The arrow of time, is the name reason given to the "one-way direction" or "asymmetry" of time by British astrophysicist Arthur Eddington in the macroscopic universe.  Its direction, according to Eddington, is determined by studying the spatial organization of atoms, molecules, and bodies, and might be drawn upon a four-dimensional relativistic map of the world.

However physical processes at the microscopic level are believed to be either entirely or mostly time-symmetric: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet as was just mentioned at the macroscopic level it appears that this is not the case. arrow of time[3]

The question as to why things appear to different on the microscopic level is an unanswered question.

Many explain the observed temporal asymmetry at the macroscopic level, the reason we see time as having a forward direction, ultimately comes down to thermodynamics, the science of heat and its relation with mechanical energy or work, and more specifically to the Second Law of Thermodynamics. That laws uses the states that the entropy of a system either remains the same or increases in every process. This phenomenon is due to the extraordinarily small probability of a decrease or that a system will return to its original configuration, based on the extraordinarily larger number of microstates in systems with greater entropy. In other Entropy  can decrease or a system can return to its original configuration, but for any macroscopic system, this outcome is so unlikely that it will never be observed in the future.

However, entropy can decrease somewhere, provided it increases somewhere else by at least as much. The entropy of a system decreases only when it interacts with some other system whose entropy increases in the process.

Yet, it is difficult to apply that definition to a quantum environment because Schrödinger wave equation that quantum mechanics uses to determine the position component of a particle when observed does so in terms of a probability distribution over the entire universe.  Therefore, to define an arrow of time for a quantum system in terms of entropy one must show there is a physical connection between the macroscopic space-time environments we live in and a particles position in that probability field when it is observed. 

Unfortunately, we define the spatial components of entropy in our macroscopic universe in terms of the space-time concepts defined by Einstein.  Therefore, to define the arrow of time in the probabilistic world associated quantum mechanics in terms of entropy we must show how it is physically connected to the spatial properties of the macroscopic universe defined by him.

Einstein gave us the ability to do this when he used the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because it provided a method of converting a unit of time he associated with energy to unit of space.   Additionally, because the velocity of light is constant, he also defined a one to one quantitative correspondence between the both the relativistic and physical properties of a space-time universe and one made up of only four *spatial* dimensions.

Dong so allow will one to physically connect the probabilities associated with Schrödinger’s wave equation to the Thermodynamic laws that governor the entropy in our macroscopic universe.

For example, the article “ Why is energy/mass quantized? ” Oct 4, 2007 showed one can derive the quantum mechanical wave/particle properties of matter in terms of an energy wave on a "surface" of a three-dimensional space manifold with respect to fourth spatial dimension by extrapolating our understanding of a resonant structure created by a wave in a three-dimensional environment.

Briefly it showed the four conditions required for resonance to occur in a three-dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one consisting of four spatial dimensions.

The existence of four *spatial* dimensions would give an electromagnetic wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold to oscillate with the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established space.

Therefore, these oscillations in a "surface" of a three-dimensional space manifold would meet the requirements mentioned above for the formation of a resonant system or "structure" in four-dimensional space if one extrapolated them to that environment.

In our three-dimensional environment the energy of a resonant system can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency.

Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy quantum mechanical associates with the particle properties of matter.

Yet one can also define its boundary conditions of its resonate structure in the terms of our perceptions of a three-dimensional environment.

For example, in our three-dimensional world, a point on the two-dimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to three-dimensional space.

 Similarly, an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate up  or down with respect to a fourth *spatial* dimension.

It is the confinement of the upward and downward oscillations of an energy with respect to a fourth *spatial* dimension by an observation is what defines the spatial boundaries associated with a particle in the article Why is energy/mass quantized? " Oct 4, 2007.

This shows the reason Quantum Mechanics can define matter in terms of a particle/wave duality and why it only presents its particle or position properties when it is observed is because its wave component is only confined to three-dimensional space when an observation is made.

However, as mentioned earlier it also provides a way to physical connect the probabilistic environment defined by SchrÃdinger wave equation to the physicality of Einstein’s relativistic universe.

The physics of wave mechanics tell us that due to the continuous properties of the wave component associated with a quantum system it would be distributed throughout the entire "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension.

For example, the energy of a vibrating or oscillating ball on a rubber diaphragm would be disturbed over its entire surface while the magnitude of those vibrations would decrease as one move away from the focal point of the oscillations.

Similarly, if the assumption outlined above, that quantum properties of matter are a result of vibrations or oscillations in a "surface" of three-dimensional space is correct those oscillations would be distributed over the entire "surface" three-dimensional space while the magnitude of those vibrations would be greatest at the focal point of the oscillations and decreases as one moves away from it. lenth[4]

(Some may question the fact that the energy wave associated with particle would be simultaneously distributed over the entire universe.  However, the relativistic properties of space-time tell us the distance perceived by objects or particles in relative motion is dependent on their velocity which become zero at the speed of light.  Therefore, from the perspective of an energy wave moving at the speed of light, the distance between all points in the universe along its velocity vector is zero.  In other words, because its electromagnetic wave component of a particle is moving at the speed of light as all electromagnetic0 energy must is it would be distributed or simultaneous exists at every point in the universe along its velocity vector.  There can be no other conclusion if one accepts the validity of Einstein’s theories.)   

As mentioned earlier the article “ Why is energy/mass quantized? ” shown a wave/particle duality of matter can be understood in terms of a resonant structure formed wave energy on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Yet the science of Wave Mechanics tells us resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,

Similarly, a particle would most probably be observed were the magnitude of the vibrations in a "surface" of a three-dimensional space manifold is greatest and would diminish as one move away from that point.

This demonstrates that one can interconnect probabilities associated with Schrödinger’s wave equation to the physicality of the Einstein’s Relativistic universe.

As was mentioned earlier the arrow of time is defined in classical system in terms of entropy or the level of randomness (or disorder) of a system and the Second law of thermodynamics which states that there is an the extraordinarily small probability that a system will return to its original configuration, based on the extraordinarily larger number of microstates in systems with greater entropy even though its. 

Additionally, the above discussion also shows one can use the same definition for the arrow of time in a quantum universe as the one used in a macroscopic one because the position of a particle in a quantum can only be determine with respect to other particles in probability field Schrodinger’s equation.  Therefore, due to the fact that there are infinite number of possibilities in the probabilistic universe of quantum mechanics there an extraordinarily small chance of that universe retuning to is original configuration when an observation is made in the future.  

Later Jeff

Copyright Jeffrey O’Callaghan 2020

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Richard Feynman the farther of Quantum Electrodynamics believed Thomson’s double slit experiment provided a mechanism for understanding the wave particle duality of energy/mass because it clearly demonstrates their inseparability and provides a mechanisms for understanding how it is propagated through space.

The wave-particle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects.  Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent, second-order consequence of various limitations of the observer.

The reason the above-mentioned experiment is so important is because it provides a mechanism for understanding how electromagnetic energy is propagated and why the particle wave dually exists purely in terms of Einstein’s Theory of Relativity.

But before we begin, we must first understand how the electromagnetic wave component of a particle’s duality is propagated through space and time.

One of the difficulties involved in doing so is that we define its movement though space in terms Maxwell’s equations which are based on the interaction between its electric and magnetic components with respect to time not space.  This presents a problem because the particle component of its duality must always be defined by its spatial position when observed. Therefore, to understand how they are related we should attempt to define its movement through space and time in term of its spatial properties.

Einstein gave us the ability to do this purely in terms spatial properties of its electromagnetic wave components when he used the constant velocity of light to defined the geometric properties of space-time because it allows one to convert a unit of time in his space-time universe to an equivalent unit of space in an environment consisting of only four *spatial* dimensions.  Additionally, because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words, by mathematically defining the geometric properties of a space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

This gives one the ability to derive the properties of an electromagnetic wave and understand its movement in terms of the spatial displacement that would be created by its observed transverse wave characteristics. 

