162

i.e. the difference in magnitude between the highest and lowest frequencies. 163 Presently, it is only experimentally confirmed to exist in gravitational fields (i.e. PV fields). “The Effect” has not been physically verified in flat space-time geometries (i.e. the free-space “0g” condition). 164 i.e. the vacuum energy density is lower between the plates. www.deltagroupengineering.com

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Force will be slightly different on Earth than Jupiter or the Moon. QE3 states that, xlix. “…. an Earth based equivalent Casimir experiment conducted on Jupiter will exclude fewer low frequency modes – preserving higher frequency modes that simply pass through the plates, resulting in a smaller Casimir Force. By contrast, the same experiment conducted on the Moon will produce a larger Casimir Force.” l. “…. a Casimir Experiment conducted in free space will produce an extremely small force (tending to zero) due to the lack of initial background field pressure. Since the Casimir Force arises from a pressure imbalance, the lack of significant ambient field pressure between the plates165 prevents the formation of large Casimir Forces.”

9.8

Comparative spectra

Note: labels of the form “2.xx, 3.xx, 4.xx” refer to QE2,3,4 respectively. EGM bandwidth comparisons of PV spectra associated with physical categories of objects may be formulated and represented graphically based upon ZPF equilibria. Determination of the ZPF equilibrium radius of subatomic particles is a sophisticated process, summarized in QE2. A complete and rigorous derivation is presented in QE3. Utilizing the EGM construct, the HRP spectral energy density equation with cubic frequency distribution may be graphically categorized into four regions (i.e. zones), these are; “Planck-scale” energy densities, “particle physics”, “astrophysics” and “cosmology”, subject to the following generalized characteristics166 [see: Fig. (2.1, 2.2)], li. Planck scale energy densities167 [see: QE4] • Narrowband high-frequency spectrum. • Narrowband modal spectrum. lii. Particle physics • Broadband high-frequency spectrum. • Narrowband modal spectrum. 165

i.e. in and around the experimental zone. See: QE2 for precise numerical determinations. 167 Refers to particulate representations of maximum permissible energy densities (i.e. Black Hole singularities). 166

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liii. Astrophysics • Moderateband168 high-frequency spectrum. • Moderateband modal spectrum. liv. Cosmology [see: Tab. (2.6, 2.7)] • Narrowband low-frequency spectrum. • Broadband modal spectrum. Sample plots,

Figure169 2.1 (illustrational only - not to scale), where, Region / Zone Applicable Category Gravitational Model Space-Time Geometry

A B Cosm. Astro. ZPF PV Flat Curved Table 2.6,

C PP PV Flat

D PS PV Curved

168

A generalized reference to spectral bandwidth relative to “narrow” and “broad” descriptors. 169 Utilizing this proportional spectral frequency characteristic in the harmonic representation of gravitational fields by the EGM method, the bifurcation phenomenon may be mathematically articulated by the relationship “ρ0 ∝ 1 / nPV” [Eq. (2.7); see: QE2]. www.deltagroupengineering.com

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Note: Cosm. (Cosmology), Astro. (Astrophysics), PP (Particle Physics) and PS (Planck Scale).

Figure 2.2 (illustrational only - not to scale), where, Region / Zone Applicable Category Gravitational Model Space-Time Geometry

E F PS PP PV PV Curved Flat Table 2.7,

G Astro. PV Curved

H Cosm. ZPF Flat

On a Cosmological scale170, the ZPF upper spectral limit is influenced by the average energy density of the present Universe. The spectral density of the ZPF remains cubic; however, the upper spectral frequency limit is lower than it was in the early Universe. Hence, the majority of ZPE is presently in the form of low-frequency modes, each containing a relatively small amount of energy. The few high-frequency modes characterizing the early Universe have bifurcated into a very large bandwidth of lowerfrequency modes as the Universe expanded to its present form. The total energy of the Universe remains constant, but is spread out over a 170

i.e. on average, with a flat space-time manifold as determined by the Wilkinson Microwave Anisotropy Probe (WMAP).

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much greater volume as cosmological expansion continues. It is demonstrated by derivation in QE3 and confirmed in QE4, that the majority proportion of the gravitational effect in a field occurs at the harmonic cut-off frequency “ωΩ ” such that all other frequencies may be usefully neglected171.

