Shadowspdf

Please visit << http://home.comcast.net/~jeffocal/shadows_publisher/index.html >> to review Shadows in a easy to navigate Publisher 2000 page by page format or << http://home.comcast.net/~jeffocal/shadows.htm >> for a continuous html format linked internally to chapter web sites. Title: The "Shadows" of four spatial dimensions. A Proposal for the Unification of Relativity and Quantum Theory. Authors: Jeffrey O’Callaghan (Author) [email protected] IM The_imagineers, Juan Echaurren (Co-Author, Collaborator) [email protected], Christian Mills (Co-Author, Collaborator, Editor) [email protected], Stefan von Weber (Collaborator) [email protected], Tjipto Juwono (Collaborator). Introduction: Common sense sometimes gives a false indication of reality. As a result, "Shadows" of other truths go unnoticed. For example, many people of the fifteenth century believed the earth was flat, even though they could see a circular “Shadow” of the earth moving across the moon during a lunar eclipse. However, Christopher Columbus along with many educated people of that time realized this to be an indication that the earth might be spherical. He trusted both his intellect and his senses more than the conventional wisdom of the time and sailed to a new world of knowledge and understanding. Abstract: Relativity and Quantum theories have been the two most successful scientific theories of modern physics. However, attempts to unify them have been unsuccessful because they are built upon different foundations. Relativity is based on the geometry of space-time while Quantum Theory is based primarily on the spatial properties of momentum and position. However, "Shadows" demonstrates these two theories have a common foundation by redefining the abstract space-time geometry of Relativity in terms of the physical geometry of four spatial dimensions thereby allowing the concepts of Relativity to be directly defined in terms of the properties of momentum and position with respect to four spatial dimensions. This allows for the defining of the common mechanism responsible for both the quantum properties of mass and energy and the Relativistic properties of space and time. "Shadows" postulates a volume of space is composed of a continuous non-quantized “field” of mass and energy. "Shadows" will derive the quantum properties of mass and energy in terms of resonate "structures" formed in space by vibrations in a continuous non-quantized mass and energy components of space. The quantum properties of these resonate "structures" will be defined in terms of a dynamic interaction between a continuous non-quantized mass and energy components of space defined by the equation E=mc^2. "Shadows" will derive the quantum properties of gravity and the relativistic properties of space and time in terms of a physical "distortion" in a three-dimensional space manifold with respect to a fourth *spatial* dimension generated by the resonate structures “Shadows” postulates is responsible for the quantum properties of mass energy.

Redefining the physical structure of the universe in terms of the geometry of four spatial dimensions enables “Shadows” to define the common unifying mechanism responsible for both the relativistic and quantum properties of gravity, mass, energy, space, and time. Conclusion: "Shadows" demonstrates the power that changing one's perspective on the physical structure of the universe can have in helping humankind understand the mechanisms responsible for the physical laws and forces of nature. ***************** "I am enough of an artist to draw freely on my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination circles the world." Einstein "Intuitive thinkers have made many of the breakthroughs in science" Louis de Broglie IMAGINATIONS SEARCH IMAGINATIONS EXPLORE

"Shadows" Collaborators Christian Mills Adjunct professor of mathematics at Weber State University Research Papers Juan Echaurren Collaborating with the applied mathematics department of the European Space Agency University of Santiago of Chile (USACH) (1985 - 1988) University of Chile (1987) Mariscal Sucre University (1995 - 1997) Arturo Prat University (2001 - 2003) FUNDAMENTOS FISICOS Y MATEMATICOS PARA LA CONSTRUCCION DE UNA TEORIA ESTRICTAMENTE ANALITICA DE LA MATERIA. MATEMATHICAL CALCULATION FOR IMPACT CONDITIONS, EJECTION OF FRAGMENTS, ENERGY DISTRIBUTIONS AND GENERATION OF HYDROTHERMAL SYSTEMS IN ISIDIS PLANITIA /MARS Modelos matemáticos en formalismo cuántico para el seguimiento de riesgos asociados a actividades específicas y su aplicación al análisis y prevención de accidentes. Published in Ciencia al Dis Internacional Mi proposito es encontrar la relacion entre Isomorfismos y espacios fisicos tetradimensionales, que explicarian de que manera los riesgos fenomenologicos de que ocurra algun evento en el espacio fisico, se materializarian en forma de energia en diversos puntos del mismo, generando densidades de probabilidad que afectarian al movimiento y estructura de cualquier objeto masico

que interactue o coexista en determinadas dimensiones fisicas de un punto en el Universo. El efecto de estas funciones de onda se materializan tanto en las orbitas de los planetas como en las velocidades orbitales de sondas espaciales en el espacio profundo, afectadas tambien por la presencia masica de los planetas. (This is Shadows) Stefan von Weber Physicist Dr. rer. nat. Dr. sc. techn. University of Applied Sciences FH Furtwangen Department of Mechanical and Environmental Engineering COSMIC MEMBRANE THEORY OF GRAVITATION

Contents Shadows PDF format Shadows Publisher Abstract Collaborators Chapter One Chapter Two Chapter Three Chapter Four Chapter Five Chapter Six

A Universe of Four *Spatial* Dimensions The Causality of the Quantum properties of mass Electromagnetic Energy in terms of a Fourth *Spatial* Dimension The Photon a Particle or Wave? Bell's theory and the EPR Paradox Planck's constant and Heisenberg's uncertainty principle The spatial properties of Photons with respect to a Fourth *Spatial* Chapter Seven Dimension The relative masses of subatomic particles in terms of a Fourth Chapter Eight *Spatial* Dimension Chapter Nine Electrical Potential Energy with respect to Four Spatial Dimensions Chapter Ten A boundary between a Third and Fourth *Spatial* Dimensio Propagation of electromagnetic energy and with respect to a fourth Chapter Eleven *spatial*dimension Chapter Twelve Gravity and the Fourth Spatial Dimension Chapter Thirteen The Unit Electric Charge Chapter Fourteen A Link between Gravitational and Electrical forces Chapter Fifteen The “Relativity” of Four "Spatial" Dimensions Chapter Sixteen The "Relativity" of Quantum Mechanics Gravitational and Kinetic Energies Linked by a Fourth *Spatial* Chapter Seventeen Dimension The Principal of Equivalence, Inertia & Absolute Reference Frames Chapter Eighteen with respect to a Fourth *Spatial* Dimension The composition and structure of Quarks with respect to a Fourth Chapter Nineteen *Spatial* Dimension Chapter Twenty The Fundamental Quantum Particles Chapter Twenty-One The Origin of the Positron in terms of a Fourth *Spatial* Dimension Chapter Twenty-Two The Dimensional Mechanics of Four *Spatial* Dimensions Chapter Twenty-Three Experimental Verification of Shadows Chapter Twenty-Four Maxwell's equations in terms of a Fourth *Spatial* Dimension Chapter Twenty-Five Cosmology of a Fourth *Spatial* Dimension Conclusion

Chapter one A Universe of Four Spatial Dimensions Discussing the properties of a universe that consists of four *spatial* dimensions is not possible until we have an understanding of how matter and energy interact to generate the physical structure of those dimensions. Therefore, we will begin our discussion not by defining space but by defining the mechanisms and processes responsible for the dimensional properties of space. "Shadows" postulates a volume of space is composed of a continuous non-quantized “field” of mass and energy. It will be shown "vibrations" in a continuous non-quantized mass and energy component of space generate the physical structures associated with the dimensional properties of space. Additionally, in Chapter two, the quantum properties of space, mass and energy will be derived in terms of integral energies associated with resonant "structures" formed in space by "vibrations" in a continuous non-quantized mass and energy component of space. The formation of these resonant "structures" will be derived in terms of a dynamic balance between a continuous non-quantized mass and energy component of space defined by the equation E=mc^2. These resonant "structures" will be called a mattercule or "quantum mass unit of space". (The justification for using the equation of E=mc^2 to define the "vibrations" in a continuous nonquantized mass and energy component of space is based on the fact that it has been experimentally confirmed to define the physical relationship between mass and energy.) There are four types of fields associated with the continuous non-quantized mass and energy components of space, the positive and negative matterfields and the positive and negative energyfields. The combination of the matter and energy fields form matterenergy. In this paper the definitions of a matterfield, energyfield, and matterenergy component of space will be developed with respect to the geometric processes and mechanisms that governors their interaction. Many of the terms used in this paper will be defined in a similar manner. Most are familiar with three out of four of the fields that define the physical structure of the universe. Mass and the attractive forces of gravity are associated with a positive matterfield component of space while positive and negative electrical charges are associated with a positive and negative energyfield component of space. However, some may not be familiar with the field associated with a negative matterfield component of space. It will be shown latter this field is associated with the mass component of anti-particles. Additional it will be shown a negative matterfield component of space is not associated with anti-gravity. (The physical mechanism responsible for a negative matterfield component of space and the mass associated with the anti particle called the positron will be developed in Chapter twenty one.)

It will be demonstrated the attractive and repulsive properties of an electrical or energy field component of space are a result of the direction of a rotational spin of a matterfield component of space. It will also be shown the attractive forces associated with mass or positive matterfield component of space is generated by a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension . This "depression" is caused by a rotational spin of a matterfield and energy field component of space. While the forces associated with anti-particles or a negative matterfield component of space is generated by an opposite rotation of a matterfield component of space. The opposite rotation of the matterfield component of space causes an "elevation" in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Additionally it will be shown the energy associated with a positive and negative matterfield component of space interact oppositely to energy associated with an energyfield or electrical component of space. In other words, the energy associated with two similar energyfields or electrical charges will oppose each other; while the energy associated two similar matterfields or "gravity fields" will attract each other. Latter it will be shown the forces associated with each one of these individual fields is related to energy gradients generated in a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by a "rotational spin" of the matterfield component of space with respect to a fourth *spatial* dimension. These four fields interact to produce the physical framework of dimensional space. However, it should be remembered these four fields are generated out of only one matter and one energy field. In Chapter three, the transmission of a photon's energy will be derived in terms of a matterenergy "wave" on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension . It will be shown this matterenergy wave is generated by "vibrations" in a continuous non-quantized mass and energy field component of space. As mentioned earlier, Chapter two will derive the physical structure and volume of a mattercule or "quantum mass unit of space" in terms of resonant "structures" generated in space by a dynamic interaction in a continuous non-quantized mass or matterfield and energy or energyfield component of a volume of space. Therefore the quantum properties of a photon are a result of a resonant "structure" generated by a "standing" wave on a "surface" of a three-dimensions space manifold with respect to a fourth spatial dimension by a dynamic interaction in a continuous non-quantized mass or matterfield and energy or energyfield component of a volume of space. The energy of individual photons will be derived in terms of the velocity of "vibrations" or interactions in a matterfield and energyfield component of space that are responsible for producing a "standing" matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension. This indicates the kinetic energy associated with the matterfield or mass component of the matterenergy wave can be defined by the Newtonian equation for the Kinetic energy of an object or E=mv^2 where "E" = the magnitude of the energyfield and "m" = the magnitude of the matterfield component of a "standing" matterenergy wave.

However, because, as will be shown in Chapter three, the velocity of interactions of the mass and energy components of a matterenergy wave are constant and equal to the velocity of light, the equation for the Kinetic energy of the mass component of the matterenergy wave can be rewritten as E=mc^2 The equation E=mc^2 defines the energy of a photon in terms of the kinetic energy of a continuous non-quantized mass component of space because it defines the internal structure of a matterenergy wave responsible for the energy of a photon in terms of the Kinetic energy of a continuous non-quantized mass component of space. Another physical property of the matterenergy fields of space and a mattercule or "quantum mass unit of space" can be illustrated by comparing it to different forms of water in the air. Water vapor is difficult to detect with the eye because it is composed of relatively small particles, while the condensed particles of water vapor or fog is easier to detect visually because the particles are physically larger. The matterenergy fields of space have similar properties. In the "vapor" state, the matter and energy field components of space are difficult to detect because they are composed of a continuous non-quantized field of mass and energy and not particles. However, in the "condensed state" or the state where the resonant "structures" responsible for a "quantum mass unit of space" defined in Chapter two exist in a volume of space, the particles or quanta of matterenergy associated with these resonant structures, such as the photon, electron, and proton, are easier to detect because they are physical larger. For example, fog is composed of an aggregation of water vapor thereby making the particles of water vapor larger and easier to detect. Similarly, photons, electrons, and protons are composed of "aggregations" of the matterenergy fields of space thereby making these “particles” or “quanta” of matterenergy fields physically larger and easier to detect. “Shadows” postulates a three-dimensional volume of space is composed primarily of a positive matterenergy field. In Chapter two it will be shown that resonant "structures" formed in space by interactions in the matter and energy field components of space are responsible for the physical framework of all quantum particles. As was shown earlier these interactions in a matter and energy field component of space are defined by the equation E=m*c^2. Mass will be derived in Chapter twelve to be the result of a distortion in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension caused by energy gradients generated by a rotational "spin" of a matterfield component of space with respect to a fourth spatial dimension. In Chapter thirteen the polarity and magnitude of the positive and negative unit electric charge will be derived in terms of a distortion in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by energy gradients generated by a rotational "spin" of an energyfield component of space with respect to a fourth spatial dimension. Therefore, because all the forces of nature including the gravitational and electrical forces associated with charged and uncharged particles have properties associated with the matterenergy fields of space, any particle, mass or force introduced into a closed spatial system will cause a change in the resonant relationship between a matter and energy field component of

the volume of space contained in that closed spatial system. This will result in the force or energy associated with that particle, mass or force to become predominant in that volume of space. The water analogy can again be used to illustrate this property of the matterenergy fields of space. If a cold surface is introduced into a humid environment, water vapor will condense to form water droplets. An effect similar to this occurs in space. If an entity with a less positive matterenergy field, such as an electron, is introduced into the matterenergy fields of space, the force or energy associated with that matterenergy field will "condense" out of the “fabric” of space and become observable. In Chapter eight the mechanism responsible for the relative mass of a proton with respect to an electron will be developed in terms of a distortion in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension . The mass of a proton will be derived in terms of a distortion or “depression” in a “surface” of a three-dimensional space manifold with respect to the fourth "spatial" dimension. This "depression" is caused by energy gradients generated in a three-dimensional space manifold by a rotational spin of the matterfield component of space. (This curvature or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is analogous to the space-time curvature or "depression" in a space-time manifold that Einstein's General Theory of Relative postulates is responsible for the force of gravity.) While an electrons mass will be derived in terms of an “opposite” distortion or “elevation” in a “surface” of a three-dimensional space manifold with respect to the fourth "spatial" dimension This "elevation" is caused by energy gradients generated in three-dimensional space manifold by an oppositely rotating matterfield component of space with respect to the rotation associated with the mass of a proton. Additionally, the relative masses of a proton and electron will be defined in terms of the relative magnitude of distortions in a “surface” of a three-dimensional space manifold caused by the energy gradients associated with a rotation of a matterfield components of space. The “strong nuclear force" that "binds" a nucleus of an atom together can be derived in terms of the resonant "structures" defined in Chapter two responsible for the physical framework of all quantum particles and the gravitational attractive forces associated with the matterfield component of a proton. As mentioned earlier Chapter two will derive the internal stability of all particles is in terms of a resonant "structure" formed in space by "vibrational" interactions of a continuous non-quantized matter and energy field component of space. "Shadows" postulates the strong nuclear force is the result of the spatial separation between protons and neutrons in a nucleus becoming small enough so that they can share their resonant energies to form one large homogenous stable resonant "structure" or particle composed of a continuous non-quantized matter and energy field component of space. These larger stable resonant "structures" are called the nucleus of atoms. The presence of a neutron in the nucleus of atoms containing more than one proton is required to form a stable nucleonic "structure" because the added the attractive force of their matterfield

component is shared with the attractive forces associated with the matterfield component of a proton. This increases the total attractive forces associated with the matterfield component of a nucleus with respect to the repulsive force associated with the electrical forces of a nucleus because a neutron does not contribute to the repulsive electrical forces of a nucleus. This allows the particles in the nucleus to become spatially close enough so they can share their resonate energies and form a single stable resonant "structure" in space. (The internal structure, stability and electrical neutrality of a neutron will be derived in Chapter nineteen in terms of an interaction between the matter and energy field components of space and a three-dimensional space manifold with respect to a fourth *spatial* dimension .) This suggest a nucleus of an atom is not composed of individual protons and neutrons but of one homogenous resonant particle "structure" made up of a continuous non-quantized of the matter and energy field component of space. The stability of a nucleus would depend upon the physical size of the resonant structure associated with that nucleus. As a general rule a nucleus becomes more unstable as its size or diameter increases because the energy associated with its resonant "structure" is dispersed over a greater volume therefore making it harder to maintain a homogenous resonate "structure". Therefore, the ability of a nucleus to attract and "hold" additional subatomic particles will decrease as the spatial separation from the center of the nucleus increases because the "boundaries" of a resonate "structure" associated with a stable nucleus decrease as the spatial distance from the center of the nucleus increases. Any particle that was beyond a certain distance from the center of the nucleus would not be effected by the proton's and neutron's ability to share the resonate energies necessary to form stable resonant "structures" in the continuous non-quantized matter and energy field components of space and would not be absorbed by the nucleus. Therefore, any point in space that is beyond this distance will not be effected by the strong nuclear force. The exact composition of space now becomes relevant to the study. “Shadows” postulates space is made up, in part, of mass because it defines the physical structure of space in terms of a dynamic resonant relationship between a continuous non-quantized mass or matterfield component of a volume of space and a continuous non-quantized energy or energyfield component of a volume of space. Therefore, a volume of space must have properties associated with mass because is, in part, made up of mass. In other words, the space between objects with no subatomic particles present possesses properties associated with inertial mass. Following this logic, a question is presented: Why haven't the inertial properties of space been detected? Stepping back in history may shed light on the answer to this question. Many people of the fifteenth century did not realize the Earth was spherical because its curvature was small compared to their scope of their vision. However, the shadow of the earth on the moon during a lunar eclipse gave an opportunity to view the spherical shape of the earth from a distance. Similarly, the reason we have not yet detected the inertial properties of a volume of space is that their effects are small compared to our scope of our "vision".

There is however, “Shadows” that gives us an opportunity to "view" the inertial properties of a volume of space from a "distance" in terms of the red shift of spectral lines emanating from stars. Astronomers have noted that our universe appears to be expanding. This idea is based on the shifting of the spectral lines coming from stars called the red shift. One interpretation is that stars are moving away from the earth and the greater the distance a star is from the earth the faster it is moving away. This observation of light is similar to that of sound. The pitch of a train's whistle is lower when it is moving away and its velocity determines the difference in pitch. Astronomers have interpreted the red shift in a similar manner. The greater the shift towards the red end of the spectrum the faster the star is moving away from the earth. However, another explanation is possible. The frequency of spectral lines is an indication of the energy they posed at the point that they were generated. The frequency of light is also an indication of the energy it has at the point it is observed. Red light has less energy than blue light. If space did posses the properties “Shadows” associates with a continuous non-quantized mass component of space, light would dissipate energy while traveling through it. Therefore, each spectral line would lose energy due to the inertial properties of a continuous nonquantized mass component of a volume of space causing it to shift towards the red end of the spectrum. This indicates the magnitude of the red shift may not be entirely a result of the movement of stars away from us. Instead, a portion of the energy loss associated with the red shift may be the result of the inertial properties of space. However, a blue shift could still be observed in a stars spectrum if the velocity of a star moving in our direction imparted more energy to the spectral lines than was dissipated by the inertial properties of space it traveled through. If the inertial properties of space do dissipate a portion of the energy of spectral lines, then the assumption that the greater the distance a star is from us the faster it is moving away may not be valid. It may be because the greater a stars distance the greater the red shift would be because each spectral line would have more time to dissipate energy as it traveled through space. (The reason the inertial properties of a volume of space does not effect the velocity of light will be discussed latter in Chapter three.) This "Tired Light" concept of the energy loss associated with red shifting of photons by it's interaction with space has been dismissed by many because no Compton scattering is observed in red shifted photons. (Compton scattering would be the result of the interaction of the quantum properties of a photon with other quantum particles.) However, in Chapter three it will be shown the energy associated with photons is the result of interactions between the matter and energy field components internal to the mattercule or "quantum mass unit of space" defined in Chapter two.

Therefore, according to the mechanism defined by "Shadows" for the energy of a photon no Compton scattering will be observed in red shifted photons due their interaction with the matterfield component of space because the energy loss Shadows associates with the red shifting of photon is not the result of a interaction with other quantum particles. Instead, it is the result of a dynamic internal interaction between the continuous non-quantized matter and energy field components of space internal to the quantum particle called a photon. The Cosmological Principal that the universe should appear the same in all directions and the discovery by Penzias and Wilson of the uniformity of the Cosmic Background radiation in 1964 also supports the hypothesis that a portion of the energy loss associated with the red shift is a result of the "mass" or inertial components of a volume of three-dimensional space. Since the energy loss of light associated with inertial properties of a volume of space would be dependent on the distance it traveled, the universe would appear to be the same in all directions as long as one kept the distance of the observations constant. In addition, the uniformity of the magnitude Cosmic Background radiation caused by the energy loss due to the inertial properties of a volume of space will also be uniform because it to would be primarily depended on the distance that a photon has traveled through space. (The mechanism responsible for uniformity of magnitude Cosmic Background radiation will be developed in greater detail in Chapter twenty-five.) In addition, there is a direct experimental observation that supports the hypothesis that a volume of space has the properties “Shadows” associates with the continuous non-quantized mass or matterfield of space. Recently it has been determined by astronomers the universe must contain a large amounts of "dark matter" that cannot be seen directly but which we know exists because of the influence its gravitational mass has on the orbits of stars in galaxies. However, the physical properties associated with "Dark Matter" share many of the physical properties of a continuous non-quantized mass component of space. They are both composed of mass and therefore would generate gravitational energy, which would influence the orbits of stars in galaxies. Also because a continuous non-quantized mass component of space is is not particular it will not be visible. Therefore, a continuous non-quantized mass component of space will be "Dark" or invisible. This indicates the observed properties associated with dark matter may result of the existence of a continuous non-quantized mass component of space. Later in Chapter twenty-three, an experimental technique for the direct measurement of the microscopic physical properties associated with “dark matter” or inertial component of a volume of three-dimensional space will be proposed. Chapter Two The Quantum properties of mass and energy Return to Top It has been experimentally verified that energy in itself is not quantized because a photon can have any frequency and therefore any energy greater that zero or less than infinity. Additionally, the equation defining the relationship between mass and energy, E=m*c^2, also indicates that mass is completely convertible to one or more photons with energies greater than zero or less than infinity.

This is the bases for "Shadows" postulating in Chapter one that a volume of space is composed of a continuous non-quantized “field” of mass and energy. However, it will be shown the quantum properties of mass and the quantized energy of specific photons is related to resonant "structures" formed in a three-dimensional space manifold with respect to a fourth spatial dimension by "vibrations" in a continuous non-quantized mass or matterfield and energy or energyfield component of space. These resonant "structures" will be called a mattercule or "quantum mass unit of space". First we will define the mechanism responsible for generating the resonant "structures" associated with a "quantum mass unit of space" and then mathematically derive the density of the continuous non-quantized mass and energy components of space in terms of Planck's Length. In Chapter one an analogy involving the formation of a water particle in the earth's atmosphere was used to define the formation of a quantum particle in a three-dimensional space manifold with respect to a fourth spatial dimension. Water vapor in the atmosphere condenses to create particles of fog. This was shown to be analogous to a continuous non-quantized mass component of space "condensing" in a three-dimensional space manifold to form a resonant "structure" responsible for generating a "quantum mass unit of space" or particle in three-dimensional space. However, space also posses another physical property associated with water. Water is made up of discrete or "quantum" units of atoms of oxygen and hydrogen called molecules, while space is made up of "discrete" or quantum units of matter and energy "Shadows" calls a mattercule or "quantum mass unit of space". A water molecule is a result of "resonant" structures formed by the interactions of the atoms of hydrogen and oxygen. However, a "quantum mass unit of space" is the result of a resonant "structure" formed in space by interactions of a continuous non-quantized mass or matterfield and energy or energyfield components of space. A "quantum mass unit of space" is defined as the fundamental quantum unit of mass and energy. It is composed of a resonant "structure" formed in a matterenergy field of space. The sum of the energies associated with a continuous non-quantized matter and energy field component of space is identical and constant for all "quantum mass units of space" or quantum particles of the same type. This is based, in part, on the law of conservation of mass and energy which states the sum of the mass and energy components of a closed system must be conserved. As mentioned earlier "Shadows" postulates space is composed of a continuous non-quantized field of mass and energy and the quantum properties of mass and energy are the result of a resonant "structure" formed in a three-dimensional space manifold with respect to a fourth spatial dimension by the interactions or "vibrations" in a continuous non-quantized mass or matterfield and energy or energyfield component of space. The "vibrational" interactions of the continuous non-quantized mass and energy components of space responsible for the resonate "structure" of a quantum particle occur in a closed spatial system. Therefore. because these "vibrations" are "supported" by a continuous non-quantized mass component of space being "converted" to a continuous non-quantized energy component

space and a continuous non-quantized energy component space being "converted" to a continuous non-quantized mass component of space in the closed spatial system that defines a quantum particle, the law of conservation of mass / energy indicates the sum of the mass and energy components of these resonate "structures" must remain constant. The inertial properties of the continuous non-quantized mass component of space define the classical resonant "structure" of a "quantum mass unit of space" and all other quantum particles. In a classically resonating mechanical system the inertial properties of a mass interacts or resonates in a dynamic manner with the energy of a given system to define the volume and energy configurations of that system. Similarly the inertial properties of a continuous non-quantized mass component of space would interact or resonant in a dynamic manner with a continuous non-quantized energy component of space to define the volume and energy configurations of a "quantum mass unit of space" or quantum particles. The "vibrations" in a continuous non-quantized mass and energy components of space responsible for establishing the resonant a structure "Shadows" associates with a quantum particle can be understood by comparing it to the vibrations associated with a resonate or "standing" wave on the surface of water. The trough of a "resonant" or standing wave on water displaces the vertical volume of water occupied by the water with air. The volume of air represents the energy associated with the weight of the displace water. Summarily the peak of the "standing" wave displaces the air above the surface of the water with water. This displaced air represents the volume of air associated with the energy of that water. The "vibrations" in a continuous non-quantized mass and energy field component of space associated with a resonant "structures" of a "quantum mass unit of space" establishes a resonate or "standing" wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. In Chapter Ten Shadows will derive all forms of energy in terms of a "displacement" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. The trough of a resonant or "standing" matterenergy wave on a "surface" of a three-dimensional space manifold would "displace" the mass component of space "below" a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension with energy. The fourth dimensional "volume" associated with this trough would define the energy associated with the displaced mass component of space. The peak of a resonant or "standing" matterenergy wave on "surface" of a three-dimensional space manifold would "displace" the mass component of space "above" a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension with energy. The mass component of space that would be "displaced" "below" a "surface" of a three-dimensional space manifold defines the mass associated with the displaced energy component of space. These dynamic "vibrations" in a continuous non-quantized mass and energy field components of space are responsible for the resonant structures "Shadows" associates with the quantum properties of mass and energy. "Shadows" will now define the "equivalent spatial length" of the energy component of a "quantum mass unit of space".