For example, a transverse wave on the two-dimensional surface of water moves through water because it causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force is developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the surface of the water. This results in a wave to move on the surface of the water.

Similarly, an energy wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that "surface" to become displaced or rise above and below the equilibrium point that existed before the wave was present.  This would result a wave moving on the "surface" of three-dimensional space.

Therefore, classical wave mechanics, if extrapolated  to four *spatial* dimensions tells us a force will be developed by the differential displacements caused by an energy wave moving on a "surface" of three-dimensional space with respect to a fourth *spatial* dimension that will result in its elevated and depressed portions moving towards or become "attracted" to each other causing it to move through space.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly, the magnitude of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two charges than it would be for a single charge.

One can also define the directionality of electrical component of electromagnetic energy in terms of the energy associated with its "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement because classical Mechanics tells us a horizontal force will be developed by that displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards the apex of that displacement.

However, this means that one can define a physical model for the propagation of an electromagnetic field in terms of Einstein’s space-time theory because, as was shown above when he mathematically defined its geometric properties in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his theory in terms of the geometry of four *spatial* dimensions.

Yet, viewing it in terms of its spatial components also allows one to understand the mechanism responsible for the wave particle duality of a photon as observed in the Thomson’s double slit experiment and why electromagnetic energy always presents itself as a particle when it strikes the detector in the that experiment.

For example, the article, "Why is energy/mass quantized?" Oct. 4, 2007 showed that one can use the Einstein’s theories to explain the quantum mechanical properties of an electromagnetic wave by extrapolating the rules of classical resonance in a three-dimensional environment to an energy wave moving on “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in an energy wave moving in four *spatial* dimensions.

The existence of four *spatial* dimensions would give the energy wave associated with a photon the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

As was shown in that article these resonant systems in four *spatial* dimensions are responsible for the particle called a photon.

However, one can also use Einstein space-time theories when viewed in their spatial equivalent to explain how the boundaries of the standing wave responsible for creating the resonant system that article indicated was responsible of a particles formation are created.

In classical physics a standing wave is created when the vibrational frequency of a source causes reflected waves from one end of a confined medium to interfere with incident waves from the source.  This interference of the wave energy causes their peaks troughs to be reinforce in the volume they are occupying thereby creating a standing wave.

The confinement required to create a standing wave in space-time or its equivalent in four *spatial* dimensions can be understood by comparing it to the confinement a point on the two-dimensional surface of paper experiences when oscillating with respect to three-dimensional space.  The energy associated with the wave motion of that point would be confined to its two-dimensional surface and would be reflected and interfere with the incident wave when reaches three-dimensional space at its edge. Therefore, a standing would be created by its interaction with three-dimensional space.

In other words, when a wave on the surface of a piece of paper encounters the third *spatial* dimension at its edge it is reflected back allowing a standing wave to be formed on its surface.

Similarly, an electromagnetic wave moving on the surface of three-dimensional space would be confined to it and reflected back to that volume, similar to the surface of the paper if it was prevented from oscillating with respect to a four *spatial* dimensions or four-dimensional space-time.

In other words, the interference caused by the confinement of an electromagnetic wave to three-dimensional space, which is caused by it striking the detection screen in the Thomson’s double slit experiment results in the resonant standing wave to be formed in space called a photon.

That experiment is made up of "A coherent source of photons illuminating a screen after passing through a thin plate with two parallel slits cut in it.  The wave nature of light causes it wave component to interfere after passing through both slits, creating an interference pattern of bright and dark bands on the screen.  However, at the screen, the light "is always found to be absorbed as discrete particles, called photons".

When only one slit is open, the pattern on the screen is a diffraction pattern however, when both slits are open, the pattern is similar but with much more detail.  These facts were elucidated by Thomas Young in a paper entitled "Experiments and Calculations Relative to Physical Optics," published in 1803.  To a very high degree of success, these results could be explained by the method of Huygen ‘s Fresnel principle that is based on the hypothesis that light consists of waves propagated through some medium.  However, discovery of the photoelectric effect made it necessary to go beyond classical physics and take the quantum nature of light into account.

However, the most baffling part of this experiment comes when only one photon at a time impacts a barrier with two opened slits because an interference pattern forms which is similar to what it was when multiple photons were impacting the barrier.   This is a clear implication the particle called a photon has a wave component, which simultaneously passes through both slits and interferes with itself.  (The experiment works with electrons, atoms, and even some molecules too.)"

Even more puzzling is why any attempts to measure which slit that electron passed through cause the interference pattern to disappear.

Yet, as mentioned earlier one can derive the outcome of this experiment by assuming that electromagnetic energy is propagated by a wave on the "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension instead of four-dimensional space-time

For example, the reason why the interference patterns remain when only one photon at a time is fired at the barrier with both slits open or "the most baffling part of this experiment" is because, as was just shown it has an extended spatial volume which is directly related to the wavelength.

This means a portion of its energy can simultaneously pass both slits, if the diameter of its volume exceeds the separation of the slits and recombine on the other side to generate an interference pattern.

Additionally, one can also explain why the interference pattern disappears when a detector is added to determine which slit a photon has passed through.  The energy required to measure which slit it passes through interacts with it causing the wavelength of that portion to change so that it will not have the same resonant characteristics as one that passed through the other slit   Therefore, the energy passing thought that slit will not be able to interact, with the energy passing through the other one to form an interference pattern on the screen.

However, as was shown earlier one can also show the reason the interference pattern appears as a particle when electromagnetic wave contacts a detection screen is because striking it results in it being confined to three-dimensional space instead of four-dimensional space-time or four spatial dimensions, thereby creating a standing wave in either four spatial dimensions or four dimensional space-time to be created.

In other words, it clearly shows the reason all forms of energy exhibit both wave and particle properties are because they are physically made up of waves in terms of Einstein’s Theory of Relativity.

The above discussion shows that Richard Feynman was right in assuming that Thomson’s double slit experiment provided a mechanism for understanding the  wave particle duality of energy/mass because it clearly demonstrates their inseparability.

Additionally, it also provides an explanation how and why energy  is propagated through space because it shows the quantum mechanical and wave properties of energy displayed in the double slit experiment can be understood if one assumes they are made up of a resonant system in a moving in a four dimensional space-time manifold or on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension in terms Einstein theories. 

It should be remembered that Einstein’s genius allows us to choose whether to define an electromagnetic wave either a space-time environment or one consisting of four *spatial* dimension when he defined its geometry in terms of the constant velocity of light.

Later Jeff

Copyright Jeffrey O’Callaghan 2020

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It is possible, as this article will show that a standing wave in space-time is responsible for a photon.

A standing waves are created within a medium when the vibration frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source. This interference occurs in such a manner that specific points along the medium appear to be standing still. Because the observed wave pattern is characterized by points that appear to be standing still, the pattern is often called a standing wave pattern. Such patterns are only created within the medium at specific frequencies of vibration. These frequencies are known as harmonic frequencies, or merely harmonics. At any frequency other than a harmonic frequency, the interference of reflected and incident waves leads to a resulting disturbance of the medium that is irregular and non-repeating.

In March 1905 Einstein published a paper on the photoelectric effect entitled "On a Heuristic Viewpoint Concerning the Production and Transformation of Light" in which he proposed the idea of energy quanta and postulated light exists as tiny packets, or particles, called photons.

In that paper he stated Energy, in the propagation of a ray of light, is not continuously distributed over steadily increasing spaces, but it consists of a finite number of energy quanta but he did not say why.

Even so many fell the idea of light quanta contradicts the wave theory of light that follows naturally from James Clerk Maxwell’s equations for electromagnetic behavior and, more generally, the assumption of infinite divisibility of energy in physical systems.

Additionally he did not address the issue of how these "tiny packets" of energy called photons can move through space at the speed of light. This present a problem because he showed that energy and mass are equivalent and that the mass of any object or particle moving at the speed of is infinite. 
Therefore, if energy is equivalent to mass one would assume that energy required to move a photon at the speed of light would be infinite.

