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| The "Shadows" of four spatial dimensions. |
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Title: The "Shadows" of four spatial dimensions. A proposal for unifying the relativistic properties of the macroscopic universe with the quantum properties of the microscopic universe in terms of the existence of four *spatial* dimensions and a continuous non-quantized form of mass. 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 the 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: Quantum mechanics and Einstein's Relativistic Theories of have been the most successful scientific theories of modern times however, attempts to unify them and define "A Theory of Everything" have been unsuccessful. This is because their exists an incompatibility between the microscopic universe described by quantum mechanics and the macroscopic universe described by Einstein's theories regarding its physical structure. Einstein's theories define the macroscopic universe in terms of the existence of a continuous space-time metric while quantum theories define the microscopic universe in terms of discontinuous particles. Therefore, these two theories are inherently incompatible because the physical structure of the universe cannot be both continuous and discontinuous at the same time However, "Shadows" demonstrates the relativistic properties of space and time and the quantum properties of mass, energy, momentum and position can be explained and predicted by defining the universe in terms of four *spatial* dimensions and the existence of a continuous non-quantized form of mass. This would allow physicists to define a common unifying mechanism responsible for both the quantum properties of microscopic universe and the relativistic properties of the macroscopic universe. Chapter one will postulate that space is composed four *spatial* dimensions and a continuous non-quantized form of mass. Chapter two will derive the quantum or particle properties of mass in terms of integral energies associated with a resonant "structure" formed in space by "oscillations" in a continuous non-quantized form of mass. Chapter three will define the particle called a photon in terms of "oscillations" in a continuous non-quantized form of mass caused by a matter wave moving at the velocity of light on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Therefore, Chapters two and three provide a bridge between discontinuous or particle properties of the microscopic universe to the continuous properties of the macroscopic universe in terms of a continuous non-quantized form of mass. (Louis de Broglie was the first to theorize that all particles have a wave component. His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.) Time will be defined as only being a measure of the sequential ordering of the causality of an event, while the causality of gravity, momentum and the quantum properties of mass and energy will be defined in terms of the physical properties of four *spatial* dimensions. Time will then be individually linked to each coordinate plane of four-dimensional space by the mathematical and experimental observed sequential ordering of events that occur in each coordinate plane Chapter fifteen will derive the relativistic properties of gravity, space and time in terms of a distortion in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. This indicates redefining the physical structure of the universe in terms of a geometry of four *spatial* dimensions and the existence of a continuous non-quantized form of mass may enable physicists to define a common unifying mechanism responsible for both the quantum and relativistic properties of our universe. Conclusion: "Shadows" demonstrates the power that changing one's perspective 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. "Intuitive
thinkers have made many of the breakthroughs in science" "The
universe's most powerful enabling tool is ***************** |
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A Universe of Four *Spatial* Dimensions |
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The Causality of the Quantum properties of mass & energy |
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Electromagnetic Energy in terms of Four *Spatial* Dimensions |
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The Photon a Particle or Wave? |
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Bell's theory and the EPR Paradox |
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Heisenberg's uncertainty principle and four spatial dimensions |
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The Photon, a matterenergy wave? |
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The relative masses of subatomic particles in terms of a Fourth *Spatial* Dimension |
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Electrical Potential Energy and Four *Spatial* Dimensions |
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The boundary between a Third and Fourth *Spatial* Dimension |
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Propagation of electromagnetic energy in terms of Four *Spatial* Dimensions |
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Gravity and the Fourth *Spatial* Dimension |
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The relative mass of a unit electric charge |
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A Link between Gravitational and Electrical forces |
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The relativistic properties of Four *Spatial* Dimensions |
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A link between Relativity and Quantum mechanics |
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Gravitational and Kinetic Energies Linked by a Fourth *Spatial* Dimension |
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The Principal of Equivalence & Absolute Reference Frames with respect to Four *Spatial* Dimension |