Chapter three will derive the magnitude of a photon's energy in terms of a dynamic relationship between a continuous non-quantized mass and energy component of space associated with a matterenergy wave on a "surface" of a three dimensional space manifold with respect to a fourth spatial dimension. The relationship will be defined by the equation E=mc^2 where "E" = the magnitude of the energyfield component and "m" = the magnitude of the mass component of a matterenergy wave. However, the energy of the quantum particle called a photon moves at the velocity of light "c" through space. Therefore, the velocity of light "c" must be factored out of the equation E=mc^2 define the energy of a photon when defining internal resonant "vibrations" of the mass and energy field components of other "quantum mass units of space" or quantum particle that are "stationary" because with respect to an observer. This indicates the magnitude of the internal "vibrations" or interactions of the energyfield component space with respect to the matterfield component of space would be defined by the equation E=mc. The term "c" in the equation of E=mc also defines the ratio of the spatial magnitude of the nonquantized mass component of space with respect to the spatial magnitude of energy component of space internal to a resonant "structure" of a "stationary " "quantum mass unit of space". This is because "E" defines the magnitude of a continuous non-quantized energyfield component of space in terms of the spatial properties of a continuous non-quantized mass component of space. On page 169 of John A Wheeler's book, "At Home in the Universe" he defines the fundamental length of a quantum particle to be universally constant and unchanging. "There is only one truly fundamental length in nature a length free of all reference to the dimensions and rate of revolution of the planet on which we happen to live, free of any appeal to the complex properties of any solid or gas: free of every reference to the mysterious properties of any elementary particle: what we call today the Planck length, L=(hG/C^3)1/2= 1.6X10^-33 cm And what we identify with the characteristic scale of quantum fluctuations in the geometry of space". This suggests the minimum "spatial length" associated with a fundamental resonant "vibration" in a continuous non-quantized mass and energy components of space associated with a "quantum mass unit of space" is also constant and equal to Planck's length. In Chapter three the magnitude of the resonant "vibrations" in the mass and energy components of space responsible for a photon's energy will be derived in terms of the equation E=hf. Where “E” equals the energy of the photon “h” is Planck’s constant (6.547 X 10^-27 erg sec) and “f” is the frequency of the photon. In classical physics the energy associated with the vibrations in a resonant system is, in part, directly related to the energy associated with the movement or mv^2 of a mass in that system. Therefore, if magnitude of the internal "vibrations" of a continuous non-quantized mass and energy components space are responsible for the quantum fluctuations in space mentioned in John A Wheeler's book, "At Home in the Universe" they should be definable in terms of the energy associated with the velocity of the internal resonant "vibrations" of the continuous non-quantized mass and energy field components of a "quantum mass unit of space". Because Chapter three derived "vibrations" in the continuous non-quantized mass and energy components associated

with a resonant "structure" of a "quantum mass unit of space" as the result of a "movement" or "conversion" of the continuous non-quantized mass component of space to energy component of space. This indicates that one can substitute mc^2 into the equation for the energy of a photon because Chapter three showed that velocity of the "movement" of the continuous non-quantized mass component of space towards the continuous non-quantized energy component of space is constant and equal to "c". Therefore the equation E=hf rewritten in terms of a continuous nonquantized mass component (m) in space would be mc^2=hf. However Planck's constant is defined in terms of a photon which is moving at the velocity of light with respect to a stationary "quantum mass unit of space" Therefore one must factor the velocity of light out of Planck's constant to make it valid for a "quantum mass unit of space" or a quantum fluctuation that is stationary with respect to an observer. This indicates the equation mc^2=(h/c)f would define the magnitude of the "vibrations" or fluctuations in a continuous non-quantized mass and energy components of space responsible for the energy of quantum fluctuations in space. However the value of Planck's length 1.6X10^-33 cm is the spatial length associated with Planck's constant with respect to a stationary observer. Therefore the above equation can be rewritten, using the value for Planck's length and solving for "m", as m=(1.6X10^-33 cm/c^3)f . The minimum possible quantum fluctuation in space would have a frequency of one. Therefore the density of the combined continuous non-quantized mass and energy components of space in terms of the mass component of quantum fluctuations in a cubic light year of space would be on the order of m=1.6X10^-33 cm. m=1.6X10^-33 cm/c^3 gives the relative density of a mass component of a quantum fluctuation in space per cubic light year of space terms of the overall length of the mass and energy components of a quantum fluctuation. Because of the dynamic nature of the interaction between the continuous non-quantized mass and energy components of a quantum fluctuation, this density will consist of the length associated with a continuous non-quantized mass component of space and the "equivalent spatial length", defined earlier, of an energy component of a quantum fluctuation. Chapter Three Electromagnetic Energy and Four Spatial Dimensions Return to Top The propagation of electromagnetic energy is the result of a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of mass and energy. Chapter two derived the quantum properties of mass and energy in terms of resonant "structures" formed in space by "vibrations" in a continuous non-quantized mass or matterfield and energy or energyfield components of space defined by the equation E=mc^2 were "E" = the magnitude of the energyfield component of space and "m" = the magnitude of the matterfield component of

space and "c" = the velocity of light. These resonant "structures" are called a "mattercule" or "quantum mass unit of space". This chapter will derive the wave properties of electromagnetic energy in terms of resonant "structures" formed in space by "vibrations" in a continuous non-quantized mass or matterfield and energyfield components of space. Later, in Chapter four, the same mechanism used to define the wave properties of electromagnetic energy will be used to define the quantized energy associated with individual photons. The propagation of electromagnetic energy can be derived in terms of a coupling from one "quantum mass unit of space" to the next of "vibrations" in a continuous non-quantized mass and energy component of space. These "vibrations" generate a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. These "vibrations" in a continuous non-quantized matter and energy field components of space can be compared to vibrations associated with a standing wave on a surface of water. The trough of a water wave displaces the vertical volume of water occupied by the water with air. The displaced volume of the air represents the energy associated with the weight of the displace water and the peak of a water wave displaces the air above the surface of the water with water. The displaced air represents the volume associated with the energy of the displaced water. The "vibrations" in the continuous non-quantized mass and energy field components of space associated with a matterenergy wave establishes a resonate or "standing" wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension which is similar to standing wave on water. The trough of a matterenergy wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension "displaces" the mass component of space "below" the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension with energy. The four dimensional "volume" associated with the trough defines the energy associated with the displaced mass component of space. The peak of a "standing" matterenergy "displaces" the energy component of space "above" the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension with a mass component of space. The mass component of space that is "displace" "above" the "surface" of the three-dimensional space manifold defines the mass associated with the displaced energy component of space. Chapter Ten will derive all forms of energy in terms of a "displacement" in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension. Therefore displacements in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension generated by a matterenergy wave will transmit energy on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. These displacements in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension generated by a matterenergy wave are responsible for the propagation of electromagnetic energy. (Later, in Chapter twenty-four, the mechanisms responsible for the structure of Maxwell’s equations defining electromagnetic energy will be derived in terms of a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.)

The speed of light in a vacuum is constant because, as was shown in Chapter two, the ratio of the magnitude of "vibrations" a continuous non-quantized mass and energy components of a "quantum mass unit of space" is constant. In Chapter twelve a direct relationship will be derived between the density of a medium and number of "quantum mass unit of space" contained in that medium. As was mentioned earlier electromagnetic energy is propagated through space by the coupling of " vibrations" in the continuous non-quantized mass and energy components of space from one "quantum mass unit of space" to the next. Therefore, the velocity of light would be greatest in a vacuum where the density of the "quantum mass units of space" is smallest because matterenergy wave responsible for propagating a photon's would have to interact with fewer "quantum mass unit of space". The reason the velocity of light is independent of the relative velocity of an observer through space is because, as Chapter eighteen indicates, there does not exist an absolute reference frame by which its velocity can be measured. "Shadows" will now derive the mechanism responsible for the propagation of electromagnetic energy from the equation defining a photon's energy E=h*f. Chapter one showed the relative magnitude of resonate "vibrations" in a continuous non-quantized energyfield and matterfield components of space internal to a "quantum mass unit of space" was defined by the equation E=mc^2 were "E" The magnitude of the energyfield component of the vibrations and "m" = the magnitude of the matterfield component of the vibrations and "c" = the velocity of light. However, as mentioned earlier, the propagation of a photon's energy is a result of a matterenergy wave generated on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by a coupling from one "quantum mass unit of space" to the next of the resonant "vibrations" in the matter and energy field components of a "quantum mass unit of space". This indicates the term "m*c^2" could be substituted for "h" in the equation E=h*f for a photon's energy because it defines the internal mass and energy relationships of a matterenergy wave responsible for the propagation of a photon's energy. This suggests the equation of E=mc^2f could be used to define the physical mechanism responsible for the propagation of electromagnetic energy in terms of a matterenergy wave composed of the continuous non-quantized matter and energy field components of space. "Shadows" will shown the energy associated with a photon is the result of *spatial* contractions generated in a three-dimensional space manifold generated by a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. The magnitude of these *spatial* contractions will be derived in terms of the frequency of a "matterenergy wave" and the experimentally verified relationship between mass and energy defined by the equation E=mc^2. However, to accomplish this the equation given earlier of E=m*c^2*f defining the energy of a photon will have to be modified to E=m*c^2*(v/F). This is because the energy of a photon will be derived in terms of a ratio of a *spatial* contraction in a length of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with the passage of the matterenergy wave with respect to the length of a three-

dimensional space manifold with respect to a fourth *spatial* dimension with no matterenergy wave present. The term (v/F) in the equation E=m*c^2*(v/F) defines the ratio of a shortening of the length of a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the passage of a matterenergy wave" "Shadows" associates with a photon's energy. "v" equals the *spatial* "distance" between two points on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension with NO energy traveling thought it minus the *spatial* "distance" between two points separated by one wavelength in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension with energy traveling thought it, while "F" equals the length of a three-dimensional space manifold with respect to a fourth *spatial* dimension with a matterenergy wave of "0" frequency passing through it. Therefore, the dimensionless term (v/F) defines the ratio of the shortening of the length of a threedimensional space manifold with respect to a fourth *spatial* dimension caused by the passage of the matterenergy wave responsible for the propagation of the energy of a photon. This shortening in a "surface" of a three-dimensional space manifold is analogous to how a wave on the two-dimensional surface of water shortens the two-dimensional distance between two water molecules on the surface of the water. It should be remembered that when the term derived or derivation is used in this paper it does not refer to a mathematical derivation but to geometrically explaining the physical mechanism responsible for the mathematical equations. However, before we begin our discussion regarding the energy of a photon we should first examine why the equation E=m*c^2 defines the energy in a continuous non-quantized matter and energy field components of space which is moving at velocity of light with respect to a "quantum mass unit of space" that is "stationary" with respect to an observer. Next, we will derive the equation defining the energy associated with "vibrations" in a continuous non-quantized matter and energy field components that are "stationary" with respect to a "quantum mass unit of space". It has been experimentally verified by nuclear explosions the equation E=m*c^2 represents the total amount of "dynamic" energy released by a kilogram-meter of mass that is radiated thought space at the speed of light. The mechanism defining a kilogram-meter of mass a will not be developed until Chapter twelve. However, it will be shown that mass is the result of a "curvature" in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension. This "curvature" shortens the three-dimensional distance on a three-dimensional space manifold with respect to a fourth *spatial* dimension because the "chord" of the "arc" caused by this "curvature" is shorter than the "arc" itself. Therefore, a kilogram-meter of mass would be defined as the length of a "chord" in a three-dimensional space manifold caused by a four-dimensional "curvature" in the threedimensional space manifold associated with a kilogram of mass. Chapter twelve will show when mass is converted to energy the "curvature" in a surface of a three-dimensional space manifold with respect to a fourth *spatial* dimension is decreased, thereby increasing the physical length between two points on the surface of a three-dimensional space manifold with respect to a fourth spatial dimension in proportion to the quantity of mass that was converted to energy. This indicates a portion of the energy associated with mass to energy conversions is physically contained internal to the mass of an object, while a portion is contained in a physical "curvature" in a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the mass of the object.

In other words, the lengthening of space at the speed of light contributes to the total energy associated with mass to energy conversions defined by the equation E=m*c^2. Therefore the equation E=m*c^2 defines a “dynamic” component of the energy associated with "vibrations" in the mass and energy field component of a "quantum mass unit of space" when energy is "moving" at the speed of light with respect to the space and the "quantum mass unit of space". As mentioned earlier, the equation for the propagation of a photon E=h*f can be redefined in terms of the resonant properties of the matter and energy fields components of a photon to be equal E=m*c^2*(v/F). However, it was shown earlier that the propagation of a photon's energy was the result of the coupling of the magnitude of the internal resonant energies of one from one "quantum mass unit of space" to the next at the speed of light. Since the derivation of the energy of a photon will be based on the internal dynamics of the resonant "vibrations" in the matter and energy field components of a "quantum mass unit of space" which is not moving with respect to space the velocity of light "c" must be factored out of the equation E=m*c^2*(v/F). This indicates the equation for the energy of electromagnetic radiation with respect to the magnitude of the internal resonant "vibrations" in the continuous non-quantized matter and energy field components of a "quantum mass unit of space" would be E=m*c*(v/F). To this point these discussions have shown resonant "vibrations" in the matter and energy field components of a "quantum mass unit of space" and a photon defined by the equation E=m*c^2*(v/F) are responsible for propagation of a photon's energy. The mechanism responsible for the propagation of electromagnetic energy will now be derived from the relationship define by E=m*c^2*(v/F) and the experimentally verified relationship between mass and energy E=m*c^2 . As mentioned earlier the equation for the energy of a photon E=h*f can be redefined in terms of a magnitude of vibrations in the matter and energy field components of a "quantum mass unit of space" to be equal E=m*c^2*(v/F). However, the derivation of the energy of a photon will be based on the magnitude of the internal resonant "vibrations" in the mass and energy components of a "quantum mass unit of space" which is not moving at the speed of light with respect space. Therefore, the velocity "c" must be factored out of the equation E=m*c^2*(v/F). This indicates the equation for the energy of electromagnetic radiation with respect to the internal dynamics of a "quantum mass unit of space" would be E=m*c*(v/F). It is the *spatial* contractions of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the internal interactions of a continuous non-quantized matter and energy field components of space defined by the equation E=m*c*(v/F) that is responsible for a photon's energy. As mentioned earlier “Shadows” postulates the energy of electromagnetic radiation is propagated by a matterenergy wave on a three-dimensional space manifold with respect to a fourth *spatial* dimension. This matterenergy wave and a photon's energy is propagated by the coupling of the internal "vibrations" of the continuous non-quantized mass and energy components of the "quantum mass unit of space".

The shortening effect this matterenergy wave has on a three-dimensional space manifold with respect to a fourth *spatial* dimension is responsible for the energy of a photon. (As mentioned earlier, this effect is similar to how a wave on the two-dimensional surface of water shortens the two-dimensional distance between water molecules on the surface of the water.) The wavelength of a matterenergy wave associated with a "quantum mass unit of space" of a photon is inversely proportional to its frequency and therefore the magnitude of the energy associated with a physical "shortening" in a "surface" of of a three-dimensional space manifold with respect to a fourth *spatial* dimension would be directly proportional to the frequency. This "shortening" of a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is quantified by the equation E=m*c*(v/F) or E=m*c*(Mr-Mc)/F). The term (Mr-Mc)/F) in the equation E=m*c*(Mr-Mc)/F) defines the relative magnitude of the "shortening" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension in terms of the frequency of matterenergy wave responsible for a photon's energy. This is because the term "Mr" represents the *spatial* "distance" between two points in on a threedimensional space manifold with respect to a fourth *spatial* dimension with NO matterenergy wave traveling thought it and the term "Mc" represents the *spatial* "distance" two points occupy on a three-dimensional space manifold with respect to a fourth *spatial* dimension with a matterenergy wave associated with a photon moving through it and "F" equals the length of a three-dimensional space manifold with respect to a fourth *spatial* dimension with a matterenergy wave of "0" frequency moving through it. Therefore, the dimensionless term (v/F) or (Mr-Mc)/F) defines the relative "shortening" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by the passage of a matterenergy wave responsible for a photon's energy. This indicates the energy of a photon is a result of a releasing of energy stored in space by the physical shortening of a length of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the passage of a matterenergy wave. The finial equation defining the energy of a photon would be E=m*c*c*(Mr-Mc)/F) or E=mc^2*(MrMc)/F) because energy of a photon is moving at the speed of light "c" with respect to space and the internal dynamics of a "quantum mass unit of space". The equations of E=hf and E=mc^2*(Mr-Mc)/F) define the mass "m" of the matterfield component of the "quantum mass unit of space" in terms of Planck's constant "h" and the speed of light. Solving these two equation simultaneously yields the equation h=m*c^2 or M=h/c^2, where "M" equal mass or the matterfield component of the "quantum mass unit of space". This defines the wave properties of electromagnetic energy in terms of the resonant vibrations defined in Chapter two between the matter and energy field components of the "quantum mass unit of space" or the "quantum unit of space". Chapter Four The Photon a Particle or Wave? Return to Top Why does a photon behave at times like a particle and at other times like a wave? The answer to this question can be found in a mechanism that defines both the particle and wave properties of a photon in terms of a resonant "structure" generated by a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension.

Chapter one postulated three-dimensional space is composed of a continuous non-quantized “field” of mass and energy. Chapter two define the quantum or "particle" properties of mass and energy in terms of resonant "structures" formed in a three-dimensional space manifold with respect to a fourth spatial dimension by "vibrations" in a continuous non-quantized mass or matterfield and energy or energyfield component of space. Chapter three derived the wave properties of a photon in terms of a quantized matterenergy wave on a "surface" of a three dimensional space manifold with respect to a fourth spatial dimension generated by "vibrations" in a continuous non-quantized mass and energy field component of space. The quantum or "particle" properties of this matterenergy wave are related to a quantized resonant "vibration" in the continuous non-quantized mass and energy component of space, defined in Chapter two, which are responsible and the quantum or particle properties of mass and energy. Additionally, Chapter three showed a photon posses a "spatial" component which is related to a physical "shortening" of the "distance" between two points on a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the passage of a matterenergy wave responsible for its propagation. (The mechanism defining a physical shortening of a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by a matterenergy wave can be found in Chapter three however, it is analogous to how a wave on the two-dimensional surface of water shortens the two-dimensional distance between water molecules on the surface of the water.) Therefore, Chapters two and three define the wave and particle properties of individual photons in terms a common mechanism related to a matterenergy wave on the "surface" of a threedimensional space manifold with respect to a fourth spatial dimension The unique energies associated with the resonant or "particle" properties of a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension associated with a photon are demonstrated, in part, by the photoelectric effect. This effect is observed when a photo multiplier is used to count individual electrons as they are jarred or ejected from the surface of a metal by light. With the appropriate equipment, one can count the electrons as the photons of light eject them form the metal surface. The flow of electrons from the surface of the metal is observed to begin as soon as the light is turned on and reducing the intensity of the impinging light beam does not reduce the velocity or energy of the ejected electrons, however it does reduce the numbers that were ejected. This supports the quantum theory of electromagnetic energy because wave theory predicts delayed emissions of electrons. In addition, it was observed that varying the intensity of the light does not change the velocity of the electrons ejected from the metal surface but only the number. Einstein based his quantum theory electromagnetic radiation in part on these photoelectric observations. He realized these observations could only be explained by assuming photons consist of discrete "packets" or quanta of energy that is depended on their frequency. The reason delayed emission is not observed in the photoelectric effect is because as Chapters two and three indicated the energy of individual photons was the result of individual quantized resonant "structures" formed on a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension by the passage of the matterenergy wave responsible for the propagation of a photon. As was shown in Chapter three a matterenergy wave on the "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension generates a resonate "structure" or "standing wave" in a continuous non-quantized mass and energy component of space. The

energy of a resonant "structure" of a specific photon would be directly dependent on the frequency of the "standing" matterenergy responsible for its propagation. If the energy of a "standing wave" associated with a resonate "structure" of a photon of a given frequency is sufficient it will instantly eject an individual electron off a photoelectric surface and the flow of electrons will begin immediately. However, If the energy of the "standing wave" associated with the resonate "structure" of a photon is not sufficient to eject an electron off a photoelectric surface, no electrons will flow from the surface no matter how bright the light or how many photons of that frequency strike the surface. The velocity of an electron leaving a photoelectric surface is not effected by the intensity of the light because varying the intensity of the light will only cause an increase or decrease in the number of photons of a specific frequency striking the photoelectric surface. Since the energy of a "standing wave" associated with a photon of a given frequency is identical, the energy of electrons ejected off the surface of a photoelectric material by photons with identical frequencies will also be identical. However, increasing or decreasing the intensity of the light striking the photoelectric surface will increase or decrease in the number of elections ejected from the surface because the number of photons and or "standing" matterenergy waves with sufficient energy to eject electrons from the surface will increase or decrease. Therefore, the quantum or "particle" properties photon associated with the photoelectric effect can be explained in terms of a resonate "structure" generated by a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension. However, light also posses the non-quantum properties of a wave. Thomas Young demonstrated this in an experiment using a light source in front of a screen containing two slits. Each of the slits could be individual covered. On the other side of screen was a wall against which the light coming through the slits could shine. When a very dim light was shined on the screen with one hole covered, the light impacts the wall in a line between the source and hole in the screen. However, when both holes are open the light impacts the wall generating an interference pattern that is characteristic of a wave. This interference pattern is generated even when a very dim light consisting of series of single photons are allowed to pass thought a screen with two slits. Additionally when a device was used to determine which silt the individual photons passed thought the interference disappeared. This indicates that act of measuring which silt a photon passes result in destroying the interference pattern. This appears to contradict the quantum properties of light because a series of individual photons can generate an interference pattern associated with a wave when passing thought a screen with two slits. Therefore, each individual photon or quanta of light also must posses the properties associated with a wave. The wave properties of individual photons are due to the spatial component of the matterenergy wave associated with a photon. As was mentioned earlier Chapter three showed that a photon's energy has a spatial component which is related a physical shortening of a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the passage of a matterenergy wave responsible for the propagation of a photon's energy.