However, Einstein gave us a way to define electromagnetic energy in a manner which is not only consistent with his theories but also with our classical understanding of nature when, in his General Theory of Relativity he showed that matter can be converted into energy or energy into matter according to the equation E=mc2.

For example Einstein defined the origin of the mass component of particles and all other objects, such as the sun in terms of curvature or distortion in the continuous field properties of space-time not in terms of their particle properties.

QED defines the fundamental unit (quanta) of light as "bundles of pure energy traveling at the speed of light with the unique property of being both particle and wave. However this means that as light moves through space-time the peaks and troughs of its wave properties would cause positive and negative spatial displacements in the "surface’ of space time.

Yet, it is difficult to understand how a spatial displacement can be responsible for of electromagnetism and how and why its wave properties morph to the particle QED defines as the photon when it is observed or interacts with matter because he CHOSE to use time or a displacement in space-time dimension to define mass and energy and not its spatial properties.

Yet he gave us the ability to form a physical image of this how the spatial properties of a photon’s wave packet are responsible for its movement through space when he defined its geometric properties in terms of the constant velocity of light and a dynamic balance between mass and energy because that provided a method of converting a unit of time in a space-time environment to a unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forms of matter and energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, this change in perspective gives one the ability to understand how the energy of a photon can move through space at the speed of light why it becomes a particle when interacting with matter in terms of the concepts of his theories.

For example as waves travel through water; they do not take the water with them because as wave arrives it lifts the water particles, they then travel forward, down and back so that each particle completes a circle. Circling movements of particles near the surface set off smaller circling movements below them therefore the waves don’t actually move the water forward. In other words the particles in a wave do not move with respect to space but exchange their potential energy of the water for kinetic energy associated with the wave’s movement.

Similar to wave on water the trough of a light wave would create a point with a positive curvature on a "surface" of the three-dimensional space manifold with respect to a fourth *spatial dimension which would present itself as the potential energy Einstein associated with mass. That point in space would then travel forward and up and back so that each one completed a circle without moving with respect to background of space. As the wave passed this point the potential energy of positive curvature in four "spatial" dimensions Einstein associated with mass would be converted to kinetic energy associated with a moving mass. In other words the wave packet of a photon can move though space at the speed of light because similar to a wave on water light waves do not cause a point in space to move with respect to the background of space-time.

This suggest that light is not electromagnetic wave but an energy wave in space-time which is the result of the potential energy created by the trough of a wave on its "surface" being converted to the kinetic energy associated with its peak thereby causing what is called light to move through space.

However, this also tell us when viewed in terms of their spatial properties that the electromagnetic properties of a light wave are the result of its propagation and not the casualty as is suggested by Maxwell’s equations.

(Later it will be shown in terms of those spatial properties the reason why this wave becomes a particle when interacting with matter but for now we would like to focus our attention on electromagnetic properties of light or a photon’s wave packet)

As was mention earlier a wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present. A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the surface of the water.

Similarly a matter wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that "surface" to become displaced or rise above and below the equilibrium point that existed before the wave was present.

Therefore, classical wave mechanics, if extrapolated to four *spatial* dimensions tells us a force will be developed by the differential displacements caused by a matter wave moving on a "surface" of three-dimensional space with respect to a fourth *spatial* dimension that will result in its elevated and depressed portions moving towards or become "attracted" to each other.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly the magnitude of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one. Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two charges than it would be for a single charge.

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it. This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards the apex of that displacement.

This shows that one can use the spatial properties of Einstein’s theories to derive causality of the electromagnetic forces of light and how the wave packet Quantum Electrodynamics associates with a photon is propagated through space by extrapolating the laws of classical mechanics in a three-dimensional environment to one consisting of four dimensional space-time or four *spatial* dimensions.

However viewing a light in terms of the spatial instead of the time properties of his theories allows one to understand how why it always appears as a particle when measured or observed.

For example in the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can physical derive photonic properties of light by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a matter energy wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one consisting of four spatial dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold to oscillate with the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established space.

Therefore, these oscillations in a "surface" of a three-dimensional space manifold would meet the requirements mentioned above for the formation of a resonant system or "structure" in four-dimensional space if one extrapolated them to that environment.

Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with it fundamental or a harmonic of its fundamental frequency.

Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with the quantum mechanical properties of a photon.

Yet one can also define the boundary conditions required to establish the standing wave component of a resonant system mentioned earlier that is responsible for it its particle properties as defined by QED.

For example in classical physics, a point on the two-dimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to three-dimensional space.

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.

The confinement of the “upward” and “downward” oscillations of the field properties of mass with respect to a fourth *spatial* dimension is what defines the spatial boundaries that enables the formation of a resonant system which the article  “Why is energy/mass quantized?” defined as being responsible for a particle.

When a wave on water comes ashore the energy associated with its wave properties is confined to a specific region of the shoreline.

Similarly when a photon’s wave packet is measured or observed a portion of its wave energy is transmitted to the measuring instrument while some of it may be redirected or reflected similar to a wave striking the shoreline. In other word the energy wave which earlier was define as being responsible for the transmission of light interacts with measuring equipment for the same reason a water wave interacts with the shoreline.

However it also explains why light is always observed as a particle when it encounters encounters a measuring instrument or is observed.

In the quantum mechanical system described above such as light interacting with a particle, resonance only occurs when the frequency at which the force applied is equal or nearly equal to one or a multiple of the natural frequencies of the system on which it acts. In other words light when confined to three-dimensional space by interaction with a particle it will always present itself as the resonant structure that has the energy equal to one or a multiple of the natural frequency of space time. The remaining energy will be radiated through space as light with a lower frequency.

In other words the particle component of light or an electromagnetic wave is not the cause of its interaction with particles but a result of it.

However one can use the above model to explain why photons do not interact with each other because similar to waves on water if their is no obstruction to hinder their movement a wave will not interact with each other.  In other words, photon do not interfere with each other for the same reason that all energy waves do not.

Summing up, Einstein genius allows us to view his theory in either four dimensional space-time or four spatial dimensions. As was shown above changing ones perspective on his theory from time to its spatial equivalent allows one to define light as an energy wave in space and shows the electromagnetic properties are the result NOT the casualty of its propagation but a result of it. Similarly it shows the particle component of light is not the cause of its interaction with a particle but a result of it.  Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog Directory

It is important to note the validity these conclusions cannot be falsified if one accepts the validity of his theories.

Later Jeff

Copyright Jeffrey O’Callaghan 2019

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 A Quantum Singularity is a misnomer because it owes it existence to classical one created by a black hole not to its quantum mechanical properties.black_hole_singularigy 

Even so many physicists assume it is the key to unifying Quantum mechanics with Einstein’s General and Special Theories of Relativity because they believe the gravitational collapse of matter in a black hole, predicted by his theories also predicts, with equal certainty the existence of a singularity, which by definition is infinitely small and quantum mechanical in nature. Therefore, due to the fact that they are caused by gravitational forces a theory of quantum gravity would be required to define its formation.

Its existence is based on a mathematical interpretation of General Theory of Relativity which tells us that when star starts to collapse after burning up its nuclear fuel and forms a black hole the gravitational forces of its mass become large enough to cause matter to collapse to zero volume or one that is governed by quantum mechanics.

However, even though there is observational evidence for the existence of black holes there never will be any for a singularity because according to the General Theory of Relativity nothing, including light can escape form one.

For example NASA’s Hubblesite tells us that "Astronomers have found convincing evidence for a black hole in the center of our own Milky Way galaxy, the galaxy NGC 4258, the giant elliptical galaxy M87, and several others. Scientists verified its existence by studying the speed of the clouds of gas orbiting those regions. In 1994, Hubble Space Telescope data measured the mass of an unseen object at the center of M87. Based on the motion of the material whirling about the center, the object is estimated to be about 3 billion times the mass of our Sun and appears to be concentrated into a space smaller than our solar system."