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The composition and structure of Quarks with respect to Four *Spatial* Dimensions |
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The Fundamental Quantum Particles |
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The Origin of the Positron in terms of a Fourth *Spatial* Dimension |
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Dimensional Mechanics |
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Experimental Verification of Shadows |
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Maxwell's equations in terms of Four *Spatial* Dimensions |
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"Evolution" of the universe in terms of Four *Spatial* Dimensions |
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Chapter
One Defining the properties of a universe consisting of time and four *spatial* dimensions is not possible until we have an understanding of the causality of the forces that are responsible for those properties. First, time will be defined as only being a measure of the sequential ordering of the causality of an event, then the causality of the forces associated with gravity, electromagnetism, momentum and the quantum properties of mass and energy will be defined in terms of the physical properties of four *spatial* dimensions. Time will then be individually linked to each coordinate plane of four *spatial* dimensions by the experimentally observed sequential ordering of events that occur in each coordinate plane. The relativistic properties of time and space will be derived in Chapter fifteen in terms four *spatial* dimensions. "Shadows" postulates a volume of space is composed of a continuous non-quantized form or “field” of mass and energy and that interactions between these fields and four *spatial* dimensions is responsible for the casualty of the forces found in nature. There are four types of forces associated with a continuous non-quantized field of mass and energy, a positive and negative matterfield and a positive and negative energyfield. The interactions of these four forces are responsible for the geometric structure of the universe. The combination of matter and energy form matterenergy. Most are familiar with three out of four forces that define the geometric structure of the universe. Mass and the attractive force 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 force associated with a negative matterfield component of space. It will be shown latter this field is related to a mass component of anti-particles. Additionally 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 in terms of the geometry of four spatial dimensions.) All the forces of nature will be derived in terms of a geometric distortion or "displacement* in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. It will be shown the forces associated with mass of a particle is generated by a "depression" or curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. The forces associated with antiparticles is a result of an "elevation" in a "surface" of a three-dimensional space manifold with respect to a four *spatial* dimension. It will be shown that electric and magnetic forces have a common origin in terms of energy gradients generated in three-dimensional space. The attractive and repulsive properties of electric and magnetic fields will be shown to be related to interactions of the "surfaces" of a three-dimensional space manifold with the geometry four *spatial* dimensions. It will be shown how and why the forces associated with two similar electrical charges will oppose each other, while the forces associated two similar matter or "gravity fields" will attract each other in terms of the geometry of four spatial dimension and the existence of a continuous non-quantized form of mass. . These four forces interact to produce the geometric properties of space. However, it should be remembered these four forces are generated out of only one continuous non-quantized form of mass and energy. In Chapter three, the propagation of a photon will be derived in terms of a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. In Chapter two, the quantum or particle characteristics of a photon, mass, and energy will be derived in terms of a resonant system or "structure" formed in space by "vibrations" generated by a matter wave in a continuous non-quantized form of mass. These resonant structures will be called a "quantum mass unit of space". (Louis de Broglie was the first to theorize that all particles had a wave component. His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer. However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.) Therefore, Chapters two and three define a common mechanism responsible for both the quantum and wave properties of mass, energy and a photon because they define them in terms of resonant system or "structure" generated by a matter wave in continuous non-quantized form of mass. In Chapter three the energy of individual photons will be derived in terms of a rate of the frequency of "vibrations" in a continuous non-quantized form of mass that produce a resonant or "standing" matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. It will be shown that a photon's energy can be defined in terms of the equation for the Kinetic energy of an object or E=1/2*m*v^2. Where "E" equals the magnitude of the energyfield and "m" equals the magnitude of the matterfield component of a matter wave associated with a photon, and "v" would equal the "velocity" of the matter wave. Additionally Chapter fifteen will shown the velocity of light is universally constant, despite the fact that it is transmitted on a physical medium consisting of a continuous non-quantized form of mass, because of a relativistic property of time and four *spatial* dimensions. Another physical property of a continuous non-quantized form of mass 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 because its particles are physically larger. The matterenergy