When a single photon passes through a screen with a single slit, the "spatial length component" of a photon can only be transmitted along velocity vector therefore, the direction of the photon will not be altered. The photon will strike the screen on straight line between the source and hole in the screen. However, a “torque” will be generated on a single photon if it is allowed to pass though one slit in a screen with two opened slits because the "spatial length component" associated with a photon's energy can simultaneously pass or be transmitted through the two spatially separated slits in the screen. This will generate a torque on the direction of a photon after passing through the silts in the screen because of the different spatial path lengths between the two slits. Additionally, the direction of this “torque” will be dependent on the physical orientation of the length component of a photon's energy with respect to the two slits at the time the photon passed through them. Because a photon is transmitted on the "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension by a matterenergy wave the orientation of its spatial length component will vary sinusoidally with respect to time, the direction of this “torque” and therefore the direction of the photon as it moves through the two slits will vary sinusoidally with respect to time. Therefore, a series of single individual photons passing through a screen with two slits will generate a interference pattern on the screen because the torque generated by the sinusoidal varying direction of quantized "spatial length component" of the matterenergy wave will cause a sinusoidal variation in the direction of each photon that transverses the screen. This is the mechanism responsible for the wave properties of individual photons as observed in the Thomas Young experiment. However, when attempts are made to measure which slit a photon passed through it behaves like a particle because interference pattern disappears . This is because attempts to make spatial measurements regarding which silt a photon passes though results in changing the spatial component of the "standing" matterenergy wave of a photon as it passes thought the silts so that the spatial component will no longer resonant with "standing" matterenergy wave associated with it's energy component. This will result in the collapse of the wave function associated with the resonate "particle structure" of that photon and cause the disappearance of the interference pattern that is observed when no attempt is made to determine which slit the photon passed through. Defining the propagation of a photon in terms of the physical properties of a matterenergy wave on a "surface" of a three dimensional space manifold with respect to a fourth spatial dimension provides the ability to define a common physical mechanism responsible for how and why a photon can behave at times like a particle and at other times like a wave. It will be demonstrated in Chapter sixteen that this mechanism also provides a physical link between the microscopic quantum mechanical world of probability functions and macroscopic physical world of relativistic space. Chapter Five Bell's Theorem and the EPR paradox Return to Top Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of matter and energy.

In Chapter two the quantum properties of matter and energy were derived in terms of a resonant "structure" formed in space by "vibrations" in a continuous non-quantized mass or matterfield and energy or energyfield components of space. These resonant "structures" are called a mattercule or "quantum mass unit of space". Chapter three defined the transmission of all forms of energy in terms of a matterenergy wave on a "surface" of a three-dimensional space with respect to a fourth spatial dimension. This matterenergy wave is generated by coupling of "vibrations" in a continuous non-quantized matter and energy field component of space from one "quantum mass unit of space" to the next. It will be shown a quantized spatial property associated with "vibrations" in a continuous nonquantized matter and energyfield component of space are responsible for the validity of Bell's theorem and the EPR Paradox. Tjipto Juwono contributed the following explanation of the EPR paradox and John Bell's response to it. "In 1935, Einstein co-authored a paper which was intended to show that Quantum Mechanics could not be a complete theory of nature. The first thing to notice is that Einstein was not trying to disprove Quantum Mechanics in any way. In fact, he was well aware of its power to predict the outcomes of various experiments. What he was trying to show was that Quantum Mechanics could not be a complete theory of nature and that some other theory would have to be invoked in order to fully describe nature. The argument begins by assuming that there are two systems, A and B (which might be two free particles), whose wave functions are known. Then, if A and B interact for a short period of time, one can determine the wave function which results after this interaction via the Schrödinger equation or some other Quantum Mechanical equation of state. Now, let us assume that A and B move far apart, so far apart that they can no longer interact in any fashion. In other words, A and B have moved outside of each other's light cones and therefore are spacelike separated. With this situation in mind, Einstein asked the question: what happens if one makes a measurement on system A? Say, for example, one measures the momentum value for system A. Then, using the conservation of momentum and our knowledge of the system before the interaction, one can infer the momentum of system B. Thus, by making a momentum measurement of A, one can also measure the momentum of B. Recall now that A and B are spacelike separated, and thus they cannot communicate in any way. This separation means that B must have had the inferred value of momentum not only in the instant after one makes a measurement at A, but also in the few moments before the measurement was made. If, on the other hand, it were the case that the measurement at A had somehow caused B to enter into a particular momentum state, then there would need to be a way for A to signal B and tell it that a measurement took place. However, the two systems cannot communicate in any way! If one examines the wave function at the moment just before the measurement at A is made, one finds that there is no certainty as to the momentum of B because the combined system is in a superposition of multiple momentum eigenstates of A and B. So, even though system B must be in a definite state before the measurement at A takes place, the wave function description of this system cannot tell us what that momentum is! Therefore, since system B has a definite momentum and since Quantum Mechanics cannot predict this momentum, Quantum Mechanics must be incomplete. In response to Einstein argument about incompleteness of Quantum Mechanics, John Bell argued that the quantum mechanical approach to describing nature is valid and the apparent incompleteness arises from an incomplete understanding of the important quantities and constraints inherent in nature. If this is true, then one can expect that new dynamical variables will be discovered in the future which will eliminate the problems associated with the EPR paradox.

Bell has shown there must be hidden variables in quantum mechanics which will make quantum mechanics complete." John Bell derived a mathematical theorem which verified the statistical predictions of quantum mechanics could be applied to quantum particles that were "spacelike separated" or existed in different local realities. This implies the presently accepted concepts of quantum mechanics are incomplete and that there may be a "hidden variable" or mechanisms to account for the fact that quantum particles appear to "communicate" at speeds greater than the speed of light." A physical mechanism that may account for this apparent faster than light "communication" between two quantum particles is analogous to how "information" can be "communicated" from one pool ball to another on the surface of a pool table. The pool balls will represent a "quantum mass units of space" defined in Chapter two. Pool is a game in which a ball called a cue ball, is struck and as a result, the cue ball travels on the surface of the pool table until it collides with an object ball. This collision results in the “information" regarding the cue balls momentum to be "communicated" to the object ball. The object ball then begins to travel across the table until it collides with and "communicates" the "information" on its momentum to the next ball in line. The speed at which the "information" is "communicated" between the cue ball and the object ball is, in part, dependent on the time required to travel the distance between the individual balls on the table. If, however, the pool balls are physically touching each other the "communication" or "information" transfer from the first to the last ball in line will be faster because the time required for them to travel the distance between them would be minimal. In Chapter three the transmission of energy was derived in terms of a "coupling" from one "quantum mass unit of space" to next of the internal "vibrations" in a matter and energy field components of a "quantum mass unit of space". It was shown the coupling of the internal "vibrations" between the matter and energy field component of a "quantum mass unit of space" occurs at the velocity of light . The matterfield component travels a "distance" internal to a "quantum mass unit of space" and interacts or "collides" with the energyfield component of that "quantum mass unit of space" and then the energyfield component "collides" or interacts with the matterfield component of the next "quantum mass unit of space" in space. This repeated process of physical interaction and exchange of energy between the matter and energy field components of a "quantum mass unit of space" and the subsequent transfer of that energy to the next "quantum mass unit of space" is responsible for transmission of electromagnetic energy. Therefore, the speed of light or electromagnetic energy and the "information" it contains is due, in part, to the time required for the matterfield component of a "quantum mass unit of space" to "travel" far enough to "collide" or interact with the energyfield component of the next "quantum mass unit of space". This is analogous to the speed of "communication" or "information" transfer in the above example of the pool balls in that the time required for information to be transferred from the first to the last pool ball in the line was dependent on the physical distance between the individual pool balls. However both the EPR paradox and Bells theorem deal with the spatial "separation" between different local realities.

Chapter two showed the quantum properties of matter and energy were derived in terms of a resonant "structure" formed in space by "vibrations" in a continuous non-quantized matter and energyfield component of space. However it also showed that the spatial component of a quantum particle is related to the matterfield component of a resonant "structure" or "quantum mass unit of space" Therefore, the "hidden variable" which allows the transferring of information form different spatially separated local realities faster than the speed of light may be related to the spatial aspects of the matterfield component of a "quantum mass unit of space" that defined the quantum properties of mass and energy in Chapter two. As mentioned earlier, Chapter three derived the speed of light in terms of the distance the matterfield component has to "travel" in order to interact with the energyfield component internal to a resonant "structures" that makes up a "quantum mass unit of space" However, Chapter two showed the matterfield components of adjacent "quantum mass unit of space" are physically "touching" because a volume of three-dimensional space is made up of and "supported" by the matterfield component of space. Therefore the spatial distance between the matterfield component of adjacent "quantum mass units of space" will be minimal when compared to the internal distance between the matter and energy field components of "quantum mass unit of space". This would allow the matterfield components of "quantum mass unit of space" to transfer information regarding momentum of a quantum particle faster than the speed of light because the spatial distance between the matterfield components of adjacent "quantum mass units of space" is physically less than the distance between the internal matter and energy field components of a "quantum mass unit of space". Therefore time required for them to interact will be less and will result a higher rate of information transfer for the same reason the information on the cue balls momentum in the earlier example could be transferred faster when the pool balls were physically touching verses when they were not. This defines the mechanism explaining why Bell's theorem can provide mathematical verification that the statistical predictions of quantum mechanics can be applied to quantum particles or "quantum mass units of space" that are "spacelike separated" or exist in different local realities. It demonstrates that "information" regarding spatial properties such momentum or orientation could be communicated through space faster than the speed of light. Chapter Six Planck's length and the uncertainty principal Return to Top It can be shown the Heisenberg's uncertainty principle is related to Plank's length and a quantum characteristic of a "standing" matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of mass and energy. In Chapter two the quantum properties of mass and energy were defined in terms of resonant "structures" formed in space by "vibrations" in a continuous non-quantized mass and energy components of space. It was shown these resonant "structures" form a "standing" or

resonant matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. These resonant "structures" are called a mattercule or "quantum mass unit of space" On page 169 of John A Wheeler book "At Home in the Universe", he defines the "position", in terms of length, of a quantum “particle” of dimensional space or the mattercule. "There is only one truly fundamental length in nature a length free of all reference to the dimensions and rate of revolution of the planet on which we happen to live, free of any appeal to the complex properties of any solid or gas: free of every reference to the mysterious properties of any elementary particle: what we call today the Planck length, L=(hG/C^3)1/2= 1.6X10^-33 cm And what we identify with the characteristic scale of quantum fluctuations in the geometry of space". However this suggests the value of 1.6X10^-33 cm may define the scale of quantum fluctuations in the geometry of a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the "standing" or resonant matterenergy wave that defined a "quantum mass unit of space" in Chapter two Is it possible the Heisenberg's uncertainty principle may be related to the physical length of a "standing" matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with a "quantum mass unit of space" or quantum particle defined in Chapter two? Because there would be an inherent uncertainty as to the exact position or momentum of a quantum particle because its position and momentum would be distributed over the length of a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with the physical length of "standing" matterenergy wave responsible for the physical structure of a quantum particle. Additionally defining quantum particles such as an electron in terms of a "standing" or resonant matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension can also explain why quantum particles can randomly "move" or "jump" to different positions in space without ever moving thought the intervening space. Quantum particles such as a electron can appear to "jump" from one atomic orbital to the next without going through the intervening space because the physical "structure" of an electron and all quantum particles is related to a resonant "structure" generated by a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to forth *spatial* dimension. The reason electrons can "jump" from one atomic orbital to the next without going thought the intervening space is because the "standing" matterenergy associated with the quantum properties of a electron does not move from one atomic orbital to the next. Instead the resonant "structure" associated with an electron collapses in its initial atomic orbital and is then reformed in a new atomic orbital. Because no resonant "standing" matterenergy wave is generated in the intervening space between the atomic orbitals no electrons will be found their. Chapter Seven The spatial properties of Photons with respect to Four Spatial Dimensions Return to Top

The geometric properties of photons are related to a physical property of a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of mass and energy. In Chapter two the quantum properties of mass and energy were defined in terms of discrete resonant "structures" formed in space by "vibrations" in a continuous non-quantized mass and energy components of space. The formation of these resonant "structures" was derived in terms of an interaction between a continuous non-quantized mass and energy components of space. Chapter three defined the propagation of a photon's energy in terms of a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Additionally, the quantum properties of a photon were derived in terms of discrete resonate "structures" generated by "vibrations" in a continuous non-quantized mass and energy component of space caused by the passage of a matterenergy wave. The geometric properties associated with a matterenergy wave can be used to explain the following observations regarding the interference of photons made by Richard P Feynman's in his book "QED The Strange Theory of Light and Matter". On pages 17 thru 23 of Richard P Feynman's book "QED The Strange Theory of Light and Matter", he discusses what happens when light is partially reflected by two surfaces. He demonstrates by placing two glass surfaces exactly parallel to each other one can observe how the photons of light reflected from the bottom surface interact with those reflected from the top surface. Depending on the thickness of the glass he can determine, by using a photo detector, that four percent or 4 out of 100 photons reflected from the lower surface of the glass could add up to as many as 16 or none at all when they interact with the photons reflected from the upper surface of the glass. These observations of Mr. Feynman support the wave properties of electromagnetic radiation. Because according to wave theory the energy associated with the interference of the wave characteristics of 4 photons with 4 other photons will result in energy variations that corresponds to the energy associated with 0 to 16 photons. However, wave theory also predicts the energy variations should be continuous. In other words, the energy of the reflected photons should be able to take on any value between 0 and the combined energies associated with 8 photons. Unfortunately, for the wave theory of light, the energy of the reflected photons in the above experiment can only take on integral or quantum values equal to the energy of the photons that originally struck the surface of the glass. Therefore, the quantum properties of the energy of the reflected photons in the above experiment are not supported by the wave theory of light. However this apparent contraction between the above wave and quantum characteristics of a photon can be resolved if the energy of a photon is viewed in terms of resonant "structures" associated with a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. In Chapter three the quantum property of a photon was derived in terms of a discrete resonate "structure" generated in space by the passage of a matterenergy wave on a "surface" of a threedimensional space manifold with respect to four spatial dimensions.

Therefore, Chapter three defines a common mechanism responsible for both the quantum and wave properties of a photon because it defines the photon in terms of a quantized matterenergy on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. The interference of photons observed by Mr. Feynman are due to the wave properties of the matterenergy wave responsible for the propagation of a photon. If the spatial distance between two photons is equal to half of the matterenergy wave of a photon the energy associated with the wave properties of the quantized "vibrations" in the matter and energy field components of these photons will interfere and the interaction of 4 photons with 4 other photons will yield 0 photons. If the spatial distance between two photons is equal to the wavelength of the matterenergy wave of a photon the energy associated with the wave properties of the quantized vibrations in the matter and energy field components of these photons will reinforce and the interaction of 4 photons with 4 other photons will yield the energy associated with 16 photons. However, this mechanism does not explain why the energy variations caused by the interference of photons are quantized and not continuous as wave theory indicates they should be. The reason the energy of interfering photon's is not continuous is because of the discrete quantum properties associated with a resonant "structure" of a matterenergy wave responsible for the propagation of a photon's energy. The discrete energies associated with a resonant "structure" of a matterenergy could only interfere to generate matterenergy wave with an identical resonant "structure". Therefore the reflected photons could only take on integral or quantum values equal to the energy of the photons that originally struck the surface of the glass, as was observed by Mr. Feynman. However defining the energy of a photon in terms of the geometric properties of a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension also makes it possible to analyze the path of individual photons between two reflective surfaces not only in terms of their wave properties but also in terms of the directional amplitude vector of their spatial properties, as Richard P Feynman did in his book "QED". In Richard Feynman’s book "QED", he analyzed the process by which 4 photons are reflected from bottom surface of two pieces of glass in terms of the direction of their energy amplitudes. When light is reflected from a single surface, the directions of amplitude energies of the reflected photons are randomly varying with respect to photons impacting the surface. However, when photons are reflected from two surfaces the timing or direction of the energy amplitude can be synchronize between the top and bottom surfaces so they cancel or reinforce each other. As a result 4 photons reflected form the bottom surface can cause as few as 0 photons or as many as 8 photons to arrive at the top surface. As Richard Feynman pointed out in his book "QED", the time it takes a photon to move to a given point determines its directional energy amplitude because the time it takes a photon reflected from the bottom surface to reach the top surface depends on the distance between them. When to directional energy amplitudes of the 4 photons reflected from the bottom surface are opposite to those that are impacting the bottom surface they will cancel and no photons reflected from the bottom surface will arrive at the top surface. When the directional energy amplitudes of the photons reflected from the bottom surface are the same as to those that are impacting the bottom surface, they will add and 8 photons reflected from the bottom surface will arrive at the top surface. The spatial and vector properties of a matterenergy wave defines the mechanism responsible for the “redirection” of the energy amplitude of photons in terms of the resonant properties of the matter and energy field components of the mattercule.

The energy amplitude and direction of the energyfield component of a matterenergy varies sinusoidally with respect to time and direction. Therefore, at certain times the direction of the energy amplitude of two interfering photons will be reinforce while other times they cancel. Therefore defining a photon in terms of the geometric properties of a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension defines a mechanism that allowed Mr. Richard Feynman’s to analyze the process by which 4 photons are reflected from bottom surface of two surfaces in terms of the direction of their energy amplitudes. Chapter Eight The relative masses of the Proton and Electron in terms of Four Spatial Dimensions Return to Top The relative masses of protons and electrons are related to energy gradients in a threedimensional space manifold with respect to a fourth *spatial* dimension. These energy gradients are created by a rotation in a continuous non quantized mass and energy component of space. Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of mass and energy. In Chapter thirteen, the polarity, magnitude and quantum properties of the unit electric charge will be defined in terms of an energy gradient in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. The positive unit electric charge of a proton will be derived in terms of an energy gradient created by a "clockwise" "rotation" in a continuous non-quantized mass component of space while the unit electric charge of an electron will be derived in terms of an energy gradient caused by an opposite "rotation" in a continuous non-quantized mass component of space. The energy gradients created by a "rotation" of a continuous non-quantized mass component of space effects a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension similar to the way the energy or pressure gradients called high and low pressure areas in the earth's atmosphere effect the density of the air and the surface of the earth. In a high-pressure area, the rotational movement of air molecules is directed downward towards the surface of the earth. This results in the density of the air molecules at the apex of the highpressure area to be greater than the density of the air molecules in the volume of air adjacent to the apex of the high-pressure area. Conversely, in a low-pressure area the rotational movement of the air molecules is directed upward away form the surface of the earth. This result in the density of the air molecules at the apex of the low-pressure area to be less than the density of the air molecules in the volume of air adjacent to the apex of the low-pressure area. The rotation of the air molecules associated with high and low-pressure areas also affects the surfaces they contact. For example the downward motion of the air molecules in high-pressure area results in the surface of the liquid in a barometer to become depressed while the upward motion of the air molecules in a low-pressure area result in the surface of the liquid in barometer to become elevated.

The "rotational" motion of a continuous non-quantized mass component of space has a similar effects on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension . In a dimensional “high-energy volume” associated with a proton, which would be analogous to a high-pressure area in the earth’s atmosphere, the "rotational" motion of a continuous nonquantized mass component of space is directed “downward” with respect to a fourth *spatial* dimension, towards the “surface” of a three-dimension space manifold with respect to a fourth *spatial* dimension. This results in the density of the continuous non-quantized mass component of space at the apex of a dimensional “high-energy volume” to be greater than the density of the continuous non-quantized mass component in the volume of space adjacent to the apex of a dimensional “high-energy volume”. This is analogous to how the air molecules at the apex of a high-pressure area in the earth's atmosphere would be denser than the air molecules in the volume of air adjacent to the apex of a high-pressure area. Additionally the rotational energy of the energy gradients associated with a proton that is directed "downward" with respect to a fourth *spatial* dimension causes a "depression" in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. This is analogous to downward motion of the air molecules in high-pressure area depressing the surface of the liquid in a barometer. Conversely, in a dimensional “low-energy volume” associated with an electron, the "rotation" of a continuous non-quantized mass component of space is directed “upward”, with respect to a fourth *spatial* dimension, away from a "surface" of a three-dimension space manifold with respect to a fourth *spatial* dimension. This results in the density of the continuous non-quantized mass component at the apex of a dimensional “low-energy volume” to be less than the density of the continuous non-quantized mass component in the volume of space adjacent to the apex of a dimensional “low-energy volume”. This is analogous to how the air molecules at the apex of a low-pressure area in the earth's atmosphere would be less than the dense than air molecules in the volume of air adjacent to the apex of a low-pressure area. Additionally the rotational energy of energy gradients associated with a electron that is directed upward with respect to a fourth *spatial* dimension causes an "elevation" in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. This is analogous to upward motion of the air molecules in high-pressure area elevating the surface of the liquid in a barometer. Therefore mass of a proton will be relativity greater than the mass of an electron because the "downward" motion of an energy gradient in a continuous non-quantized mass component of space associated with a proton results in a higher concentration of the mass component of space in a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension than the mass component of space in an "elevation" in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension associated with the mass of an electron. Chapter Nine Electrical Potential Energy with respect to Four Spatial Dimensions Return to Top

Energy gradients in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension are responsible for an electrical potential and the ability to treat particles as mathematically points. Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of mass and energy. In Chapter eight derived the relative masses of protons and electrons in terms of energy gradients in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension generated by a "rotation" of a continuous non-quantized mass and energy components of space. Later in Chapter twelve the mass of all particles with or without an electrical charge will be derive in terms of a “quantity” of a matterfield or mass component of space "contained" in a “curvature” generated by energy gradients in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Particles can be treated as mathematical points because the energy gradients responsible for mass of all particles both charged and uncharged create conical “curvatures” in a threedimensional space manifold with respect to a fourth *spatial* dimension. Therefore, because the energy gradients responsible for the mass of all particles and objects are symmetrical, the "curvature" they generate in a three-dimensional space manifold will also be symmetrical and conical in shape. This allows the focal point of this conical "curvature" in a three-dimensional space manifold with respect to a fourth *spatial* dimension to be defined as the position of a particle in terms of a mathematical point because the mass of the particle will be symmetrical distributed around that point in space. In Chapter eight the energy gradients associated with the mass of charged particles were compared to energy gradients in the earth's atmosphere called high and low pressure areas. The relative mass of a proton and electron was derived in terms of the "rotational" direction, with respect to a fourth *spatial* dimension, of the matterfield components of space generated by energy gradients in the continuous non-quantized mass and energy components of space. However, another aspect of these energy gradients generated by a "rotation" of a matterfield component of space which was not mentioned in Chapter eight is they are responsible for electrical potential energy. An analogy involving an atmospheric barometer can be used to illustrate how a "rotation" of a matterfield component of space generates electrical potential energy. Many atmospheric barometers use mercury to measure the atmospheric pressure by measuring the separation between the surfaces of two columns mercury. One type of these devices consists of a U shaped glass tube filled with mercury that has one side sealed with the air removed so the air pressure on that side of the U tube is close to zero. The atmospheric pressure caused by the energy or pressure gradients associated with high and low pressure areas forces the surface of the mercury in the open tube upward or downward with respect to the surface of the mercury in the seal end of the tube. The atmospheric pressure or force on the surface of the mercury can be determined by measuring the distance separating the surface of the two columns of mercury and calculating the force or pressure required to cause that separation. It is also possible calculate the separation of the

surfaces of the two column by knowing the force or pressure that the atmosphere is exerting on the opened end of the tube. Chapter thirteen will demonstrate the magnitude and polarity of the unit electric charge is the result of energy gradients generated in a three-dimensional space manifold by a "rotation", with respect to a fourth *spatial* dimension, of a matterfield component of space. It will be shown the direction, with respect to a fourth *spatial* dimension, of a "rotation" of a matterfield component of space determines the polarity of the electric charge. If one defines a "counter clockwise rotation", with respect to a fourth *spatial* dimension, of the matterfield component of space as a positive electric charge, a "clockwise rotation", with respect to a fourth *spatial* dimension, of the matterfield component of space would defined a negative electric charge. These "energy gradients" in a matterenergy field component of space will cause a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to "move" “downward” or “upward” relative to the adjacent areas of the three-dimensional space manifold depending on the directional rotation of the matterfield component of space. This is analogous to how the energy gradients caused by high and low pressure areas in the earth's atmosphere causes the surface of the mercury in the open tube in the earlier example move upward or downward. Chapter ten, will derive all forms of energy including electrical potential energy, in terms of a relative *spatial* "separation", with respect to a fourth *spatial* dimension, between different "surfaces" of a three-dimension space manifold. Therefore, the magnitude of an electrical potential would be a result the magnitude of a physical separation, with respect to a fourth *spatial* dimension, of different "surfaces" of a threedimensional space manifold with respect to a fourth *spatial* dimension caused by the energy gradients in space associated with an electrical charge. The reason is analogous to why the magnitude of the differential force or pressure of the atmosphere determines the physical separation of the two surfaces of the mercury in a barometer in the earliest example. The greater the physical separation of the surfaces of the mercury in a barometer becomes the greater the differential atmospheric pressure is between those two surfaces of mercury. Summarily, the greater the physical "separation", with respect to a fourth *spatial* dimension, of different "surfaces" of a three-dimensional space manifold, the greater the differential electrical force or potential would be between those two volumes of three-dimensional space. For electrical charge, this force is measured in volts, which is an indication of the relative "electrical pressure" on the "surface" of the different three-dimensional space manifolds of in that volume of space. Chapter Ten A boundary between a Third and Fourth Spatial Dimensions Return to Top “Shadows” postulates our world of three *spatial* dimensions exists in a four *spatial* dimension universe and a distortion of the axes of a three-dimensional space manifold with respect to a fourth *spatial* dimension is responsible for the forces associated with the laws of nature.