However, as mentioned earlier we will never be able to observe a singularity because they only exist inside black hole.  Therefore to determine their reality we must rely solely on the predictions of the General Theory of Relativity regarding their formation.

Yet, as mentioned earlier there are some who say the mathematics used to predict the existence of a black hole also predicts, with equal certainty the existence of singularities.  In other words by verifying the existence of black holes though mathematics means that they have also verified the existence of singularities.

However this would only be true if the mathematics used to predict both a black hole and its singularity conform to the conceptual arguments associated with Einstein General Theory of Relativity because its existence is based solely on that mathematics of that theory and not on observations, as is the case of black holes.

In other words the fact that we can observe a black hole tells us the mathematics used to predict its existence has a valid basis in ideas of General Relativity. 

However the same cannot be said about the existence of a singularity because the conceptual arguments found in that theory tells us that we cannot extrapolate the mathematics associated with it to the formation of a black hole.

To understand why we must look at how it describes both the collapse of a star to a black hole and then what happens to its mass after its formation.

Einstein in his General Theory of Relativity predicted time is dilated or moves slower when exposed to gravitational field than when it is not.  Therefore, according to Einstein’s theory a gravitational field, if strong enough it would stop time.

In 1915 Karl Schwarzschild discovered that according to it the gravitational field of a star greater than approximately 2.0 times a solar mass would stop the movement of time if it collapsed to a singularity.  He also defined the critical circumference or boundary in space around a singularity where the strength of a gravitational field will result in time being infinitely dilated or slowing to a stop.

In other words as a star contacts and its circumference decreases, the time dilation on its surface will increase.  At a certain point the contraction of that star will produce a gravitational field strong enough to stop the movement of time.  Therefore, the critical circumference defined by Karl Schwarzschild is a boundary in space where time stops relative to the space outside of that boundary.

This critical circumference is called the event horizon because an event that occurs on the inside of it cannot have any effect on the environment outside of it.

Yet many physicists, as mentioned earlier believe the existence of a singularity is an inevitable outcome of Einstein’s General Theory of Relativity.

However, it can be shown using the concepts developed by Einstein; this is not true.

In Kip S. Thorne book "Black Holes and Time Warps", he describes how in the winter of 1938-39 Robert Oppenheimer and Hartland Snyder computed the details of a stars collapse into a black hole using the concepts of General Relativity. On page 217 he describes what the collapse of a star would look like, form the viewpoint of an external observer who remains at a fixed circumference instead of riding inward with the collapsing stars matter. They realized the collapse of a star as seen from that reference frame would begin just the way every one would expect. "Like a rock dropped from a rooftop the stars surface falls downward slowly at first then more and more rapidly. However, according to the relativistic formulas developed by Oppenheimer and Snyder as the star nears its critical circumference the shrinkage would slow to a crawl to an external observer because of the time dilatation associated with the relative velocity of the star’s surface. The smaller the circumference of a star gets the more slowly it appears to collapse because the time dilation predicted by Einstein increases as the speed of the contraction increases until it becomes frozen at the critical circumference.

However, the time measured by the observer who is riding on the surface of a collapsing star will not be dilated because he or she is moving at the same velocity as its surface.

Therefore, the proponents of singularities say the contraction of a star can continue until it becomes a singularity because time has not stopped on its surface even though it has stopped to an observer who remains at fixed circumference to that star.

But one would have to draw a different conclusion if one viewed time dilation in terms of the gravitational field of a collapsing star from the reference frames of all observers as Einstein tells we must because they are all equivalence.

Einstein showed that time is dilated by a gravitational field. Therefore, the time dilation on the surface of a star will increase relative to an external observer as it collapses because, as mentioned earlier those forces at its surface increase as its circumference decrease.

This means, as it nears its critical circumference its shrinkage slows with respect to an external observer who is outside of the gravitation field because its increasing strength causes a slowing of time on its surface. The smaller the star gets the more slowly it appears to collapse because the gravitational field at its surface increase until time becomes frozen for the external observer at the critical circumference.

Therefore, the observations of an external observer would make using conceptual concepts of Einstein’s theory regarding time dilation caused by the gravitational field of a collapsing star would be identical to those predicted by Robert Oppenheimer and Hartland Snyder in terms of the velocity of its contraction.

However, as was mentioned earlier Einstein developed his Special Theory of Relativity based on the equivalence of all inertial reframes which he defined as frames that move freely under their own inertia neither "pushed not pulled by any force and therefore continue to move always onward in the same uniform motion as they began".

This means that one can view the contraction of a star with respect to the inertial reference frame that, according to Einstein exists in the exact center of the gravitational field of a collapsing star.

(Einstein would consider this point an inertial reference frame with respect to the gravitational field of a collapsing star because at that point the gravitational field on one side will be offset by the one on the other side. Therefore, a reference frame that existed at that point would not be pushed or pulled relative to the gravitational field and would move onward with the same motion as that gravitational field.)

The surface of collapsing star from this viewpoint would look according to the field equations developed by Einstein as if the shrinkage slowed to a crawl as the star neared its critical circumference because of the increasing strength of the gravitation field at the star’s surface relative to its center. The smaller it gets the more slowly it appears to collapse because the gravitational field at its surface increases until time becomes frozen at the critical circumference.

Therefore, because time stops or becomes frozen at the critical circumference for both an observer who is at the center of the clasping mass and one who is at a fixed distance from its surface the contraction cannot continue from either of their perspectives.

However, Einstein in his general theory showed that a reference frame that was free falling in a gravitational field could also be considered an inertial reference frame.

As mentioned earlier many physicists assume that the mass of a star implodes when it reach the critical circumference. Therefore, the surface of a star and an observer on that surface will be in free fall with respect to the gravitational field of that star when as it passes through its critical circumference.

This indicates that point on the surface of an imploding star, according to Einstein’s theories could also be considered an inertial reference frame because an observer who is on the riding on it will not experience the gravitational forces of the collapsing star.

However, according to the Einstein theory, as a star nears its critical circumference an observer who is on its surface will perceive the differential magnitude of the gravitational field relative to an observer who is in an external reference frame or, as mentioned earlier is at its center to be increasing. Therefore, he or she will perceive time in those reference frames that are not on its surface slowing to a crawl as it approaches the critical circumference. The smaller it gets the more slowly time appears to move with respect to an external reference frame until it becomes frozen at the critical circumference.Therefore, time would be infinitely dilated or stop in all reference that are not on the surface of a collapsing star from the perspective of someone who was on that surface.

However, the contraction of a stars surface must be measured with respect to the external reference frames in which it is contracting. But as mentioned earlier Einstein’s theories indicate time on its surface would become infinitely dilated or stop in with respect to reference frames that were not on it when it reaches its critical circumference.

There are some who claim that irregularities in the velocity of contractions in the mass forming the black hole would allow it continue to collapse beyond its event horizon. However Einstein’s theories tells us that time would move slower for the faster moving mass components than the slower ones thereby allowing the them to catch up with their faster moving onew so they will be moving at the same speed when they reach the event horizon.

This means, as was just shown according to Einstein’s concepts time stops on the surface of a collapsing star from the perspective of all observers when viewed in terms of the gravitational forces. Therefore it cannot move beyond the critical circumference because motion cannot occur in an environment where time has stopped.

This contradicts the assumption made by many that the implosion would continue for an observer who was riding on its surface.

Therefore, based on the conceptual principles of Einstein’s theories relating to time dilation caused by a gravitational field of a collapsing star it cannot implode to a singularity as many physicists believe and must maintain a quantifiable minimum volume which is equal to or greater than the critical circumference defined by Karl Schwarzschild.