fields of space have similar properties. In the "vapor" state, a continuous non-quantized form of mass is difficult to detect because it is not made up of particles. However, in a "condensed state" or the state where a resonant "structures" defined in Chapter two exists in a volume of space, the particles or quanta of matterenergy associated with those resonant structures, (such as electron or proton) are detectable because they are physical larger. For example, fog is composed of an aggregation of water vapor thereby making the particles of water vapor detectable to the eye because they are larger. Similarly, all quantum particles are composed of "aggregations" of the matterenergy fields of space thereby making these “particles” or “quanta” of matterenergy detectable because they are physically larger. Mass and the gravitational forces will be derived in Chapter twelve to be the result of a distortion, curvature or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. This curvature or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is analogous to the curvature or "depression" in a space-time manifold that Einstein's General Theory of Relativity postulates is responsible for mass. In Chapter thirteen the polarity and magnitude of a positive and negative unit electric charge will be derived in terms of an energy gradient in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Therefore, because all the forces of nature including the gravitational and electrical forces have properties associated with the matterenergy fields of space any force acting on a closed spatial system will cause a change in the physical relationships between the matter and energy components of that volume of space. This will result in that force becoming predominant or observable 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 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. The mass of an electron 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. The “strong nuclear force" that "binds" a nucleus of an atom together can be derived in terms of a resonant "structure", defined in Chapter two, and the attractive forces are associated with the continuous non-quantized mass component of a proton and neutron. As mentioned earlier Chapter two will derive the quantum properties of all particles in terms of a resonant "structure" formed in space by "vibrations" of a continuous non-quantized form of mass. "Shadows" postulates the strong nuclear force is the result of the spatial separation between protons and neutrons in a nucleus becoming small enough so their resonant energies can interact to form one homogenous stable resonant "structure" or particle composed of a continuous non-quantized form of mass. These larger stable resonant "structures" are called atomic nuclei. The presence of a neutron in the nucleus of atoms containing more than one proton is necessary to form a stable nucleonic "structure" because the added the attractive forces of the continuous non-quantized form of mass of the neutron interacts with the continuous non-quantized mass component of a proton. This increases the ratio of the attractive or binding forces of the continuous non-quantized form of mass in a nucleus with respect to the repulsive force associated with the electrical component in a nucleus. This allows the protons and neutron in the nucleus to become spatially close enough so their resonant energies can interact to 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 components of space and a "surface" of 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 form of mass. The magnitude of the strong nuclear force is related to the size of the homogenous resonant structure associated with a nucleus. The size or diameter of a nucleus increases as is the atomic weight increases. Therefore, after a certain atomic weight is reached a nucleus will become physically too large for the individual resonant "structures" associated with the protons and neutron to uniformly share the energy require to maintain the stable resonant "structure" associated with that nucleus. This will result in that nucleus expelling the energy required to reduce its physical size to a point where a stable resonant "structure" can be maintained. Therefore, any nucleus that is physically large that this will be radioactive. Additionally, the nucleus of atoms that have an atomic weight less that the critical value for establishing homogenous resonant structure would increase its weight and size by "absorbing" energy from an external source if the energy were allowed to get spatial close enough to the nucleus so that it could become part of the internal resonant structure of that nucleus. This will result in increasing the size and atomic number of that nucleus. This indicates that the effectiveness of the stronger nuclear force in absorbing or emitting a particle will be dependent on the distance from the center of the nucleus of an atom. 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 relationship between the forces associated with a continuous non-quantized form of mass and energy. Therefore, a volume of space must have properties associated with mass because is, in part, made up of mass. Following this logic, a question is presented: Why hasn't this mass 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 them an opportunity to view the spherical shape of the earth from a distance. Similarly, the reason we may not have detected the mass associated with a continuous non-quantized mass component of space is that its effects are small compared to our scope of our "vision". There are however, “Shadows” that gives us an opportunity to "view" the properties of a continuous non-quantized mass component of space in terms of the red shift of spectral lines emanating from galaxies. Astronomers have noted that our universe appears to be expanding. This idea is based on the shifting of the spectral lines coming from galaxies called the red shift. One interpretation is that galaxies