One way of understanding the ramifications of this postulate would be to compare the geometry associated with a four *spatial* dimension universe to the geometry of an imaginary twodimensional creature living on the surface of a piece of paper in a three-dimensional universe. A two dimensional creature "living" on the surface of a piece of paper would not be aware the paper he was living on existed in a three-dimensional universe because his field of vision would be limited to surface or length and width of the paper. Therefore, he or she would not be aware of the existence of the dimension of height or the third spatial dimension because he or she could not look in the direction of a third spatial dimension. As will be shown latter, the energy three-dimensional beings use to activate their senses does NOT travel through a fourth *spatial* dimension but only along a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension . Therefore, similar to the two-dimensional creature describe above, the field of vision of threedimensional beings would be limited to the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. This means three-dimensional beings would not be aware of the existence of a fourth *spatial* dimension because three-dimensional beings cannot "look" in "direction" of the fourth *spatial* dimension. Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of mass and energy and later in Chapter two the quantum properties of mass and energy were defined in terms of resonant "structures" formed in a three dimensional space manifold by energy gradients in a continuous non-quantized mass and energy field components of space. It has been and will be shown the forces associated with the laws of nature are caused by the distorting effects these energy gradients in a continuous non-quantized mass and energy field components of space have on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. The relationship between forces and a distortion in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension can understood by comparing it to effects air pressure has on the surface of water. The forces associated with the air pressure will represent the forces "Shadows" associates with energy gradients in a mass and energy field component of space defined in Chapter two while the surface of the water will represent a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. If the two-dimensional surface of the water is undisturbed, the force the air pressure exerts on it will be perpendicular to each of the two-dimensional axes of the surface of the water because it would be applied perpendicularly along the exact surface line of the water. Increasing or decreasing the pressure will result in the movement and a distortion of the surface of the water with respect to vertical axis of three-dimensional space. Similarly, if a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension were “undisturbed” the "pressure" or "force" associated with energy gradients in threedimensional space would be simultaneously perpendicular to each of the three-dimensional axes of three-dimensional space. This is because the force would be applied "perpendicularly" along the exact "surface" "line" of each of the three-dimensional axis of the three-dimensional space manifold. Increasing or decreasing the "pressure" these energy gradients exert on the three-dimensional space manifold with respect to a fourth *spatial* dimension will result in its "surface" to become distorted with respect to the "vertical" or "W" axis of the fourth *spatial* dimension.

This would be analogues to how increasing or decreasing the air pressure caused the surface of the water to become "distorted" with respect to the vertical axis of three-dimensional space in the earlier example. It can be shown a distortion in a "surface" of the three-dimension space manifold with respect to a fourth *spatial* dimension generated by energy gradients in a continuous non-quantized matter and energy field component of space is the causality of all of the forces associated with the laws of nature. This can be understood by using the earlier analogy involving the paper. The surfaces of the x and y planes on a piece of paper are perpendicular to each other because they are fixed to the surface of the paper. However, they are not always perpendicular to the dimension of height or the vertical plain of three-dimensional space because the paper can be pick up and rotated with respect to the third dimensional plane. If the paper is rotated or curled, its surface would become curved with respect to the third *spatial* dimension and the force of gravity would then have tangential components relative to its surface. Points on the surface of the paper affected by the force of gravity would move, if they could, along the surface of the paper due to the tangential force generated by the force of gravity. Similarly x, y, and z planes of three-dimensional space are perpendicular to each other because they are fixed to the volume of three-dimensional space. However, they are not always perpendicular to the "W" axis of a fourth *spatial* dimension because they can be "rotated" with respect to the fourth *spatial* dimension, similar to the way the two-dimensional surface of a piece of paper can be rotated with respect to three-dimensional space. This generates a "curvature" or distortion in a "surface" of the three-dimensional space manifold with respect to a fourth *spatial* dimension analogous to the curvature generated in the twodimensional surface of the paper when it was rotated with respect to three-dimensional space. The tangential forces generated along a distorted or "curved" "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is the causality of all forces and motion three-dimensional space. (This "curvature" or distortion in the "surface" of a three-dimensional space manifold with respect to the fourth *spatial* dimension is analogous to the space-time curvature that Einstein postulated was responsible for the force of gravity in his General Theory of Relativity.) The effects these energy gradients have on geometry of a three-dimensional space manifold with respect to the fourth *spatial* dimensions can be compared to the effects the energy gradients called high and low pressure areas in the earth's atmosphere have on the liquid in a barometer. High and low pressure areas are a result of atmospheric rotation which cause pressure differentials or energy gradients to be formed in the atmosphere. Although high and low-pressure areas have properties of three-dimensional space because they extend vertically into the atmosphere, they affect the two-dimensional surface of a liquid in a barometer. A barometer is an instrument for measuring atmospheric pressure. In areas of high atmospheric pressure, the surface of the liquid in a barometer "sinks" or becomes depressed because the pressure is directed downward. While in areas of low atmospheric pressure the surface of the liquid raises or becomes elevated because the pressure is oppositely directed form that of high-pressure area.

This is a result of the transfer of the energy associated high or low-pressure areas to the twodimensional surface of the liquid. A similar affect occurs in a continuous non-quantized matter and energy field component of space defined in Chapter two. In Chapter eight it was shown a rotation in a matterfield component of space generates "high" and "low" energy differentials in a three-dimensional space manifold with respect to a fourth *spatial* dimensional. These four-dimensional "high" and "low" "energy" differentials generated by a rotation of a matterfield component of space affect the "surface" of a three-dimensional space manifold similar to the way high and low pressure areas in the earth's atmosphere affect two-dimensional surface of liquid in a barometer. In a four-dimensional “high-energy differential”, the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension "sinks" or becomes "depressed" because the “energy pressure" is directed “downward”. While in a four dimensional “low energy differential” the "surface" of the three-dimensional space manifold with respect to a fourth *spatial* dimension "rises" or becomes "elevated" because the "energy pressure" is oppositely directed form that of "high-energy differential”. One might ask how the “pressure” in four-dimensional space can be altered from threedimensional space to account for the forces associated with the laws of nature. This question can be answered by using the earlier analogy involving a barometer. If the liquid in the barometer used in the earlier analogy is allowed to boil, the pressure on the twodimensional surface of the liquid in the barometer would increase because the boiling liquid in the form of vapor would expand towards the three-dimensional volume above the surface, thereby increasing the pressure on the surface and causing it to move downward or become depressed. Similarly "Shadows" will shown when mass is converted to energy, the energy expands towards a fourth *spatial* dimension thereby increasing the "pressure" on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension causing it to become distorted with respect to a "vertical" or "W" axis of the fourth *spatial* dimension. If the expansion of mass to energy is directed along only along one of the three axes of threedimensional space, the "pressure" and the acceleration this "pressure" causes will be directed primarily along that dimensional axis. This will result in movement to be generated along that axis. Another way of describing how particles or masses in a third *spatial* dimension can have an affect on a fourth *spatial* dimension is by comparing the mechanism responsible for their interactions with a fourth *spatial* dimension to that of a steam engine. In a steam engine, water expands in the form of steam from the two-dimensional surface of the water. This expanding steam generates a force that "distorts" the two-dimensional geometry of the surface of a piston by causing it to move with respect to vertical axis of three-dimensional space. As mentioned earlier “Shadows” has and will demonstrate when mass is converted to energy, the mass “expands", in the form of energy, from the three-dimensional "surface" of mass in the direction of the fourth *spatial* dimension. This expanding mass in the form of energy distorts the

three-dimensional geometry of a three-dimensional space manifold by causing it to "move" with respect to the "vertical" or "W" axis of the fourth *spatial* dimensional. This is analogous to how the steam in a steam engine generates the force that results in the twodimensional surface of a piston to move or become distorted with respect three-dimensional space. Again, we can use the analogy of a two-dimensional creature to understand how the energy of three-dimensional objects can alter the geometry of three-dimensional space with respect to the fourth *spatial* dimension. However instead of "living" on the surface of a piece of paper as in the earlier example, the twodimensional creature will be “living” on the surface of water which will also be considered the surface of a piston in a steam engine. If the water was heated to the boiling point, the two-dimensional creature could not “look” down below the surface of the water were the steam was originating from. The steam, as it expand towards the volume above the surface of the water, would was increase the pressure on the surface of the water or piston causing it to move with respect to vertical axis of three-dimensional space. Because the two dimensional creature could not look down he or she could not look down to see the volume of water where the steam originates. The two-dimensional creature living on the surface of the water or piston could not directly tell that the geometry of the surface of the piston had moved with respect to three-dimensional space because as mentioned earlier he or she could not "look" in the direction that it was moving. However, if the two-dimensional creature had placed marks on the wall of the piston he or she could indirectly tell the geometry of the surface of the water or piston had changed by looking along the surface at these marks as the piston moved passed them. He or she could determine the distance the surface of the piston had moved because he or she could "see" and count these marks as the surface of the piston passed. The two-dimensional creature would then have way of determine the relative distance that the surface of the piston had moved with respect to three-dimensional space by counting these marks. Just as the two dimensional creature cannot "look" down to see the volume of water below the surface where the steam originates from, we as three-dimensional beings cannot look “down” to see the "volume" of energy below the "surface" of the mass in four-dimensional space where energy originates from. \When mass "expands" to energy it generates a force on a three-dimensional space manifold, which results in a "surface" of the three-dimensional space manifold to "move" with respect to the "W" axis of the fourth *spatial* dimension. This is analogous to how the expanding steam generates a force on the two-dimensional surface of a piston in a steam engine causing it to move with respect to three-dimensional space. In addition, three-dimensional beings could not directly tell that the "surface" of a threedimensional space manifold had "moved" or become distorted with respect to a fourth *spatial* dimension because three-dimensional beings cannot look in the direction of the fourth *spatial* dimension. However, it has and will be demonstrated throughout “Shadows” that three-dimensional beings perceive a fourth *spatial* dimension in terms of energy.

Therefore, three-dimensional beings can determine relative "distance" that a three-dimensional space manifold had "moved" with respect to the "W" axis of the fourth *spatial* dimension by determining the relative energy differences between them. As mentioned earlier a two-dimensional creature could, by counting the marks on the wall, determine how far the two-dimensional surface of the piston had moved with respect to threedimensional space. Similarly, three-dimensional beings can determine how far the "surface" of a three-dimensional space manifold had moved with respect to four *spatial* dimension by measuring the energy difference between objects . We return to our discussion of the properties of four dimensional space by examining how we as three-dimensional beings perceive the fourth *spatial* dimension. It has been and will be demonstrated throughout this paper that all forms of energy are associated with a "curvature" or distortion in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Therefore, what we human beings perceive as energy is a result of a "curvature" in the three-dimensional space manifold with respect to a fourth *spatial* dimension. The depth or magnitude of this "curvature" determines the relative magnitude of energy differential between two points in space. Chapter Eleven Propagation of electromagnetism and the Inertial Properties of Space Return to Top The propagation of electromagnetic energy is a result of an inertial property of a mass component of space and a distortion in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. In Chapter one "Shadows" postulated a volume of space is composed of a continuous nonquantized “field” of mass and energy. Chapter two derived the quantum properties of both mass and energy in terms of resonant "structures" formed in a three-dimensional space manifold by "vibrations" in a continuous nonquantized mass and energy component of space. The "vibrations" in a continuous non-quantized mass and energy component of space responsible for the quantum properties of mass and energy also generate a matterenergy on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension that defined the propagation of electromagnetic energy in Chapter three. However Chapter Three did not define how and why the inertial properties of a continuous nonquantized mass component of space are responsible for the "movement" of a matterenergy wave "across" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. One can understand how the inertial component of a continuous non-quantized mass component of space can cause a matterenergy wave to "move" "across" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by comparing it to how the inertial properties of a piece of wood with floating on the surface of water with a vertical rod attached to it can cause a wave move across the surface of water.

The surface of the wood will represent a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension and the rod will represent the “W” axis of the fourth *spatial* dimension. (The "W" axis of the fourth *spatial* dimension was defined earlier in Chapter ten.) A force applied to the rod would "distort" the surface of the water because it would cause the "surface" of part of the wood to sink below the surface water or become depressed, while part of it would rise above the surface of the water or become elevated. The buoyancy of the water would force the part of the wood that was under the surface back to the surface. The momentum due to the inertia associated with the mass of the wood would cause the part that was above the water to go below the surface. The rod and the plate would vibrate back and forth in this manner generating a wave on the surface of the water. Electromagnetic energy is propagated by a similar mechanism. In Chapter three it was shown a matterenergy wave on a "surface" of a three-dimensional space manifold generates alternating "depressions" and "elevations" in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension. These alternating "elevations" and "depressions" are propagated on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension due to the inertia of the matterfield component of space. When a "surface" of a three-dimensional manifold is "depressed" with respect to a fourth *spatial* dimension, the energy of space will force the "depression" in the "surface" of a three-dimensional space manifold back to the "surface" of that manifold. The momentum due to the inertia of the matterfield component of space associated with the "depression" will cause the "surface" of the manifold to become elevated with respect to a fourth *spatial* dimension. The momentum due to the inertia of the matterfield component of space associated with the "elevation" will cause the "surface" of the manifold to become "depressed" with respect to a fourth *spatial* dimension. This will cause a matterenergy wave to "move" "across" the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension because the momentum due to the inertia of the matterfield component of space will cause the "surface" of a three-dimensional space manifold to "oscillate" back and fourth with respect to a fourth spatial dimension. This would be analogous to the way the inertial properties of the wood caused the surface of the water to oscillate back and fourth and a wave to be generated on the surface of the water. The electrical energy of the matterenergy wave responsible for the transmission of electromagnetic energy is the result of the momentum of an inertial property of a continuous nonquantized mass component of a matterenergy interacting with mass component of objects in a three-dimensional space manifold with respect to a fourth spatial dimension. However the magnetic component of electromagnetic energy is caused by a "torque" generated on "surface" of a three-dimensional space manifold by with respect to a fourth *spatial* dimension by the passage of a matterenergy wave. The passage of a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension causes alternating "elevations" and "depressions" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. These "elevations" and "depressions" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension causes the "W" axis of a fourth *spatial* dimension to become misaligned with respect to the "surface" of the three-dimensional space manifold associated with the "elevations" and "depressions" of the matterenergy wave. The momentum associated with the inertia of a continuous non-quantized mass component of the matterenergy wave will cause the "W" axis of a fourth spatial dimension to oscillate "back" and "fourth" with respect to a "surface" of a three-dimensional space manifold.

This would be analogous to how the rod attached to the piece of wood in the earlier example oscillate back and forth respect to the surface of the water. As was shown in Chapter ten a misalignment of the "W" axis of the fourth *spatial* dimension with respect to a three-dimensional space manifold cause a force to generated in a three-dimensional space manifold. The torque generated on a "W" axis of a fourth *spatial* dimension by alternating "elevations" and "depression" in a "surface" of a three-dimensional space manifold with respect to fourth *spatial* dimension would be directed along the "surface" of a three-dimension space manifold with respect to a fourth *spatial* dimension 90 degrees out of phase with the velocity vector of the matterenergy wave. This torque is the magnetic component of electromagnetic energy and would be 90 degrees out of phase with the velocity vector of the energyfield or electrical component of electromagnetic energy because it would be directed along the "surface" of the three-dimensional space manifold with respect to a fourth *spatial* dimension. Chapter Twelve Gravity and the Fourth Spatial Dimension Return to Top Gravitational forces are the result of an energy gradient in a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by a rotation of a continuous non-quantized mass component of space. (The physical mechanism responsible for gravitational forces, proposed here, has similarities to the mechanism responsible the magnitude of a unit electric charge that will be defined in Chapter thirteen in that they are both related to energy gradients in a three-dimensional space manifold with respect to a fourth *spatial* dimension.) Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of mass and energy. In Chapter thirteen the forces associated with a unit electric charge will be derived in terms of "energy gradients" generated by a "rotation" with respect to a fourth *spatial* dimension of a continuous non-quantized mass component of space. It will be shown these energy gradients cause a distortion in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. However. an energy gradient in a three-dimensional space manifold with respect to a fourth *spatial* dimension is also responsible for the forces associated with a gravitational field. The mechanism responsible for the gravitational forces can be understood by comparing the effects energy gradients in a three-dimensional space manifold have on a "surface" of a threedimensional space to manifold with respect to a fourth *spatial* dimension to a marble and a rod on "surface" of a rubber diaphragm. The marble on the diaphragm will represent a particle on a "surface" of a three-dimensional space manifold and the rod will represent the “W” axis of a fourth *spatial* dimension. (The "W" axis of a fourth *spatial* dimension was defined earlier in Chapter ten.) If the end of the rod is orientated perpendicular to the "surface" of the diaphragm and is allowed to touch it without putting any pressure on it, the rod will be perpendicular to the "surface". The "surface" of the diaphragm will remain flat. The marble on the flat diaphragm would not move.

However, if pressure is applied to the rod, the "surface" of the diaphragm will become depressed and will no longer be perpendicular to the rod. Gravitational forces will then have a tangential component along the "surface" of the rubber diaphragm. The tangential component of the gravitational force directed along the "surface" of the diaphragm will cause the marble to move towards the apex of the depression. A similar affect occurs in a three-dimensional space manifold with respect to a fourth *spatial* dimension when an energy gradient is present in a given volume of space. The energy associated with an energy gradient that is directed "perpendicular" to a "surface" of a three-dimensional space manifold will cause a "surface" of a three-dimensional space manifold to become distorted or "depressed" with respect to a fourth *spatial* dimension. This generates a four-dimensional cone in the "surface" of the three-dimensional space manifold. (The curvature in space caused by this "depression" is analogous to the space-time curvature "The General Theory of Relativity" uses to define the force of gravity. However, they differ in that "Shadows" defines this "curvature" in terms of four *spatial* dimensions instead of fourdimensional space-time.) In Chapter ten, the magnitude of all forms of energy was derived in terms of a spatial "separation" in a "surface" of a three-dimensional manifold with respect to a fourth *spatial* dimension. In other words a spatial "separation", with respect to a fourth spatial dimension, between the "surfaces" of two three-dimensional space manifolds causes an energy differential between the "surface" of a three-dimensional space manifold connecting them. Therefore, the spatial "separation" caused by an energy gradient in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension will result in an energy differential to be developed along a "surface" of a three-dimensional space manifold. The tangential component of the energy differential associated with a spatial "separation" in the "surfaces" of two three-dimensional space manifolds directed along the "surface" of the threedimensional space manifold connecting them is responsible for gravitational forces. It causes particles to "roll" towards the apex of the depression in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. This is analogous to the marble rolling along the "surface" of the apex of the depression in rubber diaphragm. The accumulation of particles at the apex of this "depression" is responsible for the mass of planets, stars and galaxies. However, a separation in the "surfaces" of a three-dimensional space manifold with respect to a fourth spatial dimensions is also responsible for the mass of quantum particles. Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of mass and energy and Chapter two derived the quantum properties of mass and energy in terms of resonant "structures" formed in space by a dynamic interaction of a continuous non-quantized mass and energy field components of space. In Chapter eight the relative mass a proton and electron were derived in terms of the effects energy gradients in a continuous non-quantized mass and energy component of space have on the "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension. It indicated energy gradients in a continuous non-quantized mass and energy component of space cause a distortion or "separation" in the "surfaces" of two three-dimensional space manifolds on a quantum level. This results in shifting of the equilibrium point of a resonant "structure" defined in

Chapter two "towards" or "away" from the continuous non-quantized mass component of a quantum particle. This is because Chapter ten showed the direction of the force vectors associated with a continuous non-quantized mass and energy components of space "follow" a "curvature" generated by "separation" in a "surfaces" of two three-dimensional space manifolds with respect to a fourth *spatial* dimension. Therefore, in a curved or distorted "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension the attractive forces associated with continuous non-quantized mass component of a resonate "structure" defined in Chapter two will not directly oppose the repulsive associate with a continuous non-quantized energy component of quantum particles. This will generate a volume of space that will have greater concentration of a continuous nonquantized mass component of space than the sounding volume of space because the equilibrium point of the resonant "structure" defined in a quantum particle Chapter two will shift towards the continuous non-quantized mass compo of space. The concentration of the mass component of space in these resonant "structures" is responsible for the mass of quantum particles. The mechanism outlined above defines the common mechanism in terms of a "distortion" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension for the masses and gravitational forces associated with both the microscopic universe of quantum particles and the macroscopic universe of planet stars and galaxies because it defines the forces associated with their masses in terms of a common distortion in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Earlier in Chapter eleven the force of magnetism was derived in terms of a tangential displacement of the "W" axis of the fourth *spatial* dimension with respect to three-dimensional space. However, there is a difference between gravitational and magnetic forces, which is related to the orientation of the "W" axis of the fourth *spatial* dimension with respect to the "surface" of threedimensional space. Magnetism was defined in Chapter eleven in terms of a "torque" generated on the "surface" of a three-dimensional space manifold by the non-perpendicular orientation of the “W” axis of the fourth *spatial* dimension. This causes a lateral "movement" with respect three-dimensional space of magnetic objects in three-dimensional space. However, the force of gravity is the result of a "perpendicular" "separation" with respect to the “W” axis of the fourth *spatial* dimension in a "surface" of a three-dimensional space manifold that causes the "surface" of that manifold to become "depressed". The “movement” of the mass component space towards the apex of this "depression" increases the “concentration” of the continuous non quantized mass component of space at the apex of the "depression". This increase in the concentration of the continuous non-quantized mass component of space at the apex of the "depression" is responsible for the mass of objects and particles. Chapter Thirteen The Unit Electrical Charge Return to Top

The magnitude of a unit electrical charge is related to an energy gradient in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension. (The physical mechanism proposed here for magnitude of a unit electric charge has similarities to the mechanism responsible for gravitational force defined in Chapter twelve in that they are both related to energy gradients in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension .) In Chapter one "Shadows" postulated a volume of space is composed of a continuous nonquantized field of mass and energy. In Chapter nine the magnitude and polarity of an electric potential was derived in terms of an energy gradient generated in a three-dimensional space manifold with respect to a fourth *spatial* dimension by a "rotation" of a continuous non-quantized mass or matterfield component of space. It was shown the direction, with respect to a fourth *spatial* dimension, of a "rotation" of a matterfield component of space determines the polarity of an electric charge. If one defines a "counter clockwise rotation", with respect to a fourth *spatial* dimension, in a matterfield component of space as a positive electric charge, a "clockwise rotation", with respect to the fourth *spatial* dimension, in a matterfield component of space would defined a negative electric charge. However, It can be shown the magnitude of a unit electrical charge is related to the interaction of a continuous non-quantized mass component of space with a resonant "structure" that defined the quantum properties of mass and energy in Chapter two. Chapter two derived the quantum properties of mass and energy in terms of resonant "structures" formed in space by interactions of a continuous non-quantized mass and energy field components of space. It derived the formation of these resonant "structures" in terms of a dynamic interaction between the continuous non-quantized mass and energy components of space defined by the equation E=mc^2. In Chapter three, the "velocity" of "rotation" or interactions in a continuous non-quantized mass and energy field components of space was shown to be constant and equal to the speed of light. However, according to classical physics the magnitude of an energy gradient is depended on the rotational velocity the mass responsible for generating that energy gradient. This indicates the magnitude of an energy gradient associated with a resonant "structure", defined in Chapter two, responsible for the quantum properties of both a positive and negative unit electrical charge will be identical because the "rotational" velocity of the mass component of space responsible for generating the energy gradient is constant and equal to the velocity of light. Therefore the absolute value of the magnitude of both a positive and negative unit electric charge will be identical and constant. This defines a mechanism responsible for the magnitude of a unit electric charge in terms of the magnitude of energy gradients in a three-dimensional space manifold with respect to a fourth *spatial* dimension. Another factor that determines the magnitude of the unit electrical charge is related to the attractive and repulsive properties of electrical charges. In Chapter eight, it was shown that similar electrical charges repel each other because the "rotational" direction, with respect to a fourth *spatial* dimension, of the energy gradients responsible for their similar electric charge is the same. Therefore, their rotational energies will be additive and to reduce the stress on space they will attempt to move apart.

Because of the repulsive properties of similar electric charges the magnitude of a single or unit electrical charge would be related only to the resonant properties of a single quantum unit electric charge define in Chapter two. The physical interaction of the energy gradients associated with an electric charge and the properties of four *spatial* dimensions are responsible for the magnetic field generated by a unit electric charge. In Chapter eleven it was shown a magnetic force was the result of a "torque" generated the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions by energy gradients in a three-dimensional space manifold In an electric current, the axis of rotation of the energy gradients associated with the electrical energy of moving unit electrical charges will be parallel to the direction of motion. This results in the formation of concentric rotating energy gradients around an electrical current, which will be perpendicular to the direction of motion of the electrical charges and the fourth *spatial* dimension. The "torque" generated by these energy gradients a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension are responsible for generating the concentric magnetic field around a moving electric charge. Since each moving unit electric charge contributes an equal amount of "torque", there should be direct relationship between the number of moving electrical charges and the strength of the magnetic field generated by these charges. Chapter Fourteen The Linked between Gravitational and Electrical forces Return to Top The link between gravitational and electrical forces can be established by analyzing an interaction between a continuous non-quantized mass and energy field components of space. Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of mass and energy. Later in Chapter two the quantum properties of mass and energy were derived in terms of integral energies associated with resonant "structures" formed in space by interactions of a continuous non-quantized mass and energy field components of space. It derived the formation of these resonant "structures" in terms of a dynamic interaction between a continuous non-quantized energy and mass component of space defined by the equation E=mc^2. “Shadows” defined gravitational forces in Chapter twelve and electrical forces in Chapter nine in terms of a common relationship with respect to a continuous non-quantized mass and energy field components of space. Therefore, a link between gravitational and electrical forces should be found in the interaction between a continuous non-quantized mass and energy field components of the resonate structures, defined in Chapter two, responsible for the quantum properties of both gravitational and electrical forces. However, as Richard Feynman points out on pages 24 and 25 of in his book “The Character of Physical Laws” both gravitational and electrical forces also share another common relationship with respect to the inverse square law.