This means either the conceptual ideas developed by Einstein are incorrect or there must be an alternative solution to the field equations that many physicists used to predict the existence of singularities because, as has just been shown the mathematical predications made by it regarding their existence is contradictory to conceptual framework of his theories.   Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog Directory

As was mentioned earlier many physicists think the key to unifying Quantum mechanics with Einstein’s General and Special Theories of Relativity is the singularity that some of the mathematical models say exists in black holes.   However, as was show above their existence is not supported by his theories.

Later Jeff

Copyright Jeffrey O’Callaghan 2019

Please visit our  Facebook group The Road to unification of Quantum and Relativistic theories if you would like to comment or contribute to our project

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In quantum mechanics, wave function collapse is said to occur when a wave function, initially in a superposition of several states appears to reduce to one due to interaction with the external world.  This interaction is called an observation.

The measurement problem in quantum mechanics involves understanding how (or whether) wave function collapse occurs. The inability to directly observe such a collapse has given rise to different interpretations of quantum mechanics and poses a key set of questions that each interpretation must answer.

Quantum mechanics assumes it evolves deterministically according to the Schrödinger equation as a linear superposition of different states. However, when observed it is always found in a definite state.  Its future evolution is based on the state the system was discovered to be in when the measurement was made.  In other words, the measurement “did something” to the system that is not obviously a consequence of Schrödinger evolution. The measurement problem is describing what that “something” is, and how a superposition of many possible values becomes a single measured value.

To express matters differently, (paraphrasing Steven Weinberg) Schrödinger wave equation determines the wave function at any later time. If observers and their measuring apparatus are themselves described by a deterministic wave function, why can we not predict precise results for measurements, but only probabilities? As a general question: How can one establish a correspondence between quantum and classical reality.

However, Einstein unknowing may have able to define what happens to the wave function when observed by extrapolating the rules of classical mechanics to the physical properties of the space-time environment he defined.

One of the reasons he may have been unaware of this possibility is because superposition involves the spatial properties of position where as he chose define the universe in terms of time or the properties of four-dimensional space-time.  In other words, understanding the physical connection between the spatial properties of position and the time properties of Einstein space-time universe is extremely difficult for the same reasons as one would find it difficult to define a physical connection between apples and oranges.

However, Einstein gave us a way around this when he used the equation E=mc^2 and the constant velocity of light to define the geometric properties of mass and energy in a space-time universe because that provided a method of converting a unit of time in space-time environment to unit of space in one made up of four *spatial* dimensions.  Additionally, because the velocity of light is constant, he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

This would allow one to describe what happens to the linear superposition of different states when an observation is made and why it becomes a single measured value.

Additionally, it would also allow one to understand the validity of quantum mechanics assumption that particles can be defined in terms of waves, how they can be superimposed or simultaneously be in multiple positions before being observed and why their interaction with the external world must be describe in terms of probabilities.

For example, the article, “Why is energy/mass quantized?” Oct. 4, 2007 showed that one can use the Einstein’s theories to explain and understand the physicality of the wave properties of particles by extrapolating the rules of classical resonance in a three-dimensional environment to an energy wave moving on “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  It also explains why all energy must be quantized or exists in these discrete resonant systems when observed.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in an energy wave moving in four *spatial* dimensions.

The existence of four *spatial* dimensions would give an energy wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in four spatial dimensions.

As was shown in that article the ossifications of these resonant systems in four *spatial* dimensions are responsible for the wave properties quantum mechanical particles.

However, one can also explain how the boundaries of a particle’s resonant structure are defined.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly, an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.

It is the confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension which allows the resonate structure the article “Why is energy/mass quantized?” Oct. 4, 2007 showed was responsible for a particle to exist. \

In other words the reason it becomes a single measured value when observed is because when the energy wave moving through space either space-time or four spatial dimensions is confined by an observation to three-dimensional space the interference between waves reflected back and forth by that confinement sets a resonant standing wave in space which is called a particle.

In other words, Einstein give us a classical validation of the quantum mechanical assumption that particles can be thought of as waves because it shows they are made up of resonate structures formed by energy wave and why when someone observes its wave component it always appears as a particle.

Additionally, one of the most advantageous results of viewing the relativistic properties of Einstein’s theories in terms of their spatial instead of its time components is that gives us the answer to one of the most perplexing aspects of quantum mechanics; that of how and why a particle can simultaneously exists anywhere in the universe before being observed.

This is because it tells the length of an object relative to another is affected by its relative velocity and that there are no preferred reference frames by which one can measure that length. Therefore, one must not only view the distance traversed by the wave with respect to an observer who was external to it but one must also view the distance between observers from the wave’s perspective. Yet it also tells us that the length of everything including the universe from an object or wave moving at the speed of light is zero as can be seen from his formal on the right for length contraction.

Therefore, from the perspective of the energy wave the article “Why is energy/mass quantized?” showed was responsible for a particle which is moving at the speed of light with respect to all observers the distance or length between all observers no matter where they are in the universe is zero with respect to that wave.  Therefore, it exists at every point in between.

This gives us an explanation in terms of the four spatial dimensional equivalent of Einstein space-time universe for the VALIDITY of quantum mechanics assumption that a photon’s wave packet simultaneously exists everywhere in in the universe before being observed. In other words, it only “decides” where it wants to be in space when it is prevented from moving at the speed of light relative to an observer by an observation.

However, viewing Einstein theories from the perceptive of their spatial instead of their time components also allows one to derive the classical reason why one must use probabilities to determine a particles position will be before being observed.

The fact that one can, as was show in the article mentioned earlier “Why is energy/mass quantized?” derive the particle properties of an energy wave as the result of a resonant structure formed on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension also allows one to understand how a particle “decides” where is want to be in terms of our classical understanding of the world around us.

For example, the energy of a vibrating or oscillating ball on a rubber diaphragm would be disturbed over its entire surface while the magnitude of those vibrations would decrease as one move away from the focal point of the oscillations.

Similarly, if one accepts the validity of Einstein’s theories and the theoretical model that the quantum properties of a particle are a result of vibrations or oscillations in a “surface” of three-dimensional space, those oscillations as was shown above would be distributed over the entire “surface” three-dimensional space with respect to all observers while the magnitude of those vibrations would be greatest at the focal point of the oscillations and decreases as one moves away from it.

Yet the science of Wave Mechanics tells us resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point.

Similarly, a particle would most probably be found were the magnitude of the vibrations in a “surface” of a three-dimensional space manifold is greatest and would diminish as one move away from that point.

This shows how one can make intuitive “sense” of Quantum Superposition and why the wave packet of a particle decides what and where it wants to be when observed by extrapolating the rules of a classical mechanics to the spatial equivalent of Einstein’s theories.

In other words it solves the the measurement problem because it provides an understanding what happens to the wave function when it interacts with the  external world by describing what and how the superposition of many possible values becomes a single measured value when an observation is made.   Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog Directory

It should be remembered Einstein genius allows us to view his theory in either four-dimensional space-time or its equivalent in only four *spatial* dimensions.  As was shown above changing one’s perspective on his theory from time to its spatial equivalent allows one to form an intuitive understanding of quantum Superposition based on our experiences in a three-dimensional world.

Latter Jeff

Copyright Jeffrey O’Callaghan 2019

Both Einstein’s Special Theory of Relativity and Quantum Mechanics tell us a photon is massless particle that moves through space. However, they tell us nothing about how a particle can be mass less, how they interact with other particles and how the photon a particle with no mass as defined in Quantum Electrodynamics or QED has the momentum to travel though space at the speed of light.

Einstein tells us that the mass of all entities including particles approaches infinity as it approaches the speed of light.  Therefore, according to him a photon has to be massless because if it wasn’t it could not attain that speed.  However, Quantum mechanics defined photons as the fundamental unit (quanta) of light while having the unique property of being both a particle and wave. They are often described as being mass less “bundles of pure energy traveling at the speed of light.

 

However, as was just mentioned neither of these two well established and verified theories tell us what it is, how they move through space, how a particle mass less can move at the speed of light or how they interact with other particles that have mass.