9.9

Characterization of the gravitational spectrum

The EGM equations, utilized to describe fundamental particles in harmonic terms, are simplified for values of Refractive Index “KPV” approaching unity. This facilitates the representation of “g” utilizing the PV harmonic cut-off frequency “ωΩ”, leading to the formulation of a generalized cubic frequency expression. It is demonstrated that the PV spectrum is dominated by “ωΩ ” such that the magnitude of the associated gravitational Poynting Vector is usefully approximated by the total energy density, resulting in an expression for EGM Flux Intensity “CΩ_J”. The derivation sequence proceeds as follows, lv. Simplification of the EGM equations. lvi. Derivation of “g” in terms of “ωΩ ”. lvii. Formulation of a generalized cubic frequency expression in terms of “g”. lviii. Determination of the gravitationally dominant EGM frequency. lix. Derivation of “CΩ_J”.

9.10 “Planck-Particle” characteristics The minimum physical dimensions of “SchwarzschildPlanck Particle” mass and radius is derived, leading to the determination of the value of “KPV” at the event horizon of a “Schwarzschild-Planck Black Hole” (SPBH). Consequently, the magnitude of “ωΩ” at the event horizon “RBH” of a “Schwarzschild Black Hole” (SBH) is presented, yielding the singularity radius “rS” 171

The information in this paragraph should not be confused with the PV spectrum of a specific body such as a planet, in which case, the bulk of the gravitational energy [i.e. >> 99.99(%)] occurs at the harmonic cut-off frequency. The low frequency modes do not contribute significantly and may be usefully neglected from most calculations. This phenomenon has been thoroughly and rigorously explored in QE3. www.deltagroupengineering.com

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and harmonic cut-off profiles (“nΩ” and “ωΩ” from “rS” to “RBH”). The minimum gravitational lifetime of matter “TL” is also advanced such that the value of generalized average emission frequency per graviton “ωg” may be calculated. These determinations assist in the supplemental EGM interpretation with respect to the visibility of “Black Holes” (BH’s). The derivation sequence proceeds as follows, lx. Derivation of the minimum physical “Schwarzschild-Planck Particle” mass and radius. lxi. Derivation of the value of the “KPV” at the event horizon of a “Schwarzschild-Planck Black Hole” (SPBH). lxii. Derivation of “ωΩ” at the event horizon of a SPBH. lxiii. Derivation of “ωΩ” at the event horizon of a SBH. lxiv. Derivation of “rS”. lxv. “nΩ” and “ωΩ” profiles (from “rS” to “RBH”) of SBH’s. lxvi. Derivation of “TL”. lxvii. Derivation of “ωg”. lxviii. Why can't we observe BH’s?

9.11 Cosmology 9.11.1 Fundamental The primordial and present values of the Hubble constant are derived (“Hα” and “HU” respectively), leading to the determination of the Cosmic Microwave Background Radiation (CMBR) temperature “TU”. This facilitates the determination of the impact of “dark matter / energy” on “HU” and “TU” such that a generalized expression for “TU” in terms of “HU” is formulated. An experimentally implicit derivation of the ZPF energy density threshold “UZPF” is also presented. The derivation sequence proceeds as follows, lxix. Derivation of “Hα” and “HU”. lxx. Derivation of “TU”. lxxi. Numerical solutions for172 “Hα, AU, RU, ρU, MU, HU” and “TU”. lxxii. Determination of the impact of “dark matter / energy” on “HU” and “TU”. lxxiii. “TU” as a function of a generalized Hubble constant.

“AU, RU, ρU, MU” denote cosmological age, size, mass-density and total mass respectively.

172

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lxxiv. Derivation of173 “Ro”, “MG”, “HU2” and “ρU2” from “TU2”. lxxv. Experimentally implicit derivation of “UZPF”.

9.11.2 Advanced A time dependent derivation of “TU” is performed, including its rate of change and relationship to “HU”. This facilitates the articulation of the cosmological evolution process into four distinct periods dealing with the inflationary and early expansive phases. Subsequently, the history of the Universe174 is developed and compared to the Standard Model (SM) of Cosmology (SMoC). This assists in determining the cosmological limitations of the EGM construct. The question of the practicality of utilizing conventional radio telescopes for gravitational astronomy is also addressed. The derivation sequence proceeds as follows, lxxvi. Time dependent CMBR temperature. lxxvii. Rates of change of CMBR temperature. lxxviii. Rates of change of the Hubble constant. lxxix. Cosmological evolution process. lxxx. History of the Universe. lxxxi. EGM cosmological construct limitations. lxxxii. Are conventional radio telescopes, practical tools for gravitational astronomy?