are moving away from the earth and the greater the distance a galaxies 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. They assume the greater the red shift in a galaxies spectrum the faster the galaxies is moving away from the earth. However, another explanation is possible. The frequency of spectral lines is an indication of the energy they possessed at the point it was 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 were composed of a continuous non-quantized form of mass, as this paper postulates light would dissipate energy due to the "dampening" effects of its inertial properties. Therefore, each spectral line would lose energy due to the properties of a continuous non-quantized mass component 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 galaxies away from us. Instead, a portion of the energy loss associated with a red shift may be a result of light interacting with a continuous non-quantized form of mass. If space is composed of a continuous non-quantized form of mass then the assumption that the greater the distance a galaxies is from us the faster it is moving away may not be valid. It may be because the further light travels the more time it would have to dissipate energy to a continuous non-quantized form of mass as it traveled through space. (A blue shift could be observed in a galaxies spectrum if the velocity of a galaxies moving in our direction imparted more energy to the spectral lines than was dissipated by a continuous non-quantized mass component of space it traveled through.) This "Tired Light" concept of the energy loss associated with the red shifting of photons by it's interaction with particles in space has been dismissed by many because no Compton scattering is observed in red shifted photons. Compton scattering is caused by an interaction between high energy particles such as photons and electrons which results in the electron being given part of the energy (making it recoil), and a photon containing the remaining energy being emitted in a different direction from the original, so that the overall momentum of the system is conserved. If the photon still has enough energy left, the process may be repeated. This process would result in a scattering of the energy of a photon. The reason why many astronomers believe the entire redshift of a galaxie is the result of its movement away from an observer is that classical theory of charged particles interacting with an electromagnetic wave, cannot explain any shift in wavelength. Therefore, if the red shift was caused by a particle interaction one should observed the Compton scattering of light that would be associated with a particle interaction. Since no Compton scattering is observed in the red shift coming form a galaxy it is assumed by many astronomers it can only be caused by the movement of an object away from an observer. However, as will be shown in Chapter three the particle properties of a photon are the result of a resonant "system" generated by a matter wave in a continuous non-quantized form of mass moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Therefore, because a photon is made up of a matter wave in a continuous non-quantized form of mass a portion of the redshift may be the result of an interaction between the matter wave responsible for it particle properties and a continuous non-quantized form of mass. This would mean that the assumption that the entire redshift in a galaxies spectrum is a result of its movement away from us might be invalid. The Cosmological Principal that the universe should appear the same in all directions supports the hypothesis that a portion of the energy loss associated with the red shift is a result of the properties of a continuous non-quantized mass component of space. Since the energy loss of light associated with a continuous non-quantized mass component of space would only be dependent on the distance it traveled, the universe would appear to be the same in all directions as long as one kept the observational distance constant. In addition, there is direct observational evidence that supports the hypothesis that a volume of space has contains a measurable quantity of a continuous non-quantized form of mass. 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 that astronomers have associated with "Dark Matter" share the same physical properties of a continuous non-quantized form of mass. They are both composed of mass and therefore would generate gravitational energy, which would influence the orbits of stars in galaxies and because it is a continuous form of mass, it would not be detectable by modern instrumentation because they are calibrated to detect mass in its particle form. This strongly suggests the observed properties associated with "Dark Matter" may be the result of a continuous non-quantized mass component of space. Later in Chapter twenty-three, an experimental technique for the direct measurement and observation of the continuous non-quantized mass component of space. Chapter
Two 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 basis for
postulating in Chapter one that space is
composed of four *spatial* dimensions and a continuous
non-quantized form of mass and energy. Chapter
Three EM radiation is propagated
through space by a matter wave, supported by vibrations in a
continuous non-quantized form of mass moving on a "surface"
of a three-dimensional space manifold with respect to a fourth
*spatial* dimension. Chapter