Granted Quantum Electrodynamics (QED) describes how light and matter interact and is the first theory where full agreement between quantum mechanics and Special Relativity is achieved in terms of an exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.  However, it tells us nothing how a photon moves through space and the causality of the electromagnetic properties of its wave component which are a fundamental part of its definition.

Yet Einstein also was unable to define an electromagnetic wave and how it moves through space in terms of his Special and General Theories of Relativity even though he used electromagnetic energy to define their physical existence.

However, Einstein gave us a way to define what a photon is, derive its electromagnetic properties, how it moves thought space and interacts with matter in a manner which is not only consistent with his theories but also with our classical understanding of nature when, in his General Theory of Relativity he showed that matter can be converted into energy or energy into matter according to the equation E=mc2.

For example, Einstein defined the origin of the mass component of particles and all other objects, such as the sun in terms of curvature or distortion in the continuous field properties of space-time not in terms of its particle properties.  Specifically, he defined mass and its potential energy in terms of positive curvature in the spatial geometry of our universe which causes energy to become concentrated at the apex of that curvature.

However, in doing so he also defined the kinetic energy released when mass is converted to energy as reduction, an opposite or a negatively directed curvature in space-time. In other words when defined the potential energy of mass in terms of a positive curvature he indirectly defined the kinetic energy created by its disassociation in terms of negative curvature in space-time.

As was mentioned earlier QED defines the fundamental unit (quanta) of light as “bundles of pure energy traveling at the speed of light with the unique property of being both particle and wave.  However, this means that as light moves through space-time the peaks and troughs of its wave properties would cause positive and negative spatial displacements in its “surface’.

Unfortunately, Einstein made it difficult to understand the how these spatial displacements can be responsible for the properties of electromagnetism and a photon because he CHOSE to use time or a space-time dimension to define mass and energy and not their spatial properties.

Yet he gave us the ability to form a direct picture of this how the spatial properties of a photon’s wave packet are responsible for its movement through space when he defined its geometric properties in terms of the constant velocity of light and a dynamic balance between mass and energy because that provided a method of converting a unit of time in a space-time environment to a unit of space in four *spatial* dimensions.  Additionally, because the velocity of light is constant, he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forms of matter and energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, this change in perspective gives one the ability to understand how light moves through space, why QED defines it as a massless particle and why this wave becomes a particle when interacting with matter in terms of the concepts of his theories.

For example, as waves travel through water; they do not take the water with them because as wave arrives it lifts the water particles, they then travel forward, down and back so that each particle completes a circle. Circling movements of particles near the surface set off smaller circling movements below them therefore the waves don’t actually move the water forward.  In other words, the particles in a wave do not move with respect to space but exchange their potential energy of the water for kinetic energy associated with the wave’s movement.

Similar to wave on water the trough of a light wave would create a point with a positive curvature on a “surface” of the three-dimensional space manifold with respect to a fourth *spatial dimension which as was mentioned earlier would present itself as potential energy Einstein associated with mass.  That point in space would then travel forward and up and back so that each one completed a circle without moving with respect to background of space.  As the wave passed this point the potential energy of positive curvature in four spatial dimensions Einstein associated with mass would be converted to kinetic energy he associated with the peak or upward movement in the “surface” of a three-dimensional space manifold with respect to a fourth spatial dimension.  In other words, the wave packet of a photon can move though space at the speed of light because similar to a wave on water light waves do not cause a point in space to move with respect to the background.

This suggest that light is not electromagnetic wave but an energy wave in space-time which is the result of the potential energy created by the trough of a wave on its “surface” being converted to the kinetic energy associated with its peak thereby causing what is called light to move through space.

However, also tell us when viewed in terms of their spatial instead of their time properties the electromagnetic properties of a light wave are the result NOT the casualty of its propagation.

(Later it will be shown in terms of those spatial properties the reason why this wave becomes a particle when interacting with matter but for now we would like to focus our attention on electromagnetic properties of light or a photon’s wave packet.) 

As was mention earlier a wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become “attracted” to each other and the surface of the water.

Similarly, an energy wave on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that “surface” to become displaced or rise above and below the equilibrium point that existed before the wave was present.

Therefore, classical wave mechanics, if extrapolated  to four *spatial* dimensions tells us a force will be developed by the differential displacements caused by an energy wave moving on a “surface” of three-dimensional space with respect to a fourth *spatial* dimension that will result in its elevated and depressed portions moving towards or become “attracted” to each other.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly, the magnitude of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two charges than it would be for a single charge.

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its “peaks” and “troughs” that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards the apex of that displacement.

This shows that one can use the spatial properties of Einstein’s theories to derive causality of the electromagnetic forces of light and how the wave packet Quantum Electrodynamics associates with a photon is propagated through space by extrapolating the laws of classical mechanics in a three-dimensional environment to one consisting of four-dimensional space-time or four *spatial* dimensions.

However, viewing a light wave in terms of the spatial instead of its time properties of his theories allows one to understand how it interacts with particles and why it always appears as one when interacting with them.

For example, the article, “Why is energy/mass quantized?” Oct. 4, 2007 showed that one can use the Einstein’s theories to explain and understand the physicality of the wave properties of a photon and all other particles by extrapolating the rules of classical resonance associated with a standing  wave in a three-dimensional environment to an energy wave moving on “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  One can also understand why all energy must be quantized or exists in these discrete resonant systems when observed.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in a matter wave moving in four *spatial* dimensions.

The existence of four *spatial* dimensions would give an energy wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in four spatial dimensions.

As was shown in that article these resonant systems in four *spatial* dimensions are responsible for a photon’s quantum mechanical properties.

However, one can also use the four-dimensional equivalent to explain how the spatial boundaries of a particle’s resonant structure are defined.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly, an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.

The confinement to three dimensional space of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the geometric spatial boundaries of the standing wave associated with a particle in the article “Why is energy/mass quantized?

This provides the ability to understand, in classical terms the inseparability of the wave-particle duality of energy/mass because it clearly demonstrates how one is dependent on the other.

It also defines in classical terms the reason, why all measurements or observations of electromagnetic energy takes the form particles and not waves.

Classical wave mechanics tells us a resonate standing wave pattern is created within a medium when the vibrational frequency of the source causes the reflected waves from one end of the medium to interfere with incident waves from the source.

In other words, when the wave properties of a photon or any other particle is confined to three-dimensional space by an observation the reflected waves from one end of the confinement caused by that observation or an interaction with another particle interfere with the reflected ones resulting in a standing wave being form.  As was mentioned earlier, the article, “Why is energy/mass quantized?” Oct. 4, 2007 showed the resonate properties of that standing wave are responsible for the quantum or particle properties all systems.

This tells us the photonic or particle component of light or an electromagnetic wave is not the cause of its interaction with particles but a result of it.

Summing up, Einstein genius allows us to view his theory in either four-dimensional space-time or four spatial dimensions.  As was shown above changing one’s perspective on his theory from time to its spatial equivalent allows one to define light as a matter energy wave in space-time and shows the electromagnetic properties are the result NOT the casualty of its propagation.  Additionally, it can also show the particle component of light is not the cause of its interaction with a particle but a result of it.

It is important to remember the validity these conclusions cannot be falsified if one accepts the validity of his theories.

Later Jeff

Copyright Jeffrey O’Callaghan 2019

 

Quantum entanglement is the name given to quantum mechanical assumption that all particles remain connected so that actions performed on one affect the other, even when separated by great distances.

The rules of quantum physics state that an unobserved photon exists in all possible states simultaneously but, when observed or measured, exhibits only one state.  

Entanglement occurs when a pair of particles, such as photons, interacts physically. For example a laser beam fired through a certain type of crystal can cause individual photons to be split into pairs of entangled photons even when they are separated by a large distance, hundreds of miles or even more.