9.11.3 Gravitational An engineering model is developed to explain how gravitational effects are transmitted through space-time in terms of EGM wavefunction propagation and interference. The derivation sequence proceeds as follows, lxxxiii. Gravitational propagation: the mechanism for interaction. lxxxiv. Gravitational interference: the mechanism of interaction.

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“Ro” and “MG” denote galactic radius and mass respectively. “HU2”, “ρU2” and “TU2” represent transformations of “HU”, “ρU” and “TU”. 174 As defined by the EGM construct. www.deltagroupengineering.com

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9.11.4 Particle The following characteristics are derived utilizing EGM principles, lxxxv. The photon and graviton mass-energies lower limit. lxxxvi. The photon and graviton Root-Mean-Square (RMS) charge radii lower limit. lxxxvii. The photon charge threshold. lxxxviii. The photon charge upper limit. lxxxix. The photon charge lower limit.

9.12 Key point summary Under the EGM construct, the following assertions were derived, xc. The EGM spectrum is a harmonic description of mass-energy represented as conjugate EM wavefunction pairs; incrementally above “0(Hz)”, tending to the Planck Frequency and obeying a Fourier distribution. Key generalized spectral features are, • It is discrete and harmonically continuous. • The highest frequency is a harmonic multiple of the fundamental (i.e. lowest freq.). • Each wavefunction represents a population of photons such that each conjugate photon pair constitutes a graviton. • Where appropriate, due to the principle of massenergy equivalence and the law of conservation of energy, it may also be referred to as the PV spectrum. xci. The ZPF is an EM frequency spectrum referring to the QV spectrum of globally flat space-time geometry. However, such a configuration cannot physically exist; thus, the ZPF takes the form of a generalized reference to the QV field throughout the “Quinta Essentia” series (i.e. QE2-4) such that, • The number of harmonic modes approaches infinity. • The highest frequency tends to zero. xcii. The PV is an EM frequency spectrum obeying a Fourier distribution at displacement “r” describing a mass “M” induced gravitational field such that, • It denotes a polarized form of the ZPF spectrum.

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•

xciii. xciv.

xcv. xcvi.

xcvii.

xcviii.

xcix.

The population of spectral modes decreases as mass increases. • Maximum spectral frequency increases as mass increases. • The fundamental spectral frequency increases as mass increases. • Spectral frequency bandwidth increases as mass increases. A vanishing volume containing infinite energy does not exist under the EGM construct. Although on the human scale the quantity of ZPF energy is trivial, on the astronomical or cosmological scale, it becomes extremely large when approaching the dimensions of the visible Universe. The EGM spectrum is a simple, but extreme, extension of the EM spectrum. The ZPF equilibrium radius of astronomical bodies coincides with the mean radius (see: QE3), representing the mathematical boundary (within EGM) delineating mass composition and the gravitational field surrounding it. The EGM harmonic representation of fundamental particles175 is derived by considering all matter to be radiators of populations of conjugate photon pairs176, suggesting that the quintessential building-block of all atoms, chemical elements, molecules and material forms in the Cosmos is the photon. EGM is a method and not a theory because: (i) it is an engineering approximation and (ii), the mass and size of most subatomic particles are not precisely known. It harmonizes all fundamental particles relative to an arbitrarily chosen reference particle by parameterising ZPF equilibrium in terms of “ωΩ”. The formulation of table177 (4.5) is a robust approximation based upon PDG data. Other interpretations are possible, depending on the values utilized. For example, if one re-

175

i.e. the harmonic pattern expressed in terms of “Stω”. The majority of energy contained within a PV spectrum occurs at the spectral limit; hence, the spectrum may be usefully approximated by a single conjugate wavefunction pair at the harmonic cut-off frequency. See: QE2,3 for further information. 177 Refer to the proceeding chapter. 176

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c.

ci.

cii.

ciii.

civ.