Four 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 by examining the resonant "structures" defined in Chapter two responsible for the particle characteristics of a photon and the matter wave that Chapter three showed was responsible for the propagation of a photon's energy. Chapter two derived the particle characteristics of a photon in terms of the discrete energy associated with a resonant "system" formed in space by oscillations in a continuous non-quantized form of mass. Chapter three defined the resonant "system" of a photon in terms of the characteristics of a matter wave moving in a continuous non-quantized form of mass. Therefore, Chapters two and three define a common mechanism responsible for both the particle and wave characteristics of a photon in terms of a resonant "system" caused by a matter wave in a continuous non-quantized form of mass. The photoelectric effect demonstrates one of the particle characteristics of a photon. The photoelectric effect is the emission of electrons from matter upon the absorption of electromagnetic energy. The emission of electrons from matter is observed to begin as soon as the electromagnetic energy strikes it. This supports the particle aspect of a photon 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 but only their numbers. Einstein based his quantum or particle theory of 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 mentioned earlier Chapter two showed the energy of individual photons is the result of a resonant "system" caused by oscillations in a continuous non-quantized form of mass Therefore, the energy of a specific photon would be directly dependent on the frequency of the resonant "system" that defines its energy. If the energy associated with a resonant "system" of a photon of a given frequency is sufficient it will instantly eject an individual electron off a photoelectric surface. The velocity of an electron leaving a photoelectric surface is not affected by the intensity of the light because varying its intensity will only cause an increase or decrease in the number of photons of a specific frequency striking the photoelectric surface. Since the energy of the resonate "system" associated with a photon of is directly dependent on it's frequency, the energy and therefore the velocity 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 the number of elections ejected from the surface because the number of resonate "structures" of sufficient energy to eject electrons from the surface will increase or decrease. Therefore, the particle characteristics of a photon associated with the photoelectric effect can be explained in terms of a resonate "system" generated by a matter wave in a continuous non-quantized form of mass. However, light also posses the non-particle characteristics 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 covered individually. On the other side of screen was a wall against which the light coming through the slits could shine on. 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 particle characteristics of a photon 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, also posses the characteristics of a wave. The wave characteristics of individual photons is due to the fact that its energy, as was shown in Chapter three is propagated though space by a resonant "system" generated by a matter wave in a continuous non-quantized form of mass. When a single photon passes through a screen with a single slit, the spatial component associated with the wavelength of its resonant "system" can only be transmitted along velocity vector of the photon and 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 component associated with the wavelength of its resonant "system" 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 slits. Because the resonant "system" of a photon is transmitted by a matter wave, the orientation of its spatial component will vary sinusoidally with respect to time. This means the direction of the “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 opened slits will generate a interference pattern on the screen because the torque generated by the sinusoidal varying direction of the spatial component associated with a matter wave will cause a sinusoidal variation in the direction of each photon that transverses the screen. This is the mechanism responsible for the wave characteristics of individual photons as observed in the Thomas Young experiment. However, when attempts are made to measure which slit a photon passed through the interference pattern disappears and it behaves like a particle. This is because attempts to measure which silt a photon passes through changes the characteristics of the matter wave passing through that slit. Therefore, that component of the matter wave responsible for its resonant "structure" will no longer interfere with component that is passing though the other slit. This will result in the collapse of the wave function and the disappearance of the interference pattern that is observed when no attempt is made to determine which slit the photon passed through. Therefore defining the propagation of a photon in terms of a resonant matter wave in a continuous non-quantized form of mass answers the question "Why does a photon behave at times like a particle and at other times like a wave?" Chapter
Five Tjipto Juwono contributed the following explanation of a 1935 paper co-authored by Einstein, Podolsky, and Rosen, which presented what has been called the EPR paradox. "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 there must be a "hidden variable" that would allow Quantum Mechanics to become a complete theory of 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's argument about incompleteness of Quantum Mechanics, John Bell derived a mathematical formula that quantified what you would get if you made measurements of the superposition of the multiple momentum eigenstates of two particles. If local realism was correct, the correlation between measurements made on one of the pair and those made on its partner could not exceed a certain amount, because of each particle's limited influence. This gave physicists the ability to test the whether particles can instantly influence other particles when they are "spacelike separated" or exist in different local reality. The "hidden variable" that Einstein was referring to in the previous article that would "make quantum mechanics complete" may be related to the existence of a continuous non-quantized form of mass. Chapter one postulated that space