In other words when observed, Photon A takes on an up-spin state. Entangled Photon B, though now far away, takes up a state relative to that of Photon A (in this case, a down-spin state). The transfer of state between Photon A and Photon B takes place at a speed of at least 10,000 times the speed of light, possibly even instantaneously, regardless of distance.

The phenomenon so riled Albert Einstein he called it “spooky action at a distance.” and in 1935 he along with Podolsky Rosen proposed the following thought experiment which came to be called the EPR Paradox.

Its intent was 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 it. 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 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.

In other words he showed there must exist inequities in the measurements made on pairs of particles that cannot be violated in any world that included both their physical reality and their separability because of the limited influence they can have on each other when they are “spacelike” separated.

When Bell published his theorem in1964 the technology to verify or reject it did not exist. However in the early 1980s, Allen Aspect performed an experiment with polarized photons that showed that the inequities it contained were violated.

In other words the measurements made by Allen Aspect made on the polarized photon verified that Bells inequity was violated by finding a correlation between the probabilities of each particle being in a given configuration based on the concepts of quantum mechanics. When this correlation was found many assumed that somehow photons must be entangled or physical connected even though they were in different local realities

Many took this as verification of quantum mechanics assumption that all particles are entangle no matter how far apart they are.

However Einstein, Podolsky, and  Rosen specified in the description of their experiment “two systems, A and B (which might be two free particles)” not just a photons because they knew  that Special Relativity gives a reason why they would entangled which were different from those give by quantum mechanics.

As was mentioned earlier according to quantum mechanics act of measuring the state of a pair of entangled photons instantly affects the other no matter how far they are apart. However Einstein Special Theory of Relativity tell us that because photons must always be moving at the speed of light they can never be separated with respect to an external observer no matter how far apart he or she perceives them to be.

That theory tells that that there is no preferred reference frames by which one can measure distance. Therefore one can not only view the distance covered by a photon with respect to an observer who was external to them but must also look at that distance from a photon’s perspective.

However Einstein tells us that a photon traveling at the speed of light does not experience the passage of distance relative to an observer because as is shown by putting its velocity in his equation for length contraction along its velocity vector the physical distance between them becomes zero.

Therefore one cannot use photons to verify that Bell’s inequity is violated because even though they appear to be at different points when measured by an observer who is not moving at the speed of light they are not because according to Einstein the distance between those points from the perspective of all photons is always zero and therefore they must always be entangled.

This suggests the reason Bells inequity is and MUST be violated for all photons is because Einstein tells us the length contraction associated with the fact that they are they are moving at the speed of light means they are physically entangled or connected at the time of measurement no matter how far apart they appear to be to an observer.  However this is not the reason defined by quantum mechanics.

In other words the “hidden variable” that Einstein was so sure existed that would allow Quantum Mechanics to be complete theory of nature at least for photon is his Special Theory of Relativity.  However Quantum Entanglement may exist for particles other than photon but as we have just seen it cannot be verified by using them as test subjects.

Later Jeff

Copyright 2019 Jeffrey O’Callaghan

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In physics, the conservation laws state the measurable property of an isolated physical system does not change as the system evolves over time. They include the laws of conservation of energy, linear momentum, angular momentum, and electric charge.

However these laws suggest the existence of another more fundamental one that physically defines their causality.
For example Einstein told us that time dilates and space contracts as the energy and momentum of reference frames increase.

In other words there appears to a one to one correspondence between the effects momentum and energy has on the dimensional properties of space-time.

However the fact that the energy and momentum have a common effect on those properties suggests there may be a physical connection between them and their conservation laws.

For example Einstein told us the mass of a particle created in accelerators increases the curvature in space-time causing the physical distance between two points external to it to decrease by a measurable amount.  If that particle decays that curvature returns to where it was before that mass was created.  In other words physical properties of space are conserved in the creation, destruction or redistribution of mass.  Additionally he also told us that concentrating it in the form of a particle causes time to dilate by a measurable amount with respect to its external space-time environment and when that particle decays time is returned to normal rate of change. 

In other words in all reactions involving mass the physical properties of space-time are conserved because they always return to their original value before it was either created or destroyed.

One can also connect the causality of the law of conservation of all forms of energy to the physical properties of a space-time environment.

For example it can be shown the causality of charge conservation is also directly related to the symmetries of the space-time environment defined by Einstein.

However it will be easier to explain if one coverts it to its equivalent in four *spatial* dimensions.

(The reason will become obvious later on in this discussion.)

Einstein gave us the ability to do this when defined the geometric properties of space-time in terms of the constant velocity of light because that provided a method of converting a unit of time in a space-time environment to a unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use Einstein’s theories to qualitatively and quantitatively derive the displacement he associated with energy in a space-time universe in terms of four *spatial* dimensions is the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy including those associated with charge can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This allows one to derive the physical properties of charge in terms a displacement in that “surface” with respect to a fourth *spatial* dimension.

For example if one raises a cup of water above its surface it will be given a measurable amount of potential energy with respect to that surface while at the same time a force will be developed that will be directed downward towards it.  Additionally the level of the water will be lowered by the exact amount that was removed by the lifting of the cup above its surface.  If one pours the water back the levels will return it original depth.  In other words the level of the water is conserved due to the symmetry of its surface levels.

However as was shown in the article “Defining energy” Nov 27, 2007 if one raises, with respect to a fourth *spatial* dimension the volume of three-dimension space associated with a charge it will be given a measurable amount of potential energy with respect to that “surface” while at the same time a force will be developed that will be directed downward towards it.  Additionally the energy level of three-dimensional space not associate with that charge will be lowered by the exact same amount.  If one calls the volume space that was raised up a negative charge one would call the lowering of the “surface” of three dimension space caused by that a positive charge. If one neutralizes the negative charge by bring it in contact with that “surface” it will return to its original level and the charge will be neutralized.  This shows how one can derive the causality of charge conservation in term of the symmetry imposed by Einstein theories. 

In other words symmetry imposed by Einstein’s space-time environment means that charge must be conserved because the creation of one must always be offset by the other.

This is true in environments consisting of either four *spatial* dimensions or four dimensional space-time because as was shown earlier they are quantitative and qualitative interchangeable.

However it also allows one to understand how the conservation laws of nature are physically connected to each other in terms of the physical geometry of our universe.

It should be remember Einstein’s genius allows us to choose to derive the conservation laws either a space-time environment or one consisting of four *spatial* dimension when he defined their environments in terms energy and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the origins of the conservation laws of physics.

Later Jeff

Copyright Jeffrey O’Callaghan 2016

For the past 50 years, the Standard Model of particle physics has given us a complete mathematical description of the particles and forces that shape our world with the exception of gravity.  It predicts with so much accuracy the microscopic properties of particles and the macroscopic ones of stars and galaxies that many physicists feel it is the ultimate theory of matter and energy.

But as Charles Seife mentions on page 142 of his book Alpha & Omega “Taken literally the plain vanilla form of the Standard model does not say anything about particle mass at all: in fact if theorists try to put mass in to its equations they blowup and become meaningless.”

In 1964 Peter Higgs showed that one can solve this problem and explain why particles have inertial or rest mass if one assumes space is permeated by what is called a Higgs field.

He was able to show that if the particles called boson change their velocity or accelerate, then the Higgs field should exert a certain amount of resistance or drag which according to his theory is the origin of mass.  In a slightly more precise terminology, the origin of mass is an interaction between a particle and the (nonzero) Higgs field.  It also assumes the disturbance created by mass as it moves through this field would break it’s symmetry triggering the Higgs mechanism, causing the bosons it interacts with to have mass and generate the particle called the Higgs boson.

In 4 July 2012, the ATLAS and CMS experiments at CERN’s Large Hadrons Collider announced they had each observed a new particle the Higgs boson which many physicists tell us confirms the existence of the Higgs field.

However the Standard model’s explanation of mass as a broken symmetry of a spatial environment does not tell us what it is symmetrical to.  In other words it does not answer the question “What spatial boundary or axis are the components of the Higgs field asymmetrical to?”