applies the method presented in QE3 based upon other data; the values of “Stω” in table (4.5) might differ. However, in the absence of exact experimentally measured mass and size information, there is little motivation to postulate alternative harmonic sequences, particularly since the current formulation fits the available experimental evidence extremely well. If all mass and size values were exactly known by experimental measurement, the main sequence formulated in QE3 (or a suitable variation thereof) will produce a precise harmonic representation of fundamental particles, invariant to interpretation. Table (4.5) values cannot be dismissed due to potential multiplicity before reconciling how, • EGM generates radii values substantially more accurate than any other contemporary method178. • “ωΩ” is capable of producing a “Top quark” mass value – the SM of particle physics cannot. • Extremely short-lived leptons179 cannot exist, or do not exist for a plausible harmonic interpretation. • Any other harmonic interpretation, in the absence of exact mass and size values determined experimentally, denote a superior formulation. The cosmological inflation and accelerated expansion phenomena emerge naturally within the EGM construct and are not presumed a priori as part of the modeling process. Dark matter / energy are not required by the EGM construct to predict experimentally verified results. In fact, it is mathematically demonstrated that “dark” influence upon “H0” and “T0” is less than “1(%)”. The present values of deceleration parameter and cosmological constant (“q0” and “Λ0” respectively) are derived and precisely quantified under the EGM construct. The SMoC interpretation of the sign “±” associated with ZPF energy is opposite to the EGM construct. That is, the SMoC interprets ZPF energy as a positive quantity; EGM interprets it as a negative quantity.

178

It is a noteworthy result that EGM is capable of producing the Neutron Mean Square (MS) charge radius as a positive quantity. Conventional techniques favor the non-intuitive form of a negative squared quantity. 179 i.e. with lifetimes of “< 10-29(s)”.

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cv. Where appropriate, due to the principle of mass-energy equivalence and the law of conservation of energy180, the EGM spectrum may also be referred to as the PV spectrum. Note: numerical simulations substantiating all claims exist in QE2-4.

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In terms of equilibration. www.deltagroupengineering.com

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10 EGM Results Summary 10.1 Harmonic representation of fundamental particles Particles may be classified according to a precise harmonic relationship amongst harmonic cut-off frequencies. The “EGM harmonic representation of fundamental particles” equation yields harmonic values relative to a designated reference particle. Harmonics not matching known particles in the Standard Model are assigned “theoretical” designations (“Th.”). Proton Harm.

Electron Harm.

Quark Harm.

Elec. (e), Elec. Neutrino (ν ν e) L2, ν2 (Th. Lepton, Neutrino) L3, ν3 (Th. Lepton, Neutrino) Muon (µ µ), Muon Neut. (ν νµ)

Stω = 1 2 4 6 8

Stω = 1/2 1 2 3 4

Stω = 1/14 1/7 2/7 3/7 4/7

L5, ν5 (Th. Lepton, Neutrino) Tau (ττ), Tau Neutrino (ν ντ) Up, Down quark: (uq), (dq) Strange quark (sq) Charm quark (cq) Bottom quark (bq) QB5 (Th. quark or Boson) QB6 (Th. quark or Boson) W Boson Z Boson Higgs Boson (H) (Th.) Top quark (tq)

10 12 14 28 42 56 70 84 98 112 126 140

5 6 7 14 21 28 35 42 49 56 63 70

5/7 6/7 1 2 3 4 5 6 7 8 9 10

Exis. and Th. Particles181 Proton (p), Neutron (n)

Table182 4.5

181

Although the newly predicted Leptons are within the kinetic range181 and therefore “should have been experimentally detected”, there are substantial explanations discussed in QE2,3. 182 Appears similarly as “Particle Summary Matrix 3.3” in QE3 and table (4.5) in QE2,4. www.deltagroupengineering.com

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Note: Exis. (Existing), Th. (Theoretical), Harm. (Harmonics), Elec. (Electron) and Neut, (Neutrino).

10.2 Periodic table of fundamental particles The harmonic relationship amongst fundamental particles allows for their hierarchical arrangement into a representation mimicking the periodic table of atomic elements. Assuming “QB5,6” to be Intermediate Vector Bosons (IVB’s), EGM conjectures that the periodic table of elementary particles may be constructed as follows:

Table 4.9, (i) *Where, “SC” denotes coupling strength at “1(GeV)”183. “James William Rohlf”, Modern Physics from α to Z, John Wiley & Sons, Inc. 1994. 183

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(ii) The values of “Stω” in table (4.9) utilize the proton as the reference particle. This is due to its Root-Mean-Square (RMS) charge radius and mass-energy being precisely known by physical measurement.