is composed of a continuous non-quantized form of mass and four *spatial* dimensions instead of four dimensional space-time . Later in Chapter two, a quantum particle was defined in terms of a resonant system or "structure" formed in space by "oscillations" in a continuous non-quantized form of mass and energy. Chapter three derived the propagation of EM radiation in terms of a matter or matterenergy wave "moving" at the velocity of light on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. It was shown this matterenergy wave is generated by oscillations in a continuous non-quantized form of mass. How the existence of a continuous non-quantized form of mass would allow for communications between two quantum particles that are "spacelike separated" would be 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 the resonant "structures" in a continuous non-quantized form of mass and energy that defined a quantum particle 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. However if the pool balls are physically contacting each other the "communication" or "information" transfer from the first to the last ball in line will be almost instantaneous because the time required for them to travel the distance between them would be minimal. Chapter three derived the velocity of EM radiation and the information it carries in terms of a conversion of a continuous non-quantized form of mass to a continuous non-quantized form of energy and a conversion of a continuous non-quantized form of energy to a continuous non-quantized form of mass. Therefore, the speed or velocity of electromagnetic energy and the "information" it contains is due, in part, to the time required for this conversion to take place. This would be analogous to the speed of "communication" or "information" transfer in the earlier 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 time required for them to travel through the space between them. This is because speed of the transfer of information by EM radiation would be dependent on the time required for a continuous non-quantized form of mass to "travel the distance" required for it to interact with a continuous non-quantized form of energy. However, both the EPR paradox and Bells theorem deal with rate at which the information regarding the momentum of quantum particles can be communicated between different local realities. Since the momentum of a quantum particle would be directly related to its continuous non-quantized mass component, the "hidden variable" which would allow the transferring of information regarding its momentum from different "spatially separated" local realities at speeds greater than that of light may be related to the existence of a continuous non-quantized form of mass. If space were made up of a continuous non-quantized form of mass as is postulated in Chapter one each resonant "structure" that defined a quantum particle in Chapter two would be in direct physical contact with other quantum particles through the continuous non-quantized form of mass that makes up the space between them. Therefore the transfer of the information related their momentum would be almost instantaneous for the same reason as the information transfer between the pool balls that were physically connect or touching was almost instantaneous in the earlier example. This indicates two quantum particles may be "spacelike separated" with respect to the electromagnetic energy but not with respect to the information carried by a continuous non-quantized mass component of space. This defines a physical mechanism explaining why Bell's theorem may provide mathematical verification for the instantaneous communication between quantum particles that exist in different local realities in terms of the existence of a continuous non-quantized form of mass and energy. Chapter
Six The Heisenberg uncertainty principle states that locating a particle in a small region of space makes the momentum of the particle uncertain; and conversely, that measuring the momentum of a particle precisely makes the position uncertain. However, it can be shown the uncertainty of the position and momentum of a particle is physically related to the internal structure of the resonant system that defines a particle in Chapter two. Chapter one postulated a volume of space is composed of four *spatial* dimensions and a continuous non-quantized form of mass. In Chapter two, a particle was defined in terms of a resonant system or "structure" formed in space by oscillations in a continuous non-quantized form of mass. Chapter three showed the energy or momentum of a particle is related to oscillations in a continuous non-quantized form of mass generated by a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. (Louis de Broglie was the first to theorize that all particles had a wave component. His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer. However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.) Therefore, both the momentum and position of a particle is related to a matter wave in a continuous non-quantized form of mass. This is because, as was shown in Chapter Three momentum of a particle is related to the wavelength of a matter wave in a continuous non-quantized form of mass. While, as was shown in Chapter two the position of a particle is related to where in space resonant "structure" associated with the matter wave component of that particle can be found. However, the probability of finding a specific value for the momentum of a particle is dependent on the energy distribution of the matter wave that defines its energy while the probability of finding a specific value for the position of a particle will be dependent on the spatial distribution of the resonant system that defines it position. The uncertainty involved in simultaneously measuring both the momentum and position of a particle is related to fact that both of their values are dependent on the same matter wave in a continuous non-quantized form of mass. The accuracy