As was mentioned earlier the addition of the Higges field to the Standard Model gives us an almost complete mathematical description of the particles and forces that shape our world in terms of broken symmetries because it does not incorporate the gravitational forces into it.

Einstein on the other hand mathematically derived the causality of gravity in terms of an asymmetrical property of a space-time environment.

However the fact that Einstein used the broken symmetry of a space-time environment to derive gravity or the forces associated with mass suggests he may have provided a method of defining the physical mechanism responsible for the symmetry breaking the Standard Model assumes is responsible for that mass.

This is true even though time is only observed to move in one direction forward and never appears to stop so therefore does not have a boundary by which one can define asymmetries. 

However he gave us the ability redefine the asymmetries in a space-time environment responsible for mass in terms of their spatial properties when he defined them in terms of the constant velocity of light because that provided a method of converting a unit of time to its equivalent unit of space in four *spatial* dimensions.

Additionally because the velocity of light is constant it also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of only four *spatial* dimensions.

The fact that one can use Einstein’s theories to qualitatively and quantitatively define the displacement he associated with gravitational energy and mass in a space-time environment in terms of four *spatial* dimensions is bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy including that associated with mass can also be defined in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This would allow one to define the asymmetrical properties or broken symmetries Einstein associated with gravity in terms of a spatial displacement in the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.

However it also allows the Standard Model to use Einstein theories define the asymmetry associated with the energy of the mass component of particles in terms of their spatial instead the time properties of space.

For example the symmetry of the mathematics of the Standard Model tells us that particles and antiparticles are always created in pairs.  However the only way to explain this in a space-time environment is to assume that they are moving backwards in time.  Yet, as was mentioned earlier no one has ever observed time to move backwards.

Yet if one interprets the symmetry of the Standard Model in terms of its spatial instead of its space-time properties as was shown above to be possible one would realize that because we can move in two direction upwards and downwards in the spatial dimensions one can easily define the symmetrical boundary between particles and antiparticles in terms the equal distance they would occupy above and below the physical “surface” of a three-dimensional space manifold with respect to fourth *spatial* dimension.

Yet one can also define asymmetrical properties of the Higgs field the Standard Models assumes is responsible for mass in terms of object or particle occupying the volume either above or below the physical “surface” of a three dimensional space manifold with respect to fourth *spatial* dimension.

In other words converting or transposing Einstein space-time theories to their spatial equivalent as was done above shows that the asymmetries the Standard Model associates with mass and those Einstein associated with gravity share a common property of the geometry of space. 

It should be remember Einstein’s mathematical model which defines the physical geometry of our universe tells us that an all objects must simultaneously exist in both a space-time environment and one consisting of four spatial dimension because as was shown above one can use his mathematics to define two identical universes; one in four dimensional time and another made up of only four *spatial* dimensions. 

Which one we use to define a solution to a problem, as mentioned earlier is only dependent on how an observer interprets his mathematics

Later Jeff

Copyright Jeffrey O’Callaghan 2016

Have you ever wondered why so many seeming rational scientists make seemly irrational assumptions to explain why our universe behaves the way it does and why Einstein was unable see, as Robert Oerter pointed out in his book “The Theory of Almost Everything: the magic of relativistic Quantum electrodynamics or QED.


For example he tells one reason he may have felt this way is because it defines the charge around a solitary electron as being caused by the spontaneous creation and evaporation of virtual electron-positron pairs which then instantaneously disappear.  In other words when a virtual electron-positron pair is created near the (real) electron, the (imaginary) virtual positron will be attracted toward the real electron, while the virtual electron is repelled. Therefore there should be a resulting separation of charge

I think most rational people would consider someone irrational if they tried to convince l us the reason why they were late for work was because a swam of virtual or imaginary cars were blocking the road and disappeared after we showed up.

Shouldn’t we hold our scientists to the same degree of rationality?

Most who have studied the history of science are aware that Einstein was vehemently opposed to many of the fundamental components of quantum mechanics such as the existence of virtual particle’s to explain an isolated charge. 

This was true even though he was able, in his General Theory of Relativity to derive the force of gravity in terms of the geometry of space and time while being unable to do the same for electromagnetism and charge, as was documented by the American Institute of Physics.

“From before 1920 until his death in 1955, Einstein struggled to find laws of physics far more general than any known before. In his Theory of Relativity, the force of gravity had become an expression of the geometry of space and time. The other forces in nature, above all the force of electromagnetism, had not been described in such terms. But it seemed likely to Einstein that electromagnetism and gravity could both be explained as aspects of some broader mathematical structure. The quest for such an explanation — for a “unified field” theory that would unite electromagnetism and gravity, space and time, all together — occupied more of Einstein’s years than any other activity”.

One reason why it was difficult of him to visualize electromagnetic fields including those around a single charge may have been because he chose to define the universe in terms of four dimensional space-time instead of four *spatial* dimensions because, as will be shown below it easier to visualize the properties of electrometric waves and charge in terms of their spatial rather time or space-time properties.

However he did provide a method of understanding them in terms of their common properties when he chose to define gravity in a space-time environment in terms of the equation E=mc^2 and constant velocity of light because that give him the ability to redefined it terms of the spatial properties of four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with gravity in terms of four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forces can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

One of the advantages to using this technique is that it allows one to define the physicality of gravitational and electrical forces including those around a single electron in the same terms.

For example In the article “Gravity in four spatial dimensions” Dec. 15, 2007 it was shown one can derive gravitational forces in terms of curvature or physical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as well as one in a four dimensional space-time environment.

However the article “What is electromagnetism? Sept, 27 2007 showed one can also derive the forces associated with electromagnetism in terms of a similar displacement in the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly that article showed it is possible to derive the forces associated with an electromagnetic wave by extrapolating the laws of Classical Wave Mechanics in a three-dimensional environment to a matter wave moving on a “surface” of three-dimensional space manifold with respect to a fourth *spatial* dimension.

A wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become “attracted” to each other and the surface of the water.

Similarly a matter wave on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that “surface” to become displaced or rise above and below the equilibrium point that existed before the wave was present.

Therefore, classical wave mechanics, if extrapolated  to four *spatial* dimensions tells us a force will be developed by the differential displacements caused by a matter wave moving on a “surface” of three-dimensional space with respect to a fourth *spatial* dimension that will result in its elevated and depressed portions moving towards or become “attracted” to each other.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly the magnitude of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two charges than it would be for a single charge.

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its “peaks” and “troughs” that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards the apex of that displacement.

However, as was mentioned earlier gravity can also be explain in terms of a differential force caused by a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This shows how one can define a common mechanism for the causality of both electromagnetism and gravity in terms of a “unified field” consisting of four *spatial* dimension by extrapolating the laws of classical mechanics in a three-dimensional environment to four *spatial* dimensions. 

In other words one can visualize the fact that unlike charge attract each other while like ones repel in terms of the asymmetrical properties of space-time or four spatial dimensions.

Einstein was unable to accomplish this in terms of four-dimensional space-time because time is only observe to move in one direction forwards and therefore making it difficult to visualize the bi-directional movement of the spatial component of a matter wave moving on its “surface” that is responsible for electromagnetism . 

However it also give a more rational explanation of the charge around a solitary electron than the spontaneous creation and evaporation of virtual electron-positron pairs because it shows that it can be understood in terms of a physical displacement in a “surface” of a three-dimension space manifold with respect to fourth spatial dimension.

In other words it shows that electric forces are related to a physical displacement in a surface of a three dimensional space manifold with respect to a either a higher spatial or time dimension thereby eliminating the need to evoke the existence of virtual electron-positron pairs to understand the behavior of a charge around a solitary electron.

It should be remember Einstein’s genius allows us to choose to define charge in either a space-time environment or one consisting of four *spatial* dimension when he defined that environment in terms mass energy and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the physicality of charge.

Latter Jeff

Copyright Jeffrey O’Callaghan 2016

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