"The inverse square law appears again in the electrical laws, for instance, Electricity also exerts forces inversely as the square of the distance, this time between charges, and one thinks perhaps that the inverse square of distance has some deep significance. No one has ever succeeded in making electricity and gravity different aspects of the same thing." Later he talks about the ratio of gravitational attraction to electrical repulsions: "The ratio of the gravitational attraction to electrical repulsions is given by a number with 42 digits tailing off. (The exact number was given in a diagram as Gravitation attraction / Electrical repulsion = 1/(417 X 10^42) Now therein lies a very deep mystery. Where could such a tremendous number come form? If you ever had a theory from which both of these things are to come how could they come in such disproportion? What equation has a solution which has for two kinds of forces an attraction and repulsion with that fantastic ratio." This suggests gravitational and electrical forces should also share a “common relationship” in terms of the magnitude of an interaction between a continuous non-quantized mass and energy field components of space. Chapter nine derived the magnitude of electrical potential or energy in terms of a continuous nonquantized energyfield component of space. Chapter twelve derived the magnitude of gravitational force or energy in terms of a continuous non-quantized mass component of space. Chapter two defined the relationship between a continuous non-quantized mass and energy field components of space in terms of the equation of E=mc^2. Were "E" equals the magnitude of the energyfield component of space, "m" equals the magnitude of the mass component of space, and "c" equals the speed of light. Therefore, one should be able to compare “The ratio of the gravitational attraction to electrical repulsions” in terms of the equation E=mc^2 because it defines the relationship between a continuous non-quantized mass component of space responsible for gravitational force and a continuous non-quantized energyfield component of space responsible for electrical force. Solving the equation E=m*c^2 that defines the magnitude of the mass component of space in terms of the energyfield component of space for the mass component of space or "m" gives m=E/c^2. The law of gravitation states that F=g*m*m/r^2. Therefore, by substituting the equation derived above for the magnitude of the energyfield component of the space in terms of the mass component of space the law of gravitation can be rewritten as F=(E/c^2)^2/r^2. Since, as mentioned earlier the energyfield component of space is responsible for electrical energy the equation F=(E/c^2)^2/r^2 defines the magnitude of gravitation force associated with the energy or electrical component of space in terms of the mass component of space. This also means it defines the relative magnitude, strength or ratio of gravitational energy to electrical energy in terms of the inverse square of the distance between the objects because the mass component of the mattercule is responsible for gravitational force. Using 9.0 x 20 cm/sec for the speed of light "c" squared and substituting we obtain F=E/(9.0 X 20)^2/r^2 or F=E/(8.1 X 10^41).

The value of 1/(8.1 X 10^41) represents the value of the ratio of “Gravitation attraction / Electrical repulsion” Richard Feynman was referring to in the earlier quote from his book “The Character of Physical Laws”, because it numerically defines the ratio of gravitational energy to electrical energy with respect to the continuous non-quantized mass and energy field components of space. This method does not give the exact value of 1/(417 X 10^42) for “the ratio of the gravitational attraction to electrical repulsions" is because it only took into account the internal mass and energy relationships of the resonant structures responsible of the quantum properties of gravitational and electrical forces. "Shadows" appears to have solved the “very deep mystery” as to why the inverse square law can be applied to both gravitational and electric forces by “making electricity and gravity different aspects” of a common interaction between a continuous non-quantized mass and energy field component of space. "Shadows" also answers Mr Feynman's question as to why " how could they (gravitational and electrical forces) come in such disproportion". Chapter Fifteen The “Relativity” of Four Spatial Dimensions Return to Top Einstein’s Theory of Relativity has been one of the most successful theories in the history of modern science. It has had remarkable success in explaining and predicting the experimentally observed time dilation and mass increase associated with relative velocities based primarily on the constancy of the velocity of light. However, it has also had some remarkable failures in that it has been unable to either explain or predict the quantum properties of both matter and energy. It has been and will be shown these failures can be eliminated by redefining the space-time geometry of Relativity in terms of a three-dimensional space manifold with respect to a fourth *spatial* dimension. This will allow for a more a logical explanation and prediction of the quantum properties of both matter and energy that are consistent with the relativistic properties space and time than is provided for by the "Theory of Relativity". This indicates the geometry of a three-dimensional space manifold with respect to a fourth *spatial* dimension proposed here is a more accurate and complete method of defining the physical structure of the universe than the space-time geometry of Relativity because it not only allows one to accurately explain and predict the relativistic properties of space and time but also the quantum properties of matter and energy. Earlier in Chapter twelve, the forces associated with gravity were defined in terms of a distortion or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. The curvature caused by a distortion in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is analogous to the space-time curvature Relativity postulates is responsible for gravitational forces. Therefore, both Relativity and "Shadows" define gravitational energy in terms of a distortion or "depression" in a four dimensional space manifold.

However, "Shadows" also defines the momentum or energy associated with relative velocities in terms an "elevation" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension . The justification for defining the energy of relative velocities in terms of an "elevation" instead of a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is because the energy associated with relative velocities is oppositely directed from that of gravitational energy. Therefore, a distortion in a three-dimensional space manifold with respect to a fourth *spatial* dimension "Shadows" associates with the energy of relative velocities should be oppositely directed form the distortion it associates with gravitational energy. There are numerous experimental observations to support this conclusion. The kinetic energy associated with the orbital velocities of satellites opposes the gravitational attractive energy associated with the mass of the earth and the energy associated with relative velocity of a rockets exhaust opposes the earth’s gravitational field. These experimental observations strongly suggest that if one defines gravitational energy (as was done in Chapter twelve) in terms of a "depression" in a "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension , one should define the energy associated with relative velocities in terms of opposite distortion or "elevation" in a "surface" of a threedimensional space with respect to the fourth *spatial* dimensions. The “elevation” in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with relative velocities is responsible for the mass increase observed in relative velocities. Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of mass and energy. In Chapter twelve, the magnitude of the "rest" mass of an object was defined in terms of the "quantity" of a continuous non-quantized mass component of space "contained" in a "volume" of a “depression” a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension generated by a gravitational field. "Shadows" defines the mass increase associated with relative velocities in terms of a “quantity” of a continuous non-quantized mass component of space "contained" in a “volume” of an “elevation” in a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension associated with the energy of the relative velocity of an object. The continuous non-quantized mass component of space contained in an "elevation" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would be analogous to the mass contain in the volume of a wave on the surface of water. A mass floating on water generates depression in the surface of the water. A wave on water causes the surface of the water and the mass floating on the water to rise. The total mass of the vertical volume of space occupied by the mass and the water would be equal to the mass of the object plus the mass of the water contain in the vertical volume of space occupied by the water and the mass. The elevation in the surface of the water caused by a wave would be analogous to the "elevation" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with the relative velocity of a moving object. The mass of the object must be added to the mass of the water that makes up the wave to define the total mass contained in the vertical volume of space occupied by the mass and water.

Similarly, the continuous non-quantized mass component of space "contained" in an "elevation" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the energy associated with the relative velocity of an a moving object must be added to the "rest" mass of the object occupying that volume of space to obtain the total mass "contained" in that volume of space. Therefore, the total mass of an object viewed by an observer in relative motion to that object will consist of two components. The first would be the "rest" mass or the gravitational mass component of the object. This would be equal to the magnitude of a continuous non-quantized mass component of space "contained" in a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with a gravitational field that is not moving relative to an external observer. The second would be the magnitude of a continuous non-quantized mass component of space contained in a "volume" of an “elevation” in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension “Shadows” associates with the velocity of an object relative to an external observer. Since the magnitude of the “elevation” in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension in space is related to the relative velocity of an object, the increase in mass associated with the relative velocity of the object with respect to an external observer will be dependent on the relative velocity of an object. Therefore the total mass of an object in relative motion to an external observer will be the sum of the rest mass of an object and the mass associated with a continuous non-quantized mass component of space contained in a "volume" of an “elevation” in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Using the following analogy, the relationship between relative velocity, time and length can be understood. Assume that two “2 dimensional creatures” are living on the surface of two pieces of paper resting on a desktop. Also, assume the two creatures can view the surfaces of the other piece of paper, which are separated a pencil. If the diameter of the pencil is increased, the relative curvature between the surfaces of the two pieces of paper will increase. Each of these creatures, when viewing the other piece of paper will only perceive the twodimensional translation of the three-dimensional curvature generated by the pencil. Therefore, they will view the distance between two points on the surface of the other as shorter since they will view that distance as the two-dimensional translation of the three-dimensional curvature in the surface of the paper. The movement of “time” on both surfaces will also be affected. Each will view the others “time” as moving slower because they will view the two-dimensional translation of its movement through the curvature in three-dimensional space.

Chapter ten showed three-dimensional beings perceive energy in terms of the magnitude of a relative “separation” in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Therefore increasing the energy differential or velocity between two objects would be analogous to how increasing the diameter of the pencil in the earlier example increases the relative separation and the curvature between the two surfaces of the two pieces of paper. Since three-dimensional beings can only view the three-dimensional translation of a "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension that an object in relative motion to an observer generates they will view the length of an object to be shorter with respect to a similar object that is not in motion with respect to an observer. This is analogous to why the length of a line would appear shorter to the two-dimensional "creature" viewing the surface of the paper that was separated by the pencil. Time will also appear to move slower or become dilated for observers who are in relative motion with respect to each other because three-dimensional beings will only view the three-dimensional translation of time as it moves along the "curvature" in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Since the magnitude of a "curvature" in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is related to the relative velocity of an object, the magnitude of the time dilation and the foreshortening of the length of an object will also be related to its velocity. The Lorentz transformations derived from the “Shadows” model will take on the same form as the Lorentz transformations derived from Relativity. This is because the “Shadows” model postulates the energy associated with relative velocities causes a physical curvature in the "surface" of the boundary between the third and fourth *spatial* dimension. Therefore observer (A) who in an inertial reference frame that he considers to be stationary with respect to observer (B) who is in an inertial reference frame that is in relative motion to observer (A) will measure the distance that observer (B) moves thought threedimensional space to be shorter than that measured by observer (B). This is because observer (A) can only view the three-dimensional translation or the cord of the arc generated by the curvature in four *spatial* dimensions that observer (A) associates with the kinetic energy of the relative velocity of observer (B). Also because the actual distance that observer (B) moves through threedimensional space is greater than the distance measured by observer (A) it will appear to observer (A) that time is moving slower in observer (B’s) inertial reference frame. This is because observer (B) has to travel a greater distance at a given velocity than the distance observer (A) measures because he is viewing the cord of the curvature in the surface of three-dimensional space caused by the kinetic energy observer (A) associates with his relative velocity. Therefore it will appear to observer (A) that observer (B’s) clock is running slower because of the added time required for observer (B) to travel this additional distance that is not measured by observer (A). Therefore, because both Relativity and “Shadows” predict the physical shortening of length and the slowing of time are the result of a "curvature" in dimensional space related to the relative velocity of an object, the form of the Lorentz transformations associated with the foreshortening of an object and slowing of time will be identical for both of these models. However, “Shadows” defines the magnitude of a shortening of length and a slowing or dilation of time in terms of a "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of curvature in space-time manifold as Einstein did. Gravitational energy will also cause time to slow and length to decrease for the same reason that velocity causes time to slow and length to decrease.

Chapter twelve the derived a mechanism responsible for the force of gravity in terms of a "curvature" caused by a "depression” in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Earlier “Shadows” defined a mechanism responsible for Kinetic energy of a velocity in terms of a “curvature” caused by an “elevation” in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Therefore, because both gravitational and kinetic energies are related to a common "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension they will have a similar effect on physical properties of length and time. Therefore, both Relativity and "Shadows" predict an observer in a gravitational field will measure the length of a object to be shorter and passage of time will slower with respect to an observer who is located outside of a gravitational field However; "Shadows" defines the shortening of length and slowing of time in terms of a threedimensional space manifold with respect to a fourth *spatial* dimension instead of fourdimensional space-time manifold. The "relative" characteristics of the "curvatures" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with velocities would also make it impossible for an observer to determine if he is in motion relative to another observer or whether that observer is in motion relative to him. The mechanism defined above indicates the energy associated with velocities is related to the absolute magnitude of a difference of a "curvature" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension between two objects. Therefore, each observer would view the absolute magnitude of a "curvature" in a threedimensional space manifold with respect to a fourth *spatial* dimension associated with his or her relative velocities with respect to other observers and therefore would have no way to determine which one was in motion or stationary with respect to the other. Therefore both "Shadows" and Relativity make identical predictions with respect to the relativistic properties of space and time. However, as was mentioned earlier the "Shadows" model is a broader based because it has and will show by redefining the space-time geometry of Relativity in terms of four *spatial* dimensions allows one to define a common a mechanism responsible for the relativistic properties of space and time and the quantum properties of mass and energy. Chapter Sixteen A link between Relativity and Quantum Mechanics Return to Top “Shadows” has and will demonstrate it is possible to develop a link between the relativistic properties of space and time and the quantum properties of mass and energy by redefining the space time geometry of the "Theory of Relativity" in terms of three-dimensional space manifold with respect to a fourth *spatial* dimension. Chapter fifteen, demonstrated it is possible to define a universe in terms of a three-dimensional space manifold with respect to a fourth *spatial* dimension that makes perditions identical, with

respect to the relativistic prosperities of space and time, to those made by both the Special and General Theories of Relativity. However it has and will be demonstrated it is possible to a define mechanism that predicts the quantum properties of mass and energy in terms a three-dimensional space manifold with respect to a fourth *spatial* dimension. This indicates a geometry of a three-dimensional space manifold with respect to a fourth *spatial* dimension is a more accurate and complete method of defining the physical structure of the universe than the geometry of a space-time manifold proposed by Relativity because it not only can accurately explain and predict the relativistic properties of space and time but also the quantum properties of matter and energy. Shadows” does not attribute a physical property of causality to the dimension of time as the "Theory of Relativity" does but instead defines time only as a measure of the sequential or "incremental" ordering of the causality of an event. This definition of time is more consistent with its mathematical usage in calculus because in calculus it is only required to define time in terms of the measurement of an incremental ordering of an event as the time approaches zero or infinity. Changing ones perspective on the dimension of time from one that generates causality, as Relativity does, to one that defines it only as a reference allows for defining and understanding the common processes and mechanisms responsible for both the quantum and relativistic properties of the space, time, gravitational, electrical, and magnetic forces. Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of mass and energy. Later in Chapter two, the quantum properties of mass and energy were defined in terms of integral energies associated with a resonant "structure" formed in space by "vibrations" in a continuous non-quantized mass and energy components of space. The formation of these resonant "structures" was derived in terms of a dynamic interaction between a continuous non-quantized mass and energy components of space with respect to a three-dimensional space manifold with respect to a fourth *spatial* dimension. Chapter fifteen derived the time dilation and mass increase associated with relative velocities in terms of the same non-quantized mass and energy component of space that defined the quantum properties of mass and energy in Chapter two. It was shown, “depressions” or “elevations” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension is the causality of time dilation and the mass increase associated with relative velocities. However, the effects these "elevations" and "depressions" in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension have on space and time were defined in terms of the quantum properties of the continuous non-quantized mass and energy field component of space defined in Chapter two. This provides a link between the quantum properties of mass and energy and the relativistic properties of space and time. Chapter twelve defined gravity in terms of a quantum property of a continuous non-quantized mass component of space defined in Chapter two.

The mass of an object was defined in terms of a quantity of a continuous non-quantized mass component of space continued in a "depression" or distortion in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. It was shown that a distortion or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is responsible for the force of gravity and is analogous to the space-time distortion that the Relativity postulates is responsible for the force of gravity. However, by deriving the force of gravity in terms of a relativistic property of a distortion in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension and the quantum properties "Shadows" associates with a continuous non-quantized mass and energy component of space provides a solid link between the quantum properties of gravity, mass and energy and relativistic properties of space and time. Finally, Chapter three derived the propagation of a photon in terms of a matterenergy wave on a "surface" of three-dimensional space manifold with respect to a fourth *spatial* dimension. However, the quantum properties of a photon and a matterenergy wave were mathematically derived in terms of a quantized property of a continuous non-quantized mass and energy components of the space defined in Chapter two. This defines a common mechanism responsible both the wave and quantum properties of a photon because it defines the propagation of a photon in terms of a quantized matterenergy wave on a "surface" of a third *spatial* dimension with respect to the fourth *spatial* dimension. Additionally, it provides an ability to develop a Quantum Theory of Gravity because it defines the transmission of both gravitational and electromagnetic energy in terms of a quantum property of a continuous non-quantized mass and energy components of space defined in Chapter two. Adopting the “Shadows” model over Einstein's Special and General Theories of Relativity for scientific investigations would have several advantages primarily because it can define a common mechanism responsible for the quantum and relativistic properties of all of the forces and laws of nature. Chapter Seventeen Gravitational and Kinetic Energies Linked by Four Spatial Dimension Return to Top To understand the physical link between gravitational and non-gravitational or kinetic forces requires an understanding of the mechanism responsible for their generation. Chapter fifteen derived kinetic energy in terms of a "curvature" generated by an “elevation” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. It was shown a "slope" generated in a "surface" of a three-dimensional space manifold by this "curvature" was responsible for the forces associated with kinetic energy. Chapter twelve derived gravitational energy in terms of a "curvature" generated by a “depression” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. It was shown a "slope" generated in a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension by this "curvature" was responsible for the gravitational forces associated with mass.

(This "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension responsible for gravitational energy is analogous to a curvature in a spacetime manifold that Relativity postulates is responsible for gravitational energy.) A link between gravitational and kinetic energy can found by comparing the effects a “slope” generated by a "gravitational depression” and a "kinetic energy elevation” in a "surface" of a threedimensional space manifold with rescue to a fourth spatial dimension have on an object in threedimensional space to a marble on an incline plane. The downward acceleration experienced by a marble on an incline is proportional to the magnitude of the slope of the incline and as the magnitude of the elevation and slope of the incline increases, the magnitude of the downward acceleration of the marble increases. The "incline" generated by the physical "elevation" in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension derived in Chapter fifteen to be responsible for kinetic energy has a similar effect on object in on three-dimensional space manifold with respect to a fourth *spatial* dimension Chapter fifteen defined the magnitude of kinetic energy in terms of the magnitude of a “slope” of an “elevation” in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated. Therefore, the magnitude of the acceleration experienced by an object interacting with the "slope" of a "kinetic energy elevation” in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension will be proportional to the magnitude of the kinetic energy of that object. This is analogous to how the magnitude of the downward acceleration of the marble on the incline in the earlier example was related to the magnitude of slope of the elevation of the incline. Additionally, the direction of the acceleration caused by a "kinetic energy elevation” in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would be directed away from the apex of the "elevation". Therefore, when the kinetic energy of two objects interact the acceleration caused by their interaction will be in the same direction as the velocity of the interacting objects. The “incline” generated by a physical “depression” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension derived in Chapter twelve to be responsible for gravitational energy has an effect similar to the “elevation” in space associated with kinetic energy. However, the direction of the acceleration associated with a "gravitational depression” in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension will be oppositely directed with respect to the acceleration generated by the "elevation" in a threedimensional space manifold associated with kinetic energy. This is because the "incline" generated by a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with a gravitational energy will be towards the apex of "gravitational depression" in a three-dimensional space manifold instead of away from it as was the case with a "kinetic energy elevation”. Therefore a object interacting with “incline” in a "surface" of a three-dimensional space manifold associated with a "gravitational depression" would attain a “downward” acceleration towards, not away, from the apex of a "gravitational depression” that is proportional to the magnitude of the “slope” of the “incline” generated by that "depression".

The mass an object was derived, in Chapter twelve, to be directly related to the “slope” of a "gravitational depression” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Therefore, the magnitude of the acceleration of an object interacting with the "slope" of a "gravitational depression” in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would be proportional to the mass of the object responsible for generating that "depression" in the three-dimensional space manifold. This defines a link between gravitational and kinetic energies because both are derived in terms of a common “incline” or "slope" in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension . The mechanism responsible for gravitational accelerations is derived in terms of an "incline" caused by a “depression” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension , which results in a force being directed towards the apex of the "depression" in a three-dimensional space manifold associated with the mass of an object. While the mechanism responsible for accelerations associated with kinetic energy is derived in terms an "incline" caused by an “elevation” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. This results in a force being directed away from the apex of the "elevation" in a three-dimensional space associated with the velocity of an object. Einstein's Principle of Equivalence or the inability to distinguish gravitational and non nongravitational accelerations is due to the relative characteristics of the "inclines" generated by a "kinetic energy elevation” and a "gravitational depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension . In Chapter fifteen the magnitude of the forces associated with kinetic energy or non-gravitational accelerations such as those generated by a rocket engine were defined in terms of the relative magnitude of a "slope" generated by an "elevation" in a "surface" of a three-dimensional space with respect to the fourth spatial dimension. In Chapter twelve the magnitude of the forces associated with gravitational accelerations were defined in terms of the relative magnitude of a "slope" generated by a "depression" in a "surface" of a three-dimensional space with respect to the fourth spatial dimension. Therefore, the magnitude of the forces associated with both gravitational and kinetic energy accelerations are related to absolute value of the relative magnitude not to the "direction" of the "slope" in the "surface" of a three-dimensional space manifold with respect to the fourth spatial dimension. Gravitational and non-gravitational accelerations are indistinguishable because, as show earlier, the only difference between them is the direction of a "slope" generated by gravitational and nongravitational accelerations. This defines a physical mechanism responsible for linking between gravitational and kinetic energies. Chapter Eighteen The Principal of Equivalence, Inertia & Absolute Reference Frames with respect to Four Spatial Dimensions Return to Top

The "Principal of Equivalence" addresses the fact gravitational and non-gravitational accelerations are indistinguishable, all masses "freefall" with the same acceleration in a uniform gravitational field and all inertial reference are equivalent. The validity of the "Principal of Equivalence" is related to a common distortion in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension responsible for gravitational an non-gravitational accelerations, Chapter one postulated a volume of space is composed of a continuous non-quantized “field”of mass and energy. Chapter two derived the quantum properties of mass and energy in terms of the integral energies associated with resonant "structures" formed in space by interactions of a continuous nonquantized mass and energy field component of space. It derived the formation of these resonant "structures" in terms of a dynamic interaction between a continuous non-quantized energy and mass components of space. These resonant "structures" define a "quantum mass unit of space". Chapter twelve derived a gravitational field in terms of a distortion or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. The mass of an object was shown to be directly proportional to number of "quantum mass unit of space" contained in a "volume" of a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. The magnitude of gravitational accelerations associated with mass was shown to be directly related to the magnitude of a distortion generated by a "depression" in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension. (This distortion in a "surface" of the three-dimensional space manifold with respect to a fourth *spatial* dimension is analogous to a distortion in a space-time manifold the General Theory of Relativity is postulates is responsible for gravitational accelerations.) In Chapter fifteen and seventeen the magnitude of a non-gravitational acceleration, such as one produced by the exhaust of a rocket engine, was shown to be directly related to the magnitude of a distortion or "elevation " in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. The reason gravitational and non-gravitational accelerations are indistinguishable is because they share a common causality in terms of a "slope" generated by a distortion in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension. This can be understood by comparing the effects the force of gravity has on an object to the affects the exhaust of a rocket engine has on a box of marbles. The marbles in the box will represent a "quantum mass unit of space". If a constant force, like that produced from the exhaust of a rocket were applied to a box containing marbles it would move with a constant acceleration. However, the rate of acceleration of the box would be inversely proportional to the number of marbles in the box because the mass of the box would be directly proportional to the number of marbles in the box. Similarly, the rate of acceleration of an object experiencing a force is inversely proportional to number of "quantum mass unit of space" it contains because as mentioned earlier the mass of an object is directly proportional to the number of "quantum mass units of space" it contains.