of a measurement is determined by how much of the measurement parameter is accessed. For example, one must access more of the wavelength component of the matter wave responsible for the momentum of a particle as he or she increase the accuracy of the measurement of its momentum. However, this means that there is less of the matter wave responsible for a particle's position accessible for measurement, thereby increasing its uncertainty. This is because the same matter wave responsible for a particle's momentum is also responsible for generating the resonant system responsible for a particle's position. Therefore if a portion of it is used to measure its momentum there will be less available to measure its position thereby making that measurement less accurate Similarly, one must access more of the resonant system responsible for the position of a particle as he or she increase the accuracy of the measurement of its position. However. because the resonant system associated with a particle's position is generated by a matter wave, there will be less of the matter wave component accessible for the measurement of its momentum, thereby increasing its uncertainty. This means the uncertainty involved in the simultaneous measurement of the position or momentum of a quantum particle or "The Heisenberg's uncertainty principle" is due to the internal structure of a particle and the existence of a matter wave in a continuous non-quantized form of mass. Additionally defining particle such as an electron in terms of a resonant "structure" in a continuous non-quantized form of mass as was done in Chapter two, also explains why quantum particles appear to randomly "move" or "jump" to different positions in space without ever moving though the intervening space. An electron can "jump" from one atomic orbital to the next without going thought the intervening space because the resonant "structure" associated with an 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 system is generated in the intervening space between the atomic orbital no electrons will be found there. Defining a quantum particle in terms of resonant system formed by matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension also provides a physical mechanism responsible for probability of finding an electron at a certain position or Schrödinger's probability wave function. This is because the position of an electron in an atomic orbital would be dependent on how the energy associated the matter wave responsible for generating the resonant system is distributed around the nucleus of an atom. This defines a physical mechanism responsible Schrödinger's wave function in terms of a matter wave and the existence four *spatial* dimensions. Therefore, defining a particle in terms of resonant "structure" formed by a matter wave in a continuous non-quantized form of mass allows one to define a physical mechanism responsible for Heisenberg's uncertainty principle and Schrödinger's probability wave function. Chapter
Seven It is possible to understand how and why a photon can have of both the particle and wave properties described by Richard P Feynman in his book "QED The Strange Theory of Light and Matter" by defining it in terms of a resonant "system" in four *spatial* dimension. On pages 17 thru 23 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 distance between the glass surfaces 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 by Mr. Feynman support a wave theory of electromagnetic radiation. Because according to wave theory, the energy associated with the interference 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 16 photons. Unfortunately, for the wave theory of light, the energy of the reflected photons Richard Feynman observed in the above experiment only take on integral or quantum values equal to the energy of the photons that originally struck the surface of the glass. This indicates that a photon's energy is not transmitted by a wave but by a quantum unit or particle of energy. However, this apparent contraction between the wave and particle properties of a photon can be resolved if a photon is, as mentioned earlier viewed in terms of a resonant "system" generated by the passage of matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Chapter one postulated that space is composed of four *spatial* dimensions and a continuous non-quantized form of mass. In Chapter two, the particle properties of a photon were derived in terms of discrete resonant "systems" formed in space by oscillations in a continuous non-quantized form of mass. Chapter three derived the propagation of a photon's energy in terms of a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by oscillations in a continuous non-quantized form of mass. (Louis de Broglie was the first to theorize that all particles had a wave component. His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer. However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.) Therefore, Chapters two and three answers the question regarding how and why a photon can behave at times like a wave and at other times like a particle because it defines both its wave and particle properties in terms of a common mechanism related to matter wave in a continuous non-quantized form of mass. The wave like interference of photons observed by Mr. Feynman would be due to the wave properties of the oscillations responsible for the formation of the resonant "system" of a photon defined in Chapter two. If the distance between the two glass surfaces in Richard Feynman's experiment is equal to half of the wavelength of the oscillations in the continuous non-quantized mass component of a photon, the interference of the wave properties of those oscillations will yield the energy associated with 0 photons. If the distance between two glass surfaces is equal to the wavelength of the oscillations in a continuous non-quantized mass component of a photon, the interference of their wave properties of those oscillations will | |