10.3 EGM vs. SMoC The following table displays a summary of the key mathematical facts determined via the EGM method in comparison to those obtained via the Standard Model of Cosmology (SMoC). Key Mathematical Fact Dark matter / energy required Max Cosmological Temp ≈ 1031(K) Big Bang Temperature = 0(K) Unification with particle physics Relationship between “H0” and “T0” “H0” and “T0” are calculable to high precision “H0” and “T0” were derived from particle physics Precise determination of distinct cosmological evolutionary phases Sign of the deceleration parameter is in agreement with expectation Prediction of “accelerated cosmological expansion” Table 2.17,

SMoC Yes Yes No No No No No

EGM No Yes Yes Yes Yes Yes Yes

No

Yes

No

Yes

No

Yes

where, “H0, T0, q0, Λ0” denote the present values of Hubble constant, CMBR184 temperature, deceleration parameter and cosmological constant respectively.

10.4 Cosmological evolution process Figure (4.23) depicts the change in the temperature of the early Universe with time following the Big Bang. The EGM calculation for peak temperature predicts a Big Bang temperature of 0(K) and peak temperature of ≈ 1031(K) immediately after the Big Bang.

184

Cosmic Microwave Background Radiation. www.deltagroupengineering.com

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Figure (4.26) depicts a Planck-like curve relationship between cosmological temperature and the Hubble constant. Increasing volumetric expansion results in vacuum energy diffusion; leading to a decrease in CMBR temperature. Figure (2.4) depicts the rate of change of the Hubble constant over time, resulting in a curve defining the “inflationary” and “expansive” epochs of cosmic history. The peak of the curve marks the point at which cosmic inflation ends and expansion begins. The maximum cosmological temperature185 line marks the instant at which the rate of change of the Hubble constant switches from negative to positive. The section of the curve above “0” marks a period of positive Hubble gradient186 and below “0” marks a period of negative Hubble gradient187. Thus, EGM calculations are congruent with the physical observation that the space-time manifold is currently undergoing accelerated expansion. It is important to note that this feature is presently beyond the abilities of the SMoC to produce. Figure (2.5) depicts the following: 1. Primordial Inflation (prior to the Big Bang): the Universe may be described as “inverted and non-physical” such that the interior of the Cosmos existed outside the exterior boundary “RBH” in accordance with the “Primordial Universe” model described in QE4 such that: i. The cosmological temperature “T” increases from negative infinity to zero. ii. The rate of change of the Hubble constant over time “dHdt” increases from negative infinity to “-Hα2”. iii. The magnitude of the Hubble constant188 “|H|” decreases from positive infinity to “Hα”. 2. Thermal Inflation: the period from the instant of the Big Bang to the instant of maximum cosmological temperature such that: iv. “T” increases from zero to its maximum value. v. “dHdt” increases from “-Hα2” to zero. 185

i.e. an average value. i.e. the Universe inflated and expanded at an accelerated rate; continuing to the present day. 187 The rate of inflation was negative until the point of maximum cosmological temperature; it then began to inflate and expand at a positive rate. 188 This terminology is an abbreviated reference to “the square-root of the magnitude of the rate of change of the Hubble constant over time”, as indicated by the graph. 186

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3.

vi. “|H|” decreases from “Hα” to zero. Hubble Expansion: the period from the maximum postprimordial189 “|H|” to the present day such that: vii. “T” decreases to its present day value. viii. “dHdt” decreases from its maximum physical value to its present day value. ix. “|H|” decreases from its maximum physical190 value to its present day value.

189

i.e. bounded by the Cosmological Expansion phase. In this context, “physical” refers to the “Hubble Expansion” phase because it is experimentally observed. 190

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Figure 4.23,

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Figure 4.26,

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Figure 2.4,

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Figure 2.5, www.deltagroupengineering.com

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Periodic Table of the Elements