Another way of describing this would be to attach strings to each marble. If a force were equally applied simultaneously to each string, the force would be equally distributed on the strings and marbles in the box. If the number of marbles and strings were increased or decreased in the same proportion while maintaining the same total force on all the individual strings, the rate of acceleration would vary in direct proportion to the number of marbles. If an equal force is applied to each individual string tied to the marbles in the box, the box will accelerate as a unit. If the mass of the box is increased or decreased by adding or removing marbles, the number of strings will increase or decrease by the same amount. Therefore, because the same force is applied individually to each string the total force experienced by the box would vary in direct proportion the number of marbles contained or the box. This would result in the box of marbles experiencing constant uniform acceleration when a constant force is applied to each string no matter how many marbles were in the box. Attaching a string to each marble in the box and applying constant uniform force individually to each string illustrates why all masses "freefall" with the same acceleration in a uniform gravitational field The string will represent the attachment or interaction that each individual "quantum mass unit of space" in an object has with the "curvature" in a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with both gravitational accelerations. Chapter twelve derived the magnitude of gravitational force in terms of the magnitude of the "slope" of a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. This means a "slope" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with a "depression" will be uniform and constant in a uniform gravitational field. Therefore, in a uniform gravitational field, the force associated with a "depression" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension will interact with each individual "quantum mass unit of space" in a mass in a uniform and constant manner. The rate of acceleration for all objects in a uniform gravitational field is the same regardless of their mass because each individual "quantum mass unit of space" that makes up the mass of an object is "attached" or interacts with the constant uniform "curvature" in space associated with a uniform gravitational field. Because the mass of an object is directly proportional to the number of "quantum mass unit of space" it contains, increasing or decreasing the mass of an object makes a proportional increase or decrease the number of "quantum mass unit of space" contained in the mass. Therefore, the total gravitational acceleration experienced by an object in a uniform gravitational field will be directly proportional to its mass because increasing or decreasing the mass of an object makes a proportional increase or decrease in the number of "quantum mass unit of space" in that mass that interacts with the "curvature" in space "Shadows" associates with gravitational forces.

This is analogous to why the total force experienced by the box of marbles with the strings attached in the earlier example varied in direct proportion the number of marbles contained in the box. This means that all objects will "freefall" with the same acceleration regardless of their masses in a uniform gravitational field because the total gravitational force experience by an object in a uniform gravitational field would be directly proportional to its mass. The reason non-gravitational accelerations such as those generated by a rocket motor and gravitational accelerations are indistinguishable is related to the common causality of nongravitational and gravitational accelerations. Earlier it was mention Chapter fifteen and seventeen derived the magnitude of non-gravitational acceleration such as those generated by rocket exhaust in terms of the magnitude of a "slope" generated by an "elevation" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension and that Chapter twelve derived the magnitude of gravitational accelerations in terms of a magnitude of a "slope" generated by a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. This indicates that forces associated with gravitational and non-gravitational accelerations have a common casualty, which is related only to the magnitude of the "slope" in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension not to the "direction" of a "slope" in a "surface" of a three-dimensional space manifold. Therefore, because the forces associated with both gravitational and non-gravitational acceleration are only related to the absolute magnitude of a common "slope" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* they are indistinguishable. The mechanism responsible for inertial properties of mass is also due to the property of a “depression” in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension defined in Chapter twelve and an “elevation” in a "surface" of a three-dimensional space manifold defined in Chapter fifteen. In Chapter fifteen the "Relativistic" mass associated with relative motion was derived in terms of number of "quantum mass units of space" associated with the rest mass of an object plus the number of "quantum mass units of space" contained the "elevation" of the rest mass of an object with respect to a "surface" of a three-dimensional space manifold due to its velocity. Newton's law of inertia states, "An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force". The mechanism responsible for the validity of Newton's law of inertia is related to the fact that the total mass of an object, when viewed by an observer who is in relative motion to that object, would be the sum of the "quantum mass units of space" contained in an “elevation” in a threedimensional space manifold space associated with its relative velocity plus the "quantum mass unit of space" associated with with its rest mass. The law of conservation of mass / energy states that the sum of mass and energy components of a closed system remains constant. Therefore, because the total mass of an object is derived in terms of a closed *spatial* system with respect to its relative velocity "An object in motion must stay in motion with the same speed and in the same direction unless acted upon by an unbalance force" to maintain the validity of the law of conservation of mass / energy.

In other words to change the velocity of an object would require one to change the sum of the mass components of the closed *spatial* system that is that object. Therefore, its velocity must remain constant unless acted upon by some outside force. If it did not the law of conservation of mass and energy would be violated because the sum of the mass and energy of the closed *spatial* system "Shadows" associates with velocity would not be conserved. Finally, the inertial properties of the continuous non-quantized mass component of space are responsible for the absence of an absolute reference frame. Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of mass and energy. In an inertial or un-accelerated reference frame, there is no net external force acting on any portion of the volume of space in an reference frame. Therefore, all the non-quantized mass components of a volume of space in a reference frame would the identical velocities. This is because there would be no differential forces applied to the non-quantized mass components of space internal to that volume of space. Since this is an inherent property of all inertial reference frames, they are all equivalent and therefore no absolute reference frames can exist. This defines, in terms of Newtonian mechanics the physical process and mechanism that are responsible for equality of all inertial reference frames and therefore the absence of an absolute reference frame by which velocities can be measured. Chapter Nineteen The composition and structure of Quarks with respect to Four Spatial Dimensions Return to Top The purpose of this discussion is to define a mechanism responsible for the electrical structure of Quarks and how they combine to form protons and neutrons in terms of a geometry of a threedimensional space manifold with respect to a fourth *spatial* dimension. It will be shown the electrical properties of a quark is related to energy gradients in a threedimensional space manifold with respect to a fourth *spatial* dimension. It is based on the following definitions. There are six types of quarks UP/Down, Charm/Strange and Top/Bottom. The Up, Charm and Top have a fractional charge of 2/3. The Down, Strange and Bottom have a fractional charge of -1/3. A proton is made up of two Up and one Down quark, so two quarks of 2/3, which add up to 4/3 is balanced by a quark of -1/3, to give the proton an electrical charge of +1. By contrast, neutrons are made up of one Up quark (2/3) and two Down quarks (-1/3 + -1/3), so they add up to 0. Thus, the neutron has electrical charge of zero. The physical structure of Quarks is related the mechanism responsible for magnitude of a unit electrical charge derived in Chapter thirteen and a distortion of the coordinate planes of a threedimensional space manifold caused by energy gradients in a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In Chapter one "Shadows postulated a volume of space is composed of a continuous nonquantized “field” of mass and energy. Chapter thirteen derived the magnitude of a unit electrical charge in terms of energy gradients in a continuous non-quantized mass and energy component of space and the distorting effects they have on the coordinate planes of a three-dimensional space manifold with respect to a fourth *spatial* dimension. These energy gradients are generated by a rotation in a continuous nonquantized mass component of space. Because the rotational energy of an energy gradient responsible for the energy of a unit electric charge has characteristics of four *spatial* dimensions, the energy associated with it will be distributed between the coordinate planes of a three-dimensional space manifold with respect to a fourth *spatial* dimension. The electrical energy associated with the rotational energy of an energy gradient of a unit electric charge that is directed along a single coordinate plane of a three-dimensional space manifold with respect to a fourth *spatial* dimension that is parallel to coordinate plane of their rotational axis will generate a force parallel to that coordinate plane of the three-dimensional space manifold. However the electrical energy associated with the rotational energy of an energy gradient of a unit electric charge that is directed along the two coordinate planes of a three-dimensional space manifold with respect to a fourth *spatial* dimension that is perpendicular to coordinate plane of their rotational axis will generate a force perpendicular to those two coordinate plane of the threedimensional space manifold. This suggests the fractional electric charge of Quarks may be the result of the *spatial* "orientation" of the coordinate planes of a three-dimensional space manifold with respect to a fourth *spatial* dimension and the rotational energy of an energy gradient responsible for a unit electric charge. Because, as was mentioned earlier, the energy of a unit electric charge is related to a distortion energy gradients have the coordinate planes of a three-dimensional space with respect to a fourth *spatial* dimension. In other words 2/3's of the total rotational energy of the rotational energy of an energy gradient associated with a unit electric charge would be directed along the two three-dimensional coordinate planes that are perpendicular to the axis of rotation of the energy gradients with respect to a fourth *spatial* dimension. The remaining 1/3 of the total rotational energy associated with the rotational energy of an energy gradient of a unit electrical charge would be directed along a single coordinate plane of threedimensional space that was parallel to the rotational axis of the energy gradients with respect to a fourth *spatial* dimension. The fractional charge of the Up, Charm and Top quarks is associated with the rotational energy of an energy gradient directed along the two three-dimensional coordinate planes that are perpendicular, with respect to a fourth *spatial* dimension, to the axis of rotation of the energy gradient responsible for a unit electric charge. . Therefore, they would posses 2/3 of the total electrical charge and rotational energy associated with the energy gradients responsible for a unit electrical charge. The fractional charge of the Down. Strange and Bottom quarks is associated with the rotational energy of an energy gradient directed along a single three-dimensional coordinate plane that are parallel, with respect to a fourth *spatial* dimension, to the axis of rotation of the energy gradient responsible for a unit electric charge. Therefore, they would posses 1/3 of the total electrical charge and rotational energy associated with an energy gradient responsible for a unit electrical charge.

A proton is made up of two Up and one Down Quark. One of these Up Quarks is a result of a summation of the rotational energy associated with a positive unit electric charge that is directed along the two three-dimensional coordinate planes that are perpendicular to the rotational axis of the energy gradients with respect to a fourth *spatial* dimension. Therefore, it will have a charge of 2/3 of the total positive electrical charge of the proton. However, this results in an imbalance in the rotational energies associated with the positive unit electric charge of a proton that is directed along the single coordinate plane of three-dimensional space that is parallel to the rotational axis of the energy gradient responsible for unit electrical charge of a proton. This because the energy associated with a unit electric charge of a proton is distributed between all three coordinate planes of three-dimensional space. To balance the positive electrical energy directed along the single coordinate plane that is parallel to the rotational axis of the energy gradient associated with the unit electric charge of a proton, a proton attracts an electron whose negative electrical energy is oppositely directed along the single coordinate plane that is parallel to the axis of rotation of the electrical energy of a proton. This electric energy directed along the single coordinal plane of a proton is associated with down quark because it will have 1/3 of the energy of the energy gradient associated with the negative unit electric charge of an electron. This balances and restores the symmetry of the rotational energy of the electrical charges with respect to the single coordinate plane that is parallel, with respect to a fourth *spatial* dimension, to the positive electrical energy of the proton directed along that coordinate plane. However, as mentioned earlier the rotational electrical energies associated the both the unit negative and positive electric charges are divided or distributed between all the coordinate planes of three-dimensional space. Therefore, to balance the rotational energies associated with the unit negative electric charge of an electron directed along the two coordinate planes of three-dimensional space that are perpendicular to the axis of rotation of the energy gradients associated with the electrical energy of the electron, the proton "attacks" another Up quark. This balances the electrical energy associated with the electron with the proton's that is directed along the two coordinate planes of three-dimensional space that are perpendicular to the axis of rotation of the energy gradient associated with the electron with respect to a fourth *spatial* dimension. Therefore, to balance electrical energy associated with a positive and negative unit charge, a proton should be and is made up of two Up quarks with a charge of +2/3 and one Down quark with a charge -1/3 leaving the proton with the rotational energy associated with an electrical charge of plus one. A neutron is the result of the positive electrical charge of the proton "absorbing" or adding the negative electrical charge of the electron by the combining of the rotational energies that is directed parallel to the rotational axis of the energy gradients responsible the both the positive and negative unit electric charge. This results in the cancellation of the electrical charge of the electron and proton. This could be express in terms of quarks as the addition of two Down quarks (-1/3 + -1/3), which add up to -2/3 being added to the +2/3 charge of the up quark. This results in the neutron having an electrical charge of zero.

Since the electrical charge has been canceled and the neutron is electrically balanced, there is no need for the addition of the Up quark that was needed in the proton to balance the rotational energy associated with the Down quark. Therefore, a neutron should and does consist of one Up Quark (2/3) and two Down quarks. Chapter Twenty The relative masses of the Fundamental Quantum Particles Return to Top As Brian Greene pointed out in his book "The Elegant Universe", one of the unsolved mysteries of modern particle physics is why every fundamental particle encountered to date can be group into three families. "Physicists have recognized a pattern among these particles displayed in the following table. The matter particles neatly fall into three groups, which are often called families. Each family contains two of the quarks an electron or one of its cousins and one of their neutrino species. The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family."

Family 1

Family 2

Family 3

Particle

Mass

Particle

Mass

Particle

Mass

Electron

.00054

Muon

.11

Tau

1.9

Electron Neutrino

< 10^-8

Muon Neutrino

< .0003

Tau Neutrino

< .033

Up Quark

.0047

Charm Quark

1.6

Top Quark

189

Down Quark

.0074

Strange Quark

.16

Bottom Quark

5.2

The answer to Brian Greene's question regarding why the particles in the above table have “identical properties except for their mass, which grows larger in each successive family” is related to resonant "structures" that defined a fundamental quantum particle in Chapter two, energy gradients in a three-dimensional space manifold with respect to a fourth *spatial* dimension that defines the polarity of the unit electric charge, and a mechanism defining mass derived in Chapters twelve. In Chapter one "Shadows" postulated a volume of space is composed of a continuous nonquantized “field” of mass and energy. Later, in Chapter two, the quantum properties of mass and energy were defined in terms of integral energies associated with resonant "structures" formed in space by "vibrations" in a continuous non-quantized mass and energy components of space. The formation of these resonant "structures" was derived in terms of a dynamic interaction between a continuous nonquantized mass and energy components of space. These "resonant mass structures" are called mattercules. In Chapter eight, the relative masses of the proton and the fundamental quantum particle called the electron were derived in terms of "where" a "resonant equilibrium" was established in a continuous non-quantized mass and energy component space internal to a "resonate mass structure" defined in Chapter thirteen showed energy gradients in a three-dimensional space

manifold with respect to a fourth *spatial* dimension is responsible electrical energy and the polarity of the unit electric charge of protons and electrons. These energy gradients are caused by a rotation of a continuous non-quantized mass components of space and the polarity of an electrical charge is dependent on the rotational direction of a continuous non-quantized mass component of space. It was shown energy gradients in a three-dimensional space manifold cause the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to become either "depressed" for a positively charged particle or "elevated" for a negatively charged particle. The "elevation", with respect to the fourth spatial dimension, in a "surface" of a three-dimensional space manifold associated with the energy gradient of an electron causes the "resonant equilibrium" between a continuous non-quantized mass and energy field components of the electron to shift towards the energyfield component of space. While the "depression" in a "surface" of a three-dimensional space manifold associated with the energy gradient of a proton causes the "resonant equilibrium" between the mass and energy components of the proton to shift towards the mass component of the space. As was mentioned earlier, the relative mass of the electron with respect to the proton was derived in Chapter two between the mass and energy components was established internal to the electron and proton . In Chapter twelve, the mass of a macroscopic object, such as a star or planet was derived in terms of the quantity of a continuous non-quantized mass component of space contained in a "depression" in a three-dimensional space manifold with respect to a fourth spatial dimension. The relative magnitude of the "depression" was defined in terms of a "spatial separation", with respect to a fourth spatial dimension, of the three-dimension space manifold of an object to the three-dimensional space manifold of volume of space that does not contain an the object. This indicates the relative "spatial separation" between "surfaces" of two adjacent threedimensional space manifolds with respect to a fourth *spatial* dimension determines the mass of an object Together Chapter eight and twelve define the mechanism that determines the relative mass of all objects and particles in terms of a "spatial separation", with respect to a fourth spatial dimension, of a "surface" of a three-dimensional space manifold associated with an object to a "surface" of a three-dimensional space manifold not associated with that object. In Because Chapter twelve showed a mass of a particle depends on its "spatial separation" with respect to a fourth spatial dimension the mass of a fundamental quantum particle generated in a relatively high-energy environment will be greater than one generated in a relatively low-energy environment. However, the masses of fundamental quantum particles cannot take on any random value because the mass associated with each family is the result of a resonant relationship between the continuous non-quantized mass and energy components of space defined in Chapter two and the energy environment in which they were generated. Therefore, because there are only specific points in space where the mass and energy components of space and the energy content of their environment can resonant, each of the corresponding particle type across the three families must have a specific mass related to the energy associated with the environment in which they were generated. The particles in the first family are found in relativity low energy environments, are relatively stable, and for the most part can be observed in nature. However, the particles in the second and third families are for the most part unstable and can be observed only in high-energy particle

interactions in particle accelerators. The exception is the Muon in the second family of fundamental particles, which is observed in the high-energy environment of cosmic radiation. The relative masses of the fundamental particles increases in each successive family because as shown in Chapter ten the higher-energy environments were they are generated in results in the corresponding particles in each successive family to be formed with a greater relative "spatial separation" in terms of the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension than the particle in the preceding families. Therefore, the corresponding particles in the second family will have a greater mass than the particles in the first family because the "spatial separation", with respect to a fourth spatial dimension, of the three-dimensional space manifold associated with the second family is greater then the spatial separation", with respect to a fourth spatial dimension, of the three-dimensional space manifold associated with the first family. This will result in the particles in the second family physically having a larger “quantum volume” than corresponding particles in the first family. Similarly, the corresponding quantum particles in the third family will have a greater mass than those in the second family because the "spatial separation", with respect to a fourth spatial dimension, of the three-dimensional space manifold associated with the third family is greater then the spatial separation", with respect to a fourth spatial dimension, of the three-dimensional space manifold associated with the second family. This will result in the particles in the third family physically having a larger “quantum volume” than corresponding particles in the second family. This defines the mechanism responsible for the increase in mass of the fundamental quantum particles across the three families in terms four spatial dimensions and the resonant properties “Shadows” associated with the mass and energy components of space. The corresponding particle types across the three families have similar electrical properties because as shown in Chapter nineteen the electrical properties of a fundamental quantum particle are related to the orientation of the "W" axis of the fourth spatial dimension with the axis of threedimensional space. Therefore, each corresponding particle across the three families will have similar electrical properties because the orientation of the "W" axis of the fourth spatial dimension with respect to the axis of three-dimensional space is the same for the corresponding particles in all of the families. This defines the physical mechanism for “The corresponding particle types across the three families having identical properties except for their mass, which grows larger in each successive family”. Chapter Twenty-One The Origin of the Positron in terms of Four Spatial Dimensions Return to Top The origin of the positron can be traced to interactions between a continuous non-quantized mass and energy component of space and a three-dimensional space manifold with respect to a fourth *spatial* dimension. Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of mass and energy.

Chapter two derived the quantum properties of mass and energy was in terms of integral energies associated with a resonant "structure" formed in space by "vibrations" in a continuous nonquantized mass and energy component of space. The formation of these resonant "structures" was derived in terms of a "vibration" between a continuous non-quantized mass and energy components of space. In Chapter three, the propagation of a photon's energy was defined in terms of a matterenergy wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. This matterenergy wave was generated by a coupling of the energy associated "vibrations" in a continuous non-quantized mass and energy components of space from one region of space to the next. The "vibrations" in a continuous non-quantized mass and energy component of space caused by the passage of a matterenergy generate the resonant "structures" that define the quantum properties of mass and energy in Chapter two also define the quantum properties of a photon. However, the coupling of the energy of "vibrations" in a continuous non-quantized mass and energy component of space that are responsible for the propagation of a photon's energy are also responsible for the generation of the electron-positron pair describe in the following article provided by Elsharony Hemetis. "As is known electrons and positrons are identical twins with anti rotations. This infers that the physical structure of electrons and positrons are polar structures. Yes they are. A Photon is a magnetic field tornado of double conical structure with the Electron and positron connected at the base. If a Photon hits or enters the premises of a (super intensity) magnetic field, it breaks up forming a positron-electron pair. The electric charge is a function of the direction of the magnetic flux entering the base of the tornado or leaving out from it. Think of positrons as a magnetic flux pump made of magnetic flux similar to air and tornadoes. This theory infers that there is nothing such as elementary particles. The word elementary is a relatively absolute or a temporarily absolute that reflects the latest scientific analysis of physical structures." Chapter three showed the quantum properties of a photon were due to resonant "structures" generated in space by "vibrations" in the magnitude of a continuous non-quantized mass and energy components of the space. These "vibrations" generate a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension , which is responsible for a photon's energy. (The fourth spatial dimension was defined in Chapter ten.) The "vibrations" in the continuous non-quantized mass and energy field components of space responsible for matterenergy wave associated with the propagation of a photon can be understood by comparing it to vibrations associated with a wave on the surface of water. The trough of a wave on water displaces the vertical volume of water occupied by the water with air. The displaced volume of the air represents the energy associated with the weight of the displace water. Summarily the peak of the standing wave displaces the air above the surface of the water with water. The displaced air represents the volume associated with the energy of the displaced water. In Chapter ten, "Shadows" will derive all forms of energy in terms of a displacement of a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension The "vibrations" in a continuous non quantized mass and energy field components of space associated with a matterenergy wave responsible for the propagation of a photon establishes a wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The trough of this matterenergy wave displaces the matterfield component of space below a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension with energy. The displacement in a "surface" of the three-dimensional space manifold caused by this matterenergy wave is viewed as energy because in Chapter ten derived a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension as the casualty of energy. Similarly, the peak of this matterenergy wave displaces a "volume" of four-dimensional space above a "surface" of a three-dimensional space manifold with the matterfield component of threedimensional space. Chapter three derived the magnitude of a photon’s energy in terms of the frequency of "vibrations" a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension and defined the propagation of these "vibrations" in terms of the coupling of the energy associated with these vibrations from one region of space to the next. In Chapter eleven, the electrical and magnetic components of a photon were derived in terms of the effects it had on the "surface" of a three-dimensional space manifold with respect to the fourth spatial dimension. The electrical component of a photon’s energy was derived in terms of the energy associated with sinusoidal vibrations in the mass and energy components space that are parallel to the velocity vector of a photon and the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension While the magnetic component of a photon’s energy was derived in terms of the energy associated with the sinusoidal vibrations of the mass and energy components space that are perpendicular or tangential to the velocity vector of the photon and a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension. The polarity of the magnetic component of a photon's energy is determined by its relationship to the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension If the peak or “elevated” portion of the matterenergy wave associated with the propagation of a photon was defined as the magnetic south pole, the trough or "depressed" potion of the matterenergy wave would be defined as the north pole of the matterenergy wave. The formation of an electron-positron pair described in Hemetis article is caused by the "torque" generated by the super intense magnetic field mentioned in his article on the polar magnetic field of the matterenergy wave responsible for the propagation of a photon's energy. It results in the “twisting” of the "orientation" of the matterenergy wave so that it is no longer moving parallel to the "surface" between the third and fourth spatial dimension. Therefore, some of energy associated with the matterenergy wave will be directed above and some will be directed below the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension The torque generated by the “twisting” force associated with the super intense magnetic field will generate identical but oppositely rotating energy gradients “above” and “below” the “surface” of the three-dimensional space manifold.

These oppositely rotating energy gradients generated by a photon passing through a supper intense magnetic field are responsible for the electron-positron pair formation mention in the above article. In Chapter thirteen polarity of an electric charge was derived in terms of rotational energy of energy gradients in a continuous non-quantized mass and energy components of space. A negative electrical charge was defined in terms of a rotational direction of an energy gradient in a continuous non-quantized mass and energy field components of space, while a positive electrical charge was defined in terms of an oppositely rotating energy gradient in a continuous non-quantized mass and energy field components of space. The mass of an electron was derived in terms of the “quantity” of a continuous non-quantized mass component of space contained “elevation” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the directional rotation of energy gradients in the mass and energy components of space. As mentioned earlier, when a photon passes through a supper intense magnetic field a "torque" will be generated on the matterenergy wave associated with the propagation of a photon. This "torque" will “twist” the orientation of the matterenergy wave so it will no longer be moving parallel to the "surface" of a third spatial dimension manifold with respect to a fourth spatial dimension. This will result in two identical but oppositely rotating energy gradients one "above” the “surface” of the third and fourth spatial dimension boundary and one “below” it. The energy gradient generated by the super intense magnetic field "above" the “surface” of a three-dimensional space manifold with respect to a fourth spatial dimension will have all of physical properties associated with an electron defined in Chapter eight. However the energy gradient generated "below" the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the interaction of a photon with a supper intense magnetic will have all the physical properties associated with a positron. It will have a positive electrical charge because the rotational energy of the mass and energy field components of space associated with its electrical charge will be opposite to that of an electron. Therefore the resonant "structures" defined in Chapter two that are associated with the mass of the positron and electron are out of phase therefore, when the interact they will "annihilate" each other. This results in the release the energy associated with their combined mass. This defines the origin and physical characteristics of the positron in terms of physical properties of three-dimensional on space manifold with respect to a fourth spatial dimension. Chapter Twenty-Two The Dimensional Mechanics Return to Top Einstein predicted E=Mc^2 based primarily on the observation that the velocity of light remained constant despite the relative motion of an observer. He used mathematical arguments and conceptual thought experiments to justify his equation. His arguments were credible enough for some to expend the energy necessary to see if his predication that mass could be converted to energy was possible. This resulted in the development of nuclear power.

“Shadows” also uses mathematical and conceptual thought experiments similar to those of Einstein to demonstrate the universe is composed of four spatial dimensions instead of fourdimensional space-time. Additionally in Chapters two, three, and fifteen "Shadows" defines the relativistic properties of space and time, the quantum properties of mass and energy and the consistency of the velocity of light in terms of a common mechanism with respect of four spatial dimensions. Unfortunately, Einstein's theories could only define a mechanism for the relativistic properties of space and time and not one that could account for the quantum properties of mass and energy. Therefore, the arguments presented in this paper would appear to be more credible and more universally applicable than those presented by Einstein because they define a common mechanism responsible for both relativistic properties of space and time and the quantum prosperities of mass and energy where his theories could not. What humankind must determine is if the arguments presented in this paper are credible enough to justify expending the energy necessary to examine the all of the possibilities, including highspeed four dimensional communications networks and energy “wave guides" for transporting energy through the fourth spatial dimension analogous to how electromagnetic wave-guides transport energy between different regions of three-dimensional space. Below is a brief explanation of another potential benefit that may arise from analyzing the concepts contained the Shadows paper. The development of a device called a Magnetic Resonator which may allow for movement through the fourth spatial dimension at velocities greater than light. Chapter ten derived the mechanism responsible for accelerations of objects in three-dimensional space in terms of a "shifting" of the orientation of the “W” axis of the fourth spatial dimension with respect to the axes of three-dimensional space. (The "W" axis of the fourth spatial dimension was defined in Chapter ten.) Chapter eleven derived magnetic forces in terms of a "torque" generated on "W" axis of the fourth spatial dimension by forces in three-dimensional space. Therefore, it should be possible to build a device that will allow for the movement of objects through space by using the "torque" generated by a magnetic field. If one could fabricate a "Magnetic Resonator", a device that generates two concentric independently rotating spherical magnetic fields it MAY be possible to use the magnetic fields generated by this device to accelerate objects to velocities approaching the velocity of light. It must also be designed so that the axes of rotation of the magnetic spheres are independent so that their orientation with respect to each other can be varied. If one misaligns the orientation of the rotational axis of the two magnetic spheres so that their magnetic poles do not line up with respect to the "W" axis of the fourth spatial dimension, a differential "torque" will be generated on the "W" axis of the fourth spatial dimension internal to the spheres with respect to one of the axis of three-dimensional space external to the magnetic spheres. This will result in "shifting" the orientation of the "W" axis of the fourth spatial dimension associated with the space and objects internal to magnetic spheres with respect to the space and objects outside of the magnetic spheres. The mechanisms defined in Chapter ten indicate this differential "torque" generated by the Magnetic Resonator on the "W" axis of the fourth spatial dimension will be directed along one of the axis of three-dimension space with respect to the "W" axis of the fourth spatial dimension.

This will result in the Magnetic Resonator and its contents accelerating along that axis. If the generators of the magnetic fields were located internal to the spheres, the acceleration could be maintained as the magnetic spheres moved thought space. In addition, if the strength of the magnetic fields is large enough it may be possible to "lift" the "Magnetic Resonator" and its contents "out" of three-dimensional space into the fourth spatial dimension were according to the theoretical predictions of “Shadows” it could travel faster than the speed of light. It should be pointed out that traveling through space is different from traveling in space. This can be understood by comparing space travel using these concepts to traveling in an aircraft. When an aircraft is flying only the external parts of an aircraft, the wings and fuselage, are traveling in the atmosphere and are exposed to the forces associated with the velocity of the wind. However, the people in the cabin of the aircraft are flying through atmosphere and therefore do not experience the forces associated with the wind. In other words, the wings and fuselage absorb all of the forces associated with the wind generated by the motion of the aircraft shielding the people traveling in the cabin are from them. A similar effect would occur when a “Magnetic Resonator” is moving in space. Only the external parts or the magnetic shells of the Magnetic Resonator, which are traveling in space, will be exposed to the forces associated with acceleration and motion. However, the objects internal to the magnetic spheres would be moving through space and therefore would not experience the forces associated with acceleration. This is analogous to how objects and people in the cabin of an aircraft do not feel the forces associated with the wind. In other words, the magnetic spheres of the Magnetic Resonator will absorb some of the forces associated with the accelerations generated by the motion of the magnetic resonator through space. Unfortunately, human civilization presently does not have the technology or access to the large energy resources required to make this mode of transportation practical. However there are a number of ways in which the dimensional properties of space can be developed with present technologies for the benefit of humankind such as high speed communications networks using the faster light information transfer rates predicted by “Shadows” in the fourth spatial dimension. The number of benefits of these ideas can bring to humankind is only limited by the imagination and intellect of those who explore it. The explanation of the magnetic resonator was not meant to show us how to build it, but to give a very basic understanding of dimensional mechanics and give direction to our imagination and intellect. Imaginations search Intellects explore Chapter Twenty-Three The Experimental Verification of “Shadows” Return to Top

In Chapter one "Shadows" postulated a volume of space is composed of a continuous nonquantized “field” of mass and energy. Chapter two defined the quantum properties of mass and energy in terms of resonant "structures" formed by "vibrations" in a continuous non-quantized matter and energyfield component of space. It derived the formation of these resonant "structures" in terms of "vibrations" in a continuous nonquantized energy and mass components of space. Chapter three derived the propagation of a photon in terms of the quantized properties of a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. It was shown the quantum properties of a matterenergy wave and a photon are a result of resonant "structures" formed in a continuous non-quantized mass and energy components of space by the passage of a matterenergy wave. The mechanism responsible for the movement of a matterenergy wave on the "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension is similar to the mechanism reasonable for the movement of a wave on the surface of water. The trough of a wave on water displaces the vertical volume of water occupied by the water with air. The displaced volume of the air represents the energy associated with the weight of the displace water. Summarily the peak of the wave displaces the air above the surface of the water with water. The displaced air represents the volume associated with the energy of the displaced water. "Vibrations" in a continuous non-quantized matter and energy field component of space establishes a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension that is responsible for the propagation of a photon. The trough of this matterenergy wave displaces the mass component of space below the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension with energy. Similarly, the peak of this matterenergy wave displaces the "volume" of four-dimensional space above the "surface" of a three-dimensional space manifold with the mass component of threedimensional space. The following discussion will describe two experimental techniques, which will allow for the direct physical observation and measurement of a continuous non-quantized mass component of space responsible for the propagation of electromagnetic energy. The first method describes a modification of the Michelson-Gale experiment, which was performed to verify or refute the physical existence of a medium thought to be responsible for the propagation of electromagnetic energy by observing a fringe shift in light with respect to the rotational velocity of the earth. The second will describe a method of correlating the energy loss or anomalous acceleration NASA has observed on its deep space probes with the red shift observed in the spectra of stars. As mentioned earlier, Chapter three derived the propagation of electromagnetic energy in terms of a quantized matterenergy wave composed of the non-quantized mass and energy components of space. Therefore, because light is transmitted by a matterenergy wave, which is, in part, made up of a continuous non-quantized mass component of space, the mass component of the matterenergy wave should be affected by a gravitational field.

Michelson-Morley preformed an experiment utilizing and interferometer, as describe in Curt Renshaw’s physics home page http://renshaw.teleinc.com/papers/fizeau/fizeau.stm. Its purpose was to measure the orbital velocity of the earth as it moved though a medium that was thought to support the propagation of electromagnetic energy by observing a fringe shift in frequency of light as the apparatus was rotated through 90 degrees. It was assumed, if light did travel on a medium, the relative motion of the earth with respect to that medium it would be affected by its velocity. By rotating the test apparatus through 90 degrees, it was possible to observe the affects the movement of the earth through that medium had on the speed of light. This would analogous to the effect wind has on the speed of an aircraft. The ground speed of an aircraft is slower when traveling into the wind than when it is traveling with the wind. The fringe shift of light in the Michelson Morley experiment is a very sensitive way of determining any difference in the velocity of light with respect to direction. However, no fringe shift was observed when the experiment was preformed. This meant the speed of light was independent of the motion of the earth. There can only be two explanations for this. The first is electromagnetic energy is not transmitted through space by a physical medium and therefore the matterenergy wave that “Shadows” defines as being responsible for the propagation of light does not exist. The second possibility is the medium light travels on has the same relative velocity as the earth. This would be the case if light were physical propagated by a matterenergy wave because the continuous non-quantized mass component of a matterenergy wave would be attracted by the earth's gravitational field, as was shown in Chapter twelve, and therefore would have the same orbital velocity as the earth. Therefore, the lack of an observed fringe shift in the Michelson-Morley experiment not only supports the conclusions of Einstein's Theory of Relativity that the propagation of light is not supported by a physical medium but it also supports “Shadows” postulate that the propagation of light is supported by a physical medium composed of a continuous non-quantized mass component of space. In other words, the lack of an observed fringe shift in the Michelson-Morley experiment cannot be used to verify or refute the existence of a matterenergy wave "Shadows" postulates is responsible for the propagation of light. However, a fringe shift in light was observed in an experiment designed by Michelson-Gale, as described in Curt Renshaw’s physics home page http://renshaw.teleinc.com/papers/fizeau/fizeau.stm that appears to support the Relativistic conclusion that light is not transmitted by a physical medium. This experiment involved accurately measuring the velocity of light with respect to the earth rotation. This was accomplished by constructing a large rectangular array of pipes and mirrors with the legs lying in the direction of the earth's rotation being longer than the legs lying longitudinal to the

earth's rotation and a calibration loop in which light traveled only a negligible distance in longitudinal direction. The effect of the earth's motion through a medium that was though to support the propagation of light could be discovered by comparing the fringe displacement of light that transverses the large loop to that of the calibration loop. However, “Shadows” also predicts that a fringe shift should be observed in the Michelson-Gail experiment, which is directly related to the physical existence of a continuous non-quantized mass component of space. In Chapter three, “Shadows” defined a matterenergy wave associated with the propagation of light in terms of a quantized resonant "vibration" in a continuous non-quantized mass and energy field component of a volume of space. Because this matterenergy wave posses properties associated with mass it would be affected by the centrifugal forces associated with the earth's rotation. This would be analogous to the effect an object in a car experiences when rounding a corner. The centrifugal force resulting from a car rounding a corner results in the objects in the car being accelerated towards the outside of the circle generated by the car rounding the corner. Similarly, the mass component of a matterenergy wave would be accelerated and move towards the outside of the circle generated by the rotation of the earth. This perpendicular movement of a mass component of a matterenergy wave with respect to the direction of the matterenergy wave will affect its velocity in the same manner as moving water affects the velocity of a water wave that is moving perpendicular to its motion. A water wave moving perpendicular to the flow of water takes longer to make a round trip between two points on the surface of the water than it would take the water were not flowing with respect to the wave. Similarly, a matterenergy wave responsible for the propagation of light would take longer to make a round trip between two points on a "surface" of a three-dimensional space manifold that was moving perpendicular to the mass component of space than it would if it were not moving perpendicular to the mass component of space. This would affect the velocity of light in the Michelson-Gale experiment mentioned above resulting in the observed fringe shift. Therefore, the observed fringe shift in the Michelson-Gale experiment not only supports the conclusion of Einstein's Theory of Relativity that the propagation of light is not supported by a physical medium but it also supports the “Shadows” postulate that the propagation of light is supported by a physical medium composed of the continuous non-quantized mass component of space. However, there is an experiment that could determine if the fringe shift observed in the MichelsonGale experiment was the result of velocity related to the Earth's orbit, as Relativity predicts, or as "Shadows" predicts, is the result of the movement of a continuous non-quantized mass component space. Construct a test platform using two Michelson-Gale interferometers in which one is oriented so the calibration path is perpendicular to the earth's rotation and the other so that it is parallel to the earth's rotation. One could determine if the fringe shift observed was due the movement of a nonquantized mass component of space by comparing the magnitude of the fringe in the two interferometers.

"Shadows" predicts magnitude of the fringe shift observed in the two interferometers should be different due to the fact the distance used for measuring the parallel velocity of light with respect to the earth rotation will be different in each interferometer. This is because the time it will take the matterenergy wave to travel a given distance "upstream" through the movement of the mass component of space and back will be different between the two interferometers because the length of the upstream distance traveled by the light in each interferometer will be different. If Relativity's prediction of the fringe shift observed in the Michelson-Gail interferometers is based solely on the rotational velocity of the earth then magnitude of the fringe shift observed in Michelson-Gale interferometer that is orientated perpendicular to the rotational velocity of the earth should be identical to the one that is parallel to the earth rotational velocity. If however, the magnitude of the fringe shift observed in the Michelson gale interferometer orientated perpendicular to the earth rotation is different from the magnitude of the fringe shift observed in the one that is orientated parallel to the earth's rotation it would have a tendency to support the "Shadows" postulate that electromagnetic energy is transmitted by a matterenergy wave. As mentioned earlier, there is another independent way of confirming if space is composed of a continuous non-quantized component related to mass. It is based on the correlation of the energy loss or the anomalous accelerations NASA has observed on its deep space probes with the red shift observed in the spectra of stars. In the following article which appeared in the Physics News Update The American Institute of Physics Bulletin of Physics News http://www.aip.org/physnews/update/ Number 391, September 15, 1998 by Phillip F. Schewe and Ben Stein of NASA reported observing an anomalous acceleration in several of its space probes that is consistent with “Shadows” concept of inertial properties of the continuous non-quantized mass of volume space of a volume of space. (These findings of Phillip F Schewe and Ben Stein were confirmed in Physics News update http://www.aip.org/physnews/update/ article 447) "ANOMALOUS ACCELERATION. Data from several spacecraft, including Pioneer 10 and 11, Galileo, and Ulysses provide evidence for an unexplained, weak, long-range acceleration, a new report shows. Position and velocity information is derived from radio signals sent from the craft to the Deep Space Network back on Earth. Any change in velocity over time can be ascribed to a variety of known sources: the sun and planets, the solar wind, the Milky Way, the Kuiper belt, etc. But even after taking this all into account, as well as other possibilities such as the presence of dark matter in the solar system (only a millionth of a solar mass of dark matter could reside within the orbit of Uranus, it is estimated) or gas leakage from the vehicles themselves, a small acceleration in the direction of the Sun---8 x 10-8 cm/sec^2 for Pioneer 10---remains unaccounted for. Signs of this anomaly first appeared in the Pioneer tracking as long ago as 1980 Pioneer 10 was launched in 1972 and is presently 70 astronomical units from Earth. Now six space scientists, armed with many years of Pioneer data, supplemented with trajectory information from Galileo and Ulysses, have carried out the first thorough analysis of the problem and find the anomaly to be as persistent as ever. (The Voyager spacecraft are less useful for determining acceleration anomalies.) The researchers doubt but do not rule out the possibility of a novel gravitational effect or other kind of new physics. Alternative explanations include subtle systematic errors in the data analysis or unexpected aspects of space navigation. Further work on this problem may extend to the observed motions of planets, comets, and the proposed Pluto Express craft. (John D. Anderson et al., Physical Review Letters, 5 October 1998 contact John Anderson at JPL, 818-3543956, [email protected] or Michael Nieto at Los Alamos, 505-667-6127, [email protected] journalists can obtain copies of the article from AIP Public Information.)" As mentioned earlier Chapter one, postulates a volume of space is composed of a continuous non-quantized “field” of mass and energy.

Therefore, space with no subatomic or quantum particles present contains mass. The inertial or decelerating properties of a continuous non-quantized mass component of space are responsible for the anomalous decelerations observed in NASA space probes (In the above article, the anomalous acceleration was referring to acceleration towards the sun or a deceleration of the space probes.) The deceleration caused by a continuous non-quantized mass component of space would be analogous to the slowing or decelerating affects air has on the movement of aircraft. The inertial properties of air provide resistance to the movement of an aircraft causing it to slow or decelerate. Similarly, the inertial properties of a continuous non-quantized mass component of space would provide "resistance" to a space probes movement causing it to slow or decelerate. It may be possible to analytically verify a connection between the anomalous acceleration, which NASA has observed on several of its deep space probes and the existence of a continuous nonquantized mass component of space by comparing it to the red shift observed in the emission spectra of stars. Chapter One showed a portion of the energy loss associated with red shift observed in the spectra of stars might be due to the "resistive" or decelerating properties "Shadows" associates with a continuous non-quantized mass component of a volume of space. If the anomalous energy loss NASA's has observed in its space probes is due to a decelerating property of a continuous non-quantized mass component of space then it should be possible to correlate the energy loss of NASA's space probes to the energy loss "Shadows" associates with the red shift in the spectral lines of light because they are both related to the existence of a continuous non-quantized mass component of space. One could determine a "drag coefficient" for space by measuring the percentage of an energy loss associated with the red shifting of light that was related only to the distance it traveled. (The energy loss of red shifted light due to the relative motion of the object being observed must be factored out because it is not related to the inertial properties of the mass component of space.) Then by dividing the total distance traveled by the light by the percentage of energy loss light experiences travailing that distance one could determine the percentage of energy lost due to the inertial or decelerating properties of space per unit of distance the light has traveled. Since NASA knows the distance that the space probes have traveled, they could easily determine what percentage of their energy or momentum should be lost due to the inertial or decelerating properties of a continuous non-quantized mass component of a volume of space based on energy loss associated with red shifted light.If this correlates with the observed momentum loss of the space probes associated with the anomalous acceleration NASA has observed on its deep space probes it would have a tendency to verify the existence of a continuous non-quantized mass component of space. As was pointed out in the above Physics News Update article even after taking into account "other possibilities such as the presence of "Dark Matter" in the solar system the observed deceleration of these space probes cannot be accounted for. However, Shadows defines Dark Matter in a much broader sense than what was suggested in the article appearing in the Physics News Update regarding the deceleration of NASA space probes. It derives the existence of "Dark Matter" in terms of a continuous non-quantized mass components of three-dimensional space. This is a broader definition of "Dark Matter" than the

one suggested in the article because it attributes Dark matter to a continuous non-quantized mass component of a volume of space and NOT to any particle such as protons, neutrons, electrons or photons contained in that volume of space.Therefore, one must add the decelerating properties "Shadows" associates with a continuous non-quantized mass component of a volume of space to the decelerating properties NASA associates particular matter in the space transversed by the space probes to obtain the magnitude of the decelerations experience by the space probes. The reason the calculations regarding the decelerations made by NASA on its space probes mentioned in the above article are inaccurate is because they only used the deceleration properties they associated with the particular matter in space and did not factor in the deceleration caused by the decelerating properties of a continuous non-quantized mass component of a volume of space. Chapter Twenty-Four Maxwell's equations and Probability in terms of Four Spatial Dimensions Return to Top The "structure" of Maxwell's Equations is related to a physical property of a matterenergy on a "surface" of a three-dimensional space manifold with respect of a fourth spatial dimension. Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of mass and energy. In Chapter two, the quantum properties of mass and energy were defined in terms of integral energies associated with a resonant "structure" formed in space by "vibrations" in a continuous non-quantized mass and energy component of space. The formation of these resonant "structures" was derived in terms of a "vibration" in a continuous non-quantized mass and energy component of space' These resonant "structures" are called a mattercule or "quantum mass unit of space" . In Chapter three, the transmission of electromagnetic energy was derived in terms of a matterenergy wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. This matterenergy is generated by the coupling of "vibrations" associated with the resonant "structures" defined in Chapter two from one resonate structure to the next. These "vibrations" in a continuous non-quantized matter and energy field component of space responsible for generating a matterenergy wave are analogous to vibrations associated with a wave on the surface of water. The trough of a wave on water displaces the vertical volume of water occupied by the water with air. The displaced volume of the air represents the energy associated with the weight of the displace water. Summarily the peak of the a wave on water displaces the air above the surface of the water with water. The displaced air represents the volume associated with the energy of the displaced water. "Vibrations" in a continuous non-quantized matter and energy field component of space associated with a matterenergy wave responsible for the propagation of electromagnetic energy establish a wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension . The "trough" of a matterenergy wave displaces the matterfield component of space below a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension with

energy. The fourth dimensional "volume" associated with the trough defines the energy associated with the displaced matterfield component of space in terms of the equation E=mc^2. Similarly, the "peak" of a matterenergy wave displaces a "volume" of four-dimensional space above the "surface" of a three-dimensional space manifold with the matterfield component of three-dimensional space. The matterfield component of space that is displace above the "surface" of the three-dimensional space manifold defines the mass associated with the displaced energy component of space in terms of the equation E=mc^2. (The displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by a matterenergy wave is defined as energy because Chapter ten derived a displacement in the "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension as the casualty of energy.) First the mechanism responsible for Gauss's law of Electricity, the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity will be derived in terms of the geometric properties of four spatial dimensions. Next Gauss's law of Magnetism, the net magnetic flux out of any closed surface is zero and that there are no magnetic monopoles will be defined in terms of the distortion of "W" axis of the fourth spatial dimension with respect to the axes of three-dimensional space. Following that the physical mechanism responsible for Ampere's Law, the magnetic field in space around an electric current is proportional to the electric current that serves as its source will be derived in terms of the orientation of the "W" of the fourth spatial dimension with respect to of the energy gradients "Shadows" associates with the unit electric charge. Then the fourth of Maxwell's equations is Faraday's law of induction that any change in a magnetic environment of a coil will cause a voltage to be " induced" in the coil that is equal to the negative rate of change of the magnetic flux times the number of turns of the coil. It will be derived in terms of the rotational energy of the energy gradient associated with the unit electric charge and inertial properties of the mass component of a "quantum mass unit of space". Finally, the physical mechanism responsible for the probability of finding a certain particle at a certain position or Schrödinger's probability wave equation will be derived in terms of the resonant properties "Shadows" associates with the mass and energy components of "quantum mass unit of space". Gauss's law of electricity states the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity or "integral of E*dA =Q / permittivity". The mechanism responsible for the total electric flux out of a closed surface being equal to the charge enclosed is related to the geometric properties a matterenergy on a "surface" of a threedimensional space manifold with respect of a fourth spatial dimension. In Chapter thirteen, the polarity of the positive and negative unit electric charge was derived in terms of the rotational direction of energy gradients in a continuous non-quantized mass and energy components of space. If the positive unit electric charge was defined as being caused as having a "clockwise" rotation in a continuous non-quantized mass and energy component of three-dimensional space manifold with respect to a fourth spatial dimension, a negative unit electric charge was defined as being caused by a "counterclockwise" rotation in a continuous non-quantized mass and energy component of three-dimensional space manifold.

It was demonstrated the rotational energy of energy gradients in a continuous non-quantized mass and energy component of space generate "elevations" or "depressions" in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension . The clockwise rotation in a continuous non-quantized mass and energy components of space defining a positive unit electric charge would cause a "depression" to be formed in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. While the counter clockwise rotation in a continuous non-quantized mass and energy components of space defining a negative unit electric charge would cause an "elevation" to be formed in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. In Chapter ten the magnitude of all forms of energy including the energy associated with electrical flux was derived in terms of the absolute magnitude of a spatial "separation" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by "elevations" and "depressions" in the "surface" of a three-dimensional space manifold. The electromagnetic energy associated with electric flux is transmitted by a matterenergy wave on the surface of a three-dimensional space manifold with respect to a fourth spatial dimension. The peaks and troughs of a matterenergy wave will generate "elevations" and "depressions" in a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension that are similar to those generated by positive and negative unit electric charges. The magnitude of a spatial "separation" in a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension generated by the "peaks" and "troughs" of a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension will depend on the number of charged particle responsible for generated the matterenergy wave. Therefore, the electrical flux propagated out a closed surface by the matterenergy wave responsible for the propagation of electric flux will be equal to the sum of the energies of the unit electric charges enclosed by that surface because the total spatial "separation" in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension will be directly related to the sum of the electric charges enclosed by that "surface". This indicates the total electric flux out of the closed a "surface" a three-dimensional space manifold with respect to a fourth spatial dimension surrounding an electrical charge should be equal, as Gauss's Law of Electricity states, to the charge enclosed by that "surface". The inverse relationship of the total electric flux out of a closed surface to the permittivity of the volume of space the electric flux is transversing is related to the mechanism responsible for the transmission of electrical energy in space. As mentioned earlier, Chapter three derived the preparation of energy in terms of a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. It derived the propagation of a matterenergy wave in terms of a coupling of "vibrations" in a continuous non-quantized matter and energy field component from one "quantum mass unit of space" to the next. In Chapter twelve it was shown a direct relationship exists between the density or permittivity of a volume of space and the number or density of "quantum mass units of space" contained in that volume of space. Therefore, a matterenergy wave responsible for the propagation of electrical flux would have to interact with larger number of "quantum mass units of space" per unit distance traveled as the permittivity of space it was transversing increased. This indicates that there should be an inverse relationship of the total electric flux out of a closed surface to the permittivity of the volume of

space because each additional "quantum mass unit of space" it interacted with would cause attenuation of the energy of the matterenergy wave responsible for the transmission of electric flux. This completes the derivation of the physical mechanism responsible for Gauss's law of electricity in terms of the geometric properties of four spatial dimensions. We will now derive the mechanism responsible for Gauss's law for magnetism that the net magnetic flux out of any closed surface is zero and there are no magnetic monopoles or the integral of B*dA=0. The mechanism responsible for net magnetic flux out of a closed surface being equal to zero is the related to the orientation of the "W" axis of a fourth spatial dimension with respect to axes of a three-dimensional space manifold. (The "W" axis of the fourth spatial dimension was defined in Chapter ten.) In Chapter eleven it was shown magnetic flux is the result of a "torque" generated on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by the "nonperpendicular" orientation of the "W" axis of the fourth spatial dimension with respect to the axes of three-dimensional space. (The physical meaning of the term "non-perpendicular" orientation of the "W" axis of the fourth spatial dimension with respect to the axes of three-dimensional space was derived in Chapter ten.) The non-perpendicular "angle" of a "W" axis of the fourth spatial dimension makes with a coordinate plain in three-dimensional space would be analogous to angle a line makes when drawn through a plain on a coordinate graph. A line will always make symmetrically equal and opposite angles above and below the coordinate plain it transverses. Similarly, the “W” axis of a fourth spatial dimension will always make symmetrically equal and opposite angles "above" and "below" the coordinate plain in three-dimensional space it transverses. Therefore, the force on a "surface" of three-dimensional space resulting from the "torque" generated by the "non-perpendicular" orientation of the "W" must always be equal and opposite "above" and "below" the three-dimensional coordinate plain it traverses. This results in the net magnetic flux or force out of any closed surface always being equal to zero because the magnitude of the "torque" generated on a "surface" of three-dimensional space and the polarity associated with a magnetic field "above" and "below" the three-dimensional coordinate plain the magnetic field is transversing must be equal and opposite. This also defines the physical reason magnetic monopoles cannot exist. Magnetic monopoles cannot exist because the “W” axis of the fourth spatial dimension extends infinitely though each point in three-dimensional space. Therefore the "W" axis of the fourth spatial dimensions will generate two magnetic fields of equal and opposite polarity "above" and "below" any coordinate plain in three-dimensional space it transverses. This completes the derivation of the physical mechanism responsible for Gauss's law of Magnetism in terms of the orientation of "W" axis of the fourth spatial dimension with respect to the axes of three-dimensional space.