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Image: Spiral Galaxy

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Leonardo da Vinci, translated by Irma Anne Richter, The Notebooks of Leonardo da Vinci. (Oxford University Press, 1998), pp.276. ii J. Robinson, An Introduction to Early Greek Philosophy. (Boston: Houghton Miffin, 1968), pp. 75. iii George Johnson, Fire in the Mind: Science, Faith and the Search for Order. (New York: Alfred A Knopf Publishers, 1995). iv Bruce J. Hunt, The Maxwellians. (Ithaca and London: Cornell University Press, 1991). v A. A. Michelson and E.W. Morley, “On the Relative Motion of the Earth and the Luminiferous Aether”. Philos. Mag. S.5, 24 (151), pp.449-463 (1887). vi H. B. G. Casimir, and D. Polder, “The Influence of Retardation on the London-van der Waals Forces”. Physical Review, Vol. 73, Issue 4, pp. 360-372 (1948). vii S. K. Lamoreaux, “Demonstration of the Casimir Force in the 0.6 to 6 µm Range” Physical Review Letters. 78, 5–8 (1997). viii U. Mohideen and Anushree Roy, “A Precision Measurement of the Casimir Force between 0.1 to 0.9 mm” Physical Review Letters, vol.81, (no.21), APS, (1998). ix Benedetto, G.; Gavioso, R.; Albo, P.; Lago, S.; Ripa, D.; Spagnolo, R. “Speed of Sound in Pure Water at Temperatures between 274 and 394(K) and at Pressures up to 90(MPa)” International Journal of Thermophysics, Volume 26, Number 6, November 2005 , pp. 16671680(14). x Albert Einstein “On a Heuristic Viewpoint Concerning the Production and Transformation of Light” Annalen der Physik, 17(1905), pp. 132-148. xi Pisin Chen, Stanford Linear Accelerator Center, June 06, 2000 “Violent Acceleration and the Event Horizon” - Press Release. http://home.slac.stanford.edu/pressreleases/2000/20000606.htm xii Vesselin Petkov, “Did 20th century physics have the means to reveal the nature of inertia and gravitation?” arXiv:physics/0012025 v3 17 (December, 2000). xiii Eugene Parker, "Dynamics of the Interplanetary Gas and Magnetic Fields". The Astrophysical Journal. (1958) 128: 664. xiv Pyotr Lebedev, "Untersuchungen über die Druckkräfte des Lichtes [The Experimental Study of the Pressure of Light]”, Annalen der Physik, 1901. xv Boyer, Timothy H., “The Classical Vacuum” Scientific American, www.deltagroupengineering.com

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pp. 70-78, (August 1985). xvi (i) Ford, Brian J., “The Controversy of Robert Brown and Brownian Movement” Biologist, 39 (3): 82-83, (June 1992). (ii) “Brownian Movement in Clarkia Pollen: A Reprise of the first Observations” The Microscope, 40 (4): 235-241, (1992). xvii Compton, Arthur H. “A Quantum Theory of the Scattering of Xrays by Light Elements” Physical Review, 21, 483 - 502 (1923). xviii B. Haisch & A. Rueda, “On the relation between a Zero-PointField-Induced inertial effect and the Einstein-de Broglie formula” physics Letters A, 268, 224, (2000). xix H. E. Puthoff, “Polarizable-Vacuum (PV) Approach to General Relativity” Foundations of physics, Vol. 32, No. 6, (June 2002). xx Philo, translated by F.H. Colson, Vol. IV: On the Migration of Abraham, (Cambridge Mass.: Loeb Classic Library, Harvard University Press, No. 261, 1932). xxi Malhotra, R., Holman, M., and Ito, T “Chaos and stability in the Solar system” PNAS, 98(22):12342-12343 (2001). xxii Planck, Max, "On the Law of Distribution of Energy in the Normal Spectrum". Annalen der Physik, vol. 4, p. 553 ff (1901). xxiii Lise Meitner & Otto Robert Frisch “Disintegration of Uranium by Neutrons: a New Type of Nuclear Reaction” Nature 143: 239-240. (1939). xxiv Sir Isaac Newton, Opticks. (Chicago: Encyclopedia Britannica [1955, c1952] Book III, Part I) p.520-521. xxv Marc G. Millis, “Emerging Possibilities for Space Propulsion Breakthroughs” Interstellar Propulsion Society Newsletter, Vol. I, No. 1, (July 1, 1995). xxvi Hetherington, N.S., Encyclopedia of Cosmology (Garland Publishing Inc. New York 1993), (articles on Big Bang Cosmology, and Origins of Primordial Nucleosynthesis). xxvii Sackmann, I.-Juliana; Arnold I. Boothroyd; Kathleen E. Kraemer (11 1993). "Our Sun. III. Present and Future". Astrophysical Journal 418: 457. xxviii Peter Coles, “Inside Inflation: After the Big Bang”. New Scientist, issue 2593 (March, 2007). xxix V. Rubin, W. K. Ford, Jr., "Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions," Astrophysical Journal 159: 379 (1970).

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