We will now move on and derive the physical mechanism responsible for Ampere's law that the magnetic field in space around an electric current is proportional to the electric current which serves as its source or the integral of B*ds=the permittivity of space times the current or “I” in terms of the mass and energy components of "quantum mass unit of space". The mechanism responsible for Ampere's law can be derived from the orientation of the axis "W" axis of the fourth spatial dimension with respect to the rotational axis of the energy gradients associated with a unit electric charge defined in Chapter thirteen. It was shown in the derivation of Gauss's law of Electricity the quantized properties of the unit electrical charge defined in Chapter thirteen results in the energy gradients associated with all unit electric charges to have identical rotational energies. In an electric current the rotational axis of the energy gradients associated with individual electrically charged particles will have a common orientation along the velocity vector associated with the electrically charged particles in an electrical current. Therefore, the "torque" generated on the "W" axis of a fourth spatial dimension by the rotational energies of the energy gradient of each unit electric charge will be additive because the axis of the energy gradients of all the unit electric charges in an electrical current will have a similar orientation, This indicates the magnitude of the total "torque" they generate on the "W" axis the fourth spatial dimension will also be additive because "torque" generated by the energy gradients associated with the unit electric charges in an electric current would be additive. This results in the magnetic field in space around an electric current to be directly proportional to the electric current because, as was shown in Chapter eleven, the magnitude of a magnetic field is proportional to the magnitude of the "torque" generated on the "W" axis of the fourth spatial dimension, which in term is proportional to the electric current. The reason the magnetic field in space in Ampere's law is directly related to the permittivity of space is that, as was mentioned in the derivation of Gauss's law of Electricity, there is a direct relationship between density of the mass component of space will be greater in a volume or space and the permittivity space. This means that their will be a greater concentration of mass component of space for the energy gradients associated with a unit electric charge to interact with in volumes of space where the permittivity is greater. Therefore, the energy associated with the magnetic field generated by those energy gradients will be stronger because the mass of the system they interact with will be greater. This completes the derivation of the mechanism responsible for Ampere's law in terms of the orientation of the "W" of the fourth spatial dimension with respect to of the energy gradients Shadows associates with the unit electric charge. Lastly we shall geometrically derive the mechanism responsible for Faraday's Law of Induction, that any change in a magnetic environment of a coil will cause a voltage to be "induced" in that coil that is equal to the negative rate of change of the magnetic flux times the number of turns of the coil or the integral of E*ds= -dB/dt. The mechanism responsible Faraday's Law of Induction is related to the rotational energy of an energy gradient associated with the unit electric charge and inertial properties of the continuous non-quantized mass component of the space.

In the derivation of Gauss's Law of Magnetism, it was shown that the magnitude of magnetic flux or force is directly related to magnitude of the "torque" generated on the "W" axis of the fourth spatial dimension by the energy gradients associated with the unit electrical charges. Later in the derivation of Ampere's law it was shown the "torque" generated on the "W" axis of the fourth spatial dimension by the energy gradients associated with the individual unit electric charges in an electric current were additive. Therefore, each additional turn of a coil will add additional unit electric charges to the space affected by the energy gradients associated with the unit electrical charges in that coil and therefore, increase the total "torque" on the "W" axis of the fourth spatial dimension in the regions of space affected by that coil. This will result in each additional turn of a coil making a proportional increase the magnitude of the magnetic flux or force associated with the current in that coil because the magnitude of a magnetic field is proportional to the magnitude of the torque generated on the "W" axis of the fourth spatial dimension by an electric current. This defines the mechanism responsible for why the magnitude of the magnetic flux around that coil that is carrying an electric current is directly proportional to the number of turns in that coil. One aspect of electrical energy that has not yet been mentioned in this chapter is the mechanism responsible for the force or voltage associated with the unit electric charge. Chapter nine derived the energy associated with a voltage and magnetic flux of a unit electric charge in terms of the common rotational energy associated with energy gradients in a continuous non-quantized mass and energy components of space. This suggests that the change in the magnetic environment coil, which causes a voltage to be "induced" in that coil, may be related to inertial properties of the mass component of the energy gradients associated with the unit electrical charge. This is because Chapter nine showed the magnetic flux or field of a current in a coil has properties associated with the inertial properties of the continuous non-quantized mass component of space because the energy gradients responsible for the generation of the magnetic flux in a coil are, in part, composed of the mass component of space. This means that Newton’s third law of motion which states which states "For every action there is an equal and opposite reaction" may be applied to the voltage induced in a coil by magnetic flux may be applied to the magnetic environment of a coil. In other words, the voltage is induced in a coil is equal to the negative rate of change of the magnetic flux because the voltage is an equal and opposite reaction to the change of the magnetic flux based on Newton's third law of motion. This completes the derivation of the physical mechanism responsible for Faraday's law in terms of the rotational energy of the energy gradient associated with the unit electric charge and inertial properties of the mass component of a "quantum mass unit of space". We will now discuss the physical mechanism that is responsible for the probability functions associated with Schrödinger's wave equation. The physical mechanism responsible for probability of finding a certain particle at a certain position or the Schrödinger's probability wave function is related to the fact that the continuous non-quantized spatial and energy components of a "quantum mass unit of space" and all quantum particles defined in Chapter two vary sinusoidally with respect to time.

This is demonstrated by the equation in Chapter three of E=mc^2*(1/Mr-Mc)/F which defines the matterenergy wave associated the energy of a photon or any quantum particle. Therefore, they will interact with the environment a probabilistic manner depending on the relative orientation of the spatial and energy components internal to a "quantum mass unit of space" at the time of measurement. This defines the mechanism responsible for probability associated with Schrödinger's wave function in terms of the continuous non-quantized mass and energy component of a "quantum mass unit of space". Chapter Twenty-Five The Cosmology of Four Spatial Dimensions Return to Top The Standard Cosmological Model of the Universe postulates the universe began as a small compact "ball" of matter that exploded producing a “big bang” and that the universe is expanding due to the aftermath of the "big bang" based primarily on the frequency shifting of the spectral lines in the light coming from stars called the red shift. It interprets the red shift as an indication the stars are moving away from the earth and the greater the distance the earth is from a star the faster it is moving away. This observation of light is similar to that of sound. The pitch or frequency of a train's whistle is different when it is moving relative to an observer than when it is stationary relative to an observer. The difference in the frequency of the sound of the whistle can be used to determine the relative speed of the train's movement with respect to the observer. Similarly, many astronomers have interpreted the frequency shift associated with a red shift in terms of an overall expansion of the universe. They have calculated a rate the universe is expanding based the magnitude of the frequency shift of red shifted of photons. However, their calculations would be valid only if entire frequency shift associated with a red shift were due to the rate of expansion of the universe. Chapter one postulated a volume of space is composed of a continuous non-quantized “field” of mass and energy and that light is propagated by matterenergy wave on a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension. If this were a valid postulate it would mean the magnitude of a red shift may not be entirely a result of the expansion of the universe because a portion frequency shift associated with the red shift may be due to an interaction with a continuous non-quantized mass component of space. “Shadows” does agree with many cosmologists that the universe is presently in a state of overall expansion however it disagrees with the currently accepted rates at which this expansion is occurring and defines this expansion not in terms of a "big bang" but in terms of cycle of expansions and contractions. To understand the mechanism responsible for an interaction of light with a continuous nonquantized mass component of space and why the universe may be undergoing a cycle of expansions and contractions requires an understanding of the mechanism responsible for the quantum properties of a continuous non-quantized mass and energy component of space and how they relate to the propagation of light.

Chapter two defined the quantum properties of mass and energy in terms of resonant "structures" formed in space by "vibrations" in a continuous non-quantized mass and energy components of space. The formation of these resonant "structures was derived in terms of "vibrations" in a continuous non-quantized mass and energy component of space. The magnitude of these "vibrations" were defined by the equation E=mc^2 where "E" = the magnitude of a continuous nonquantized energy component of space and m = the magnitude of a continuous non-quantized mass component of space. These resonant "structures are call a mattercule or "quantum mass units of space". In Chapter three, the propagation of light was derived in terms of a matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. It was shown a coupling of resonant "vibrations" in a continuous non-quantized mass and energy components of space, defined in Chapter two, from one "quantum mass unit of space" to the next generates a "matterenergy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. These "vibrations" in a continuous non-quantized matter and energy field components of space responsible for generating a matterenergy wave are analogous to the vibrations associated with a wave on the surface of water. The trough of a water wave displaces the vertical volume of water occupied by the water with air. The displaced volume of the air represents the energy associated with the weight of the displace water. Summarily the peak of a water wave displaces the air above the surface of the water with water. The displaced air represents the volume associated with the energy of the displaced water. "Vibrations" in a continuous non-quantized matter and energy field component of space establishes a wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension . The trough of this matterenergy wave displaces the matterfield component of space "below" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension with energy. The fourth dimensional "volume" associated with this trough defines the energy associated with the displaced matterfield component of space. Similarly, the peak of this matterenergy wave displaces the "volume" of four-dimensional space "above" a "surface" of a three-dimensional space manifold with the matterfield component of three-dimensional space. The matterfield component of space that is displace above the "surface" of the three-dimensional space manifold defines the mass associated with the displaced energy component of space. In Chapter three, the energy of the photon was derived in terms of a "shortening" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by the passage of a matterenergy wave. While the quantum properties of a matterenergy and a photon were derived in Chapter two in terms of the quantum properties of the resonant "structures" generated in space by the passage of a matterenergy wave. (For your convenience the deviation found in Chapter three for a "shortening" of a threedimensional space manifold with respect to a fourth *spatial* dimension by the passage of a matterenergy wave is repeated below.) ** It is the *spatial* contractions of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the interaction of the continuous non-quantized matter and energy field components of space defined by the equation E=m*c*(v/F) that is responsible for the energy associated with a photon.

As mentioned earlier “Shadows” postulates the energy of electromagnetic radiation is transmitted by a matterenergy wave on a three-dimensional space manifold with respect to a fourth *spatial* dimension. The shortening effect this matterenergy wave has on the three-dimensional space manifold with respect to a fourth *spatial* dimension is responsible for the energy of a photon. (As mentioned earlier, this effect is similar to how a wave on the two-dimensional surface of water shortens the two-dimensional distance between water molecules on the surface of the water.) The wavelength associated with the matterenergy wave of a photon is inversely proportional to its frequency and therefore the magnitude of the energy associated with the physical "shortening" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would be directly proportional to the frequency. Since "Shadows" derives energy in terms of "shortening" in a threedimensional space manifold with respect to a fourth *spatial* dimension , the energy of a photon would be directly related to its frequency. This shortening of in t he three-dimensional space manifold with respect to a fourth *spatial* dimension is responsible for "Shadows" defining the energy of a photon in terms of the equation E=m*c*(v/F) or E=m*c*(Mr-Mc)/F). The term (MrMc)/F) in the equation E=m*c*(Mr-Mc)/F) defines the magnitude of the "shortening" a threedimensional space manifold with respect to a fourth *spatial* dimension in terms of the frequency of matterenergy wave that "Shadows" postulates is responsible for the energy of a photon. This is because the term "Mr" represents the *spatial* "distance" between two points in on a threedimensional space manifold with respect to a fourth *spatial* dimension with NO energy traveling thought it and the term "Mc" represents the *spatial* "distance" two points occupy on a threedimensional space manifold with respect to a fourth *spatial* dimension with a matterenergy wave associated with a photon moving through it and "F" equals the length of a three-dimensional space manifold with respect to a fourth *spatial* dimension with a matterenergy wave of "0" frequency moving through it. Therefore, the dimensionless term (v/F) or (Mr-Mc)/F) defines the ratio with respect to the velocity of light of the "length" of the shortening of the three-dimensional space manifold associated with the passage of the matterenergy wave responsible for the energy of a photon to the "length" of un-shorten space associated with space with no photons present in terms of the frequency of the matterenergy wave. This indicates the energy of a photon is the result of the releasing of the energy stored in space by the physical shortening of the length of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the movement through space of the matterenergy or electromagnetic wave "Shadows" associates with the energy of a photon. ** Chapter three derived the energy of a photon in terms of a matterenergy wave generated by interaction of a continuous non-quantized energy or energyfield “E” with a continuous nonquantized mass or matterfield components "m" of space defined by the equation E=m*c*(v/F). (The term v/F defines the magnitude of a shortening in a "surface" of a three-dimensional space with respect to a fourth *spatial* dimension due to the passage of the matterenergy responsible for propagating a photon. "v" equals the *spatial* "distance" between two points on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension with NO energy traveling thought it minus the *spatial* "distance" between two points separated by one wavelength in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension, while "F" equals the length of a three-dimensional space manifold with respect to a fourth *spatial* dimension with a matterenergy wave of "0" frequency passing through it. Therefore, the dimensionless term (v/F) defines the ratio of the shortening of the length of a threedimensional space manifold with respect to a fourth *spatial* dimension caused by the passage of the matterenergy wave responsible for the transmission of the energy of a photon.) Because a matterenergy is generated by an interaction with a mass component of space a portion of it's energy will be dissipated due to an interaction with the inertial properties of the mass component of space. This would result in a shifting of the frequency of a photon towards the red end of the spectrum because its frequency would decrease as it losses energy.

However, it can be shown using the currently accepted laws of physics a dissipation of a photon's energy due to its interaction with a continuous non-quantized mass component of space causes an increase the magnitude of a continuous non-quantized mass component in the volume of space were the energy dissipation occurs. In Chapter three, the “closed *spatial* system” defining the quantized energy of a photon was derived in terms of a resonant "structure" generated in space by a dynamic interaction of a matterenergy wave and a continuous non-quantized mass and energy component of space. According to the law of conservation of mass and energy, the sum of the mass and energy components of a close system must remain constant. Therefore, due to the law of conservation of mass / energy and the dynamic properties of the closed *spatial* mass and energy system defined in Chapter three for the energy of a photon, a dissipation in a continuous non-quantized energy component of a matterenergy wave due to its interaction with a continuous non-quantized mass component of space MUST cause an increase in the continuous non-quantized mass component of the space transversed by the matterenergy wave. (The experimentally verified equation E=mc^2 provides a basis for concluding that energy can be converted to mass because the conversion of mass to energy is has been verified experimentally. However the symmetry of the E=mc^2 strongly suggests that energy can be converted to mass.) Chapter two showed the non-quantized mass component of space is reasonable for the properties associated with volume. Therefore an increase in a continuous non-quantized mass component in a volume of space would cause the *spatial* volume of that volume to expand because the mass component of space is responsible for its volume. This expansion in a volume of space caused by the energy dissipation photons would result in an overall expansion of the total volume of the universe with respect to a fourth *spatial* dimension. However the overall expansion of the universe caused by an interaction of a photon with a continuous non-quantized mass component of space can also be derived directly from the geometry of the matterenergy wave responsible for the energy of a photon. In the earlier quoted section of Chapter three, the energy of a matterenergy wave associated with the energy of a photon was derived in terms of the "shortening" of the length of the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the passage of the matterenergy. It was shown a "shortening" of a three-dimensional distance between two points on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by the passage of a matterenergy was analogous to the shortening of two-dimensional distance between two water molecules on the surface of water by the passage of a water wave. The magnitude of the lengthening of a two-dimensional distance between two water molecules on surface of water caused by passage of a wave on water will depend on the wavelength of that wave. The longer the wavelength the greater the length of the two-dimensional distance between two water molecules on the surface will be. Similarly, the magnitude of the length of a *spatial* distance between two points on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by passage of a matterenergy wave will depend on the wavelength of that wave. The longer the wavelength the greater the length of the distance between two points on the "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.

Since wavelength associated with a matterenergy wave increases as its energy decreases the *spatial* distance between two points on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension will increase as the wavelength of the matterenergy wave increase. This means the physical length or volume of space will increase in the regions where photon's energy has been dissipated by their interaction with the continuous non-quantized mass component of space will increase. This will result in the total volume of the universe to expand with respect to a fourth *spatial* dimension. According to the mechanism defined above a portion of the observed expansion of universe associated with the energy loss of red shifted photon's would be due to the increase of the total *spatial* volume of the universe. However, the rate of expansion caused by the increase in the total *spatial* volume of universe due to these mechanisms would be considerable less than presently accepted by most of today’s cosmologist because it would not be related to the linear recessional velocity of stars. The rate of expansion of the universe due to the conversion of the energy component of a photon to the mass component of space would be related to the non-linear formula of E=mc^2 because in Chapter two the relationship between the continuous non-quantized mass component of space to the continuous non-quantized energy component of space was derived in terms of the equation of E=mc^2. If this mechanism does define one of the expansive components of the universe than the total rate of expansion of the universe would be less than that predicted my many cosmologists because this component would be defined by the non-linear formal of E=mc^2. \ However, it should be remember “Shadows” does not say that the universe is not expanding due to the linear velocity of stars however, it is saying that magnitude of their velocities may less than predict by many of today’s cosmologists. According to the above mechanism, there should be a direct relationship between the distance a photon travels and the magnitude of the red shift it experiences because a photon that travels a greater distance will have more time to interact with the continuous non-quantized mass component of a volume of space and therefore will cause a greater overall expansion of the universe. This model has been dismissed by many because of the recently observed time dilation of red shifted photons discussed at the “Errors in Tired Light Cosmology” web page ( http://www.astro.ucla.edu/~wright/tiredlit.htm ) However, the fact that time dilation has been observed in red shifted photons supports the validity of this mechanism instead of refuting it because Chapter three derived the mechanism responsible for the energy loss associated with the red shift of photons in terms of the "relativistic" foreshortening of space predicted by equation E=mc^2 and therefore would be associated with "relativistic" time dilatation. Additionally, it was pointed out on the "Errors in Tired Light Cosmology" page no "Compton effect is observed in red shifted photons. (The "Compton Effect "is the term given to the blurring of distant objects that result from the interaction of a photon with particles in the space.)

It assumes that the only mechanism that can account for the energy loss of a red shifted photon would be associated with an interaction of a photon with other quantum particles in space. Therefore, because no Compton Effect is observed in red shifted photon the energy loss cannot be the result of a photons interaction between other quantum particles in space. However, "Shadows" defines a mechanism responsible for energy loss of photons in terms of an interaction on a sub quantum or particle level because the continuous non-quantized energy component of a photon interacts directly with the continuous non-quantized mass component of the photon internal to the photon itself. Therefore, the fact that no blurring or Compton effect is observed in distant objects supports the "Shadows" model because it does not define the energy loss of a red shifted photon in terms of a particle interaction. It defines it in terms of a direct interaction between the continuous non-quantized energy component of the photon and the continuous non-quantized mass component of a volume of space internal to the photon itself. The cosmological model “Shadows” postulates defines a very high degree of symmetry between matter, gravity, electromagnetic and kinetic energy, and the transmission of electromagnetic radiation in terms of the geometry of four *spatial* dimensions. Chapter three derives the transmission of electromagnetic radiation in terms of a matterenergy wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension . This wave generates alternating "elevations" and "depressions" on a “surface” of the three-dimensional space manifold associated in with gravitational and kinetic energy. A "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions caused by a "trough" of a matterenergy wave responsible for the transmission of electromagnetic energy corresponds with the "curvature" caused by a "depression" in “surface” of space associated with gravitational energy in Chapter twelve. While a "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions caused by the "peak" of a matterenergy wave corresponds to an "elevation" in the “surface” of space associated with Kinetic energy in Chapter seventeen. Therefore, “Shadows” symmetrically defines all energy including gravitational, kinetic and the quantized electromagnetic energy of photons in terms of a common "curvature" in the "surface" of the third *spatial* dimension with respect to the fourth *spatial* dimension. Presently the universe appears to be in a state of overall expansion with respect to a fourth *spatial* dimension, due in part to the lengthening effect on space that “Shadows” associates with the energy loss of red shifted photons. However someday this expansion will crease and it will enter a contraction phase. This is primarily due to the additional gravitational attractive forces the continuous non-quantized mass component of space adds to the total mass of the universe. The velocity of contraction will increase until the contractive forces associated momentum of the mass component of the universe equals the expansive energy generated by the heat resulting from the contacting mass component of the universe. At this point in time the total energy of the universe would equal to the total mass equivalent of that energy or E=mc^2. Form that point on the velocity of the contraction will slow and be maintain by the momentum associated with the remaining mass component of the universe.

However, after a certain point in time the conversion of mass to heat generated by a contraction of the three dimensional space manifold with respect to a fourth *spatial* dimension will result in the remaining mass disassociating into photons. This will result in the universe entering an expansive phase because the expansive forces associated with the heat generated by the contraction of the universe will exceed the gravitational contractive forces associated with the remaining mass component of space. However, the expansion of the universe due to the heat generate by its contraction is accelerated by expansive forces associated with the red shifting of photons defined earlier. (The expansive force "Shadows" associates with the red shifting of photons is the recently observed force called “Dark Energy” which is causing the accelerated expansion of the universe.) Earlier it was shown the energy loss associated with the red shifting of photons is converted to the mass component of space. Therefore, this accelerated expansion will continue until the total attractive gravitational forces caused by the mass generated by the energy loss of red shifted photons again exceeds the total momentum of the mass in the universe. At this point, the contraction phase will begin again. Since the universe is a closed system, the amplitude of the expansions and contractions will remain constant because the law of conservation of mass energy dictates the total mass and energy of a closed system remains constant. This results in the universe experiencing in a never-ending cycle of expansions and contractions of equal magnitudes. Particle and star formation would not begin in the expansion phase until space had expanded enough to allow enough of the photons energy to be converted back into the mass that “Shadows” associates with space to support their formation. “Shadows” associates the Cosmic Background Radiation with the equivalent temperature of 3 degrees Kelvin discovered by Penzias and Wilson with the remnants of the energy that existed at the time when the universe changed over from an energy dominated or to one containing both photons, subatomic particles and the mass component of space. The sudden appearance of these “free” or subatomic particles destroyed the thermo equilibrium between the individual photons that had existed before their appearance because they began to interact with the photons. This Comic Background Radiation would appear to be almost a perfect Black Body Curve because at the instant this change over occurred the energy and mass components of space would be in thermo equilibrium because they would have been equally distributed throughout the entire volume of the universe. Conclusion Return to Top We have just begun a journey of intellect and imagination. Just as Columbus did not know what he would find at the end of his voyage, we do not know what awaits us at the end of ours. Many of the ideas and concepts outlined here will be modified because imagination is not reality. It will take the intellect and imagination of many to find and put all of the pieces of this puzzle together.

One person does not make a discovery, it is the result of a building of knowledge and understanding over the course of Humankind's existence. Neil Armstrong was the first person to set foot on the moon. His voyage did not start on the lunch pad of Cape Kennedy. It began in the imagination of the first human to look at the moon and imagine what it would be like to set foot on it. Imagination guides intellect and gives it the ability to discover reality. If nobody had imagined traveling to the moon, no one would have tried to make the tools and devices required to make that journey a reality. The ideas expressed in this paper allow us to imagine a universe different from the one that we are familiar with by bringing the "Shadows of another reality into clearer focus. Who knows where this imagination may take us. By moving a piece of paper you can transport a two-dimensional creature "living" on its surface through three-dimensional space. Just as our imagination guided our intellect to generate the tools and devices necessary to enable humankind to explore the moon it may guide us to generate the tools and devices necessary to transport humankind through four-dimensional space and allow us to explore a world limited only by our imagination. Reality casts Shadows Imagination illuminates Shadows Intellect explores Shadows