It can be shown Einstein may have been able to derive the internal structure of protons and neutrons if he was aware they had one before he died.  This is because he was the first to define the flexibility of the spatial dimensions when he defined the force of gravity in terms of a curvature in them.

Observations of hadrons such as protons and neutrons confirmed they are made up of distinct components called quarks of which there are six types, the UP/Down, Charm/Strange and Top/Bottom. The Up, Charm and Top have a fractional charge of 2/3. While the Down, Strange and Bottom have a fractional charge of -1/3. However, no one has been able to define their internal structure in terms of observations.

However, another property of quarks defined by Quantum Chromodynamics (QCD), is their color charge which are red, green, and blue. It assumes each one is made up of three different colors of quarks red, blue and green and only the combinations of the colors that produce “white” can be found in a stable particle.

It will be shown the color charge of each quark represents orientation of three two-dimensional plane (xy, yz, xz) of three-dimensional space responsible of its charge.

For example, red would represent the xy plane green, the yz, and blue xz. The fact that three-dimensional space contains only one of each explains why particle must be composed of one each color to be stable.

However, before we begin, we must first define how and why the color charge of a quark is related to the two-dimensional planes mentioned earlier

As was shown in Article 12 (page 61) the alternating charge of an electromagnetic wave are the result of displacement in the two-dimensional planes of space that it is moving on. .

Briefly it showed the electric and magnetic components of an electromagnetic wave are the result of a spatial displacement in the two-dimensional “surface” of three-dimension space.

One can understand the mechanism responsible by using the analogy of how a wave on the two-dimensional surface of water causes a point on that surface to become displaced or rise above or below the equilibrium point that existed before the wave was present.

The science of wave mechanics tells us a force would be developed by these displacements which would result in the elevated and depressed portions of the water moving towards or becoming “attracted” to each other and the surface of the water.

Similarly, an energy wave on the “surface” of the two spatial dimensions that are perpendicular to the axis of gravitational forces 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 the properties of two of the three spatial dimensions of our universe tell us a force will be developed by the differential displacements caused by an energy wave on it which will result in its elevated and depressed portions moving towards or become “attracted” to each other as the wave moves through space.

This would define the causality of the attractive electrical fields associated with an electromagnetic wave in terms of a force caused by the alternating displacements of a wave moving with respect to time on a “surface” of the two spatial dimensions which are perpendicular to the axis of gravitational forces.

However, it also provides a classical mechanism for understanding why similar electrical fields repel each other. This is because observations of waves show there is a direct relationship between the magnitude 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 the two spatial dimensions will be greater than that caused by a single one. Therefore, they will repel each other because the magnitude of the force resisting the displacement will be greater than it would be for a single one.

One can also derive the magnetic component of an electromagnetic wave in terms of the horizontal force developed along the axis that is perpendicular to the displacement caused by its peaks and troughs associated with the electric fields. This would be analogous to how the perpendicular displacement of a mountain generates a horizontal force on the surface of the earth, which pulls matter horizontally towards the apex of that displacement.

Even though the above explanation of how a charge is related to an alternating displacement in the “surface” of three-dimensional space it also can explain a static one in terms of their relative positions in.

For example, Einstein showed us if a two-dimensional plane is displaced with respect to another in three-dimensional space a force responsible for static charge would be developed similar as was shown earlier to how the peaks and valleys of an electromagnetic did.

As was mentioned earlier Einstein define forces such as gravity in terms of the flexibility of the spatial dimensions.

However, one can derive the internal structure of protons and neutrons if one assumes orientation of the color charges of quarks are the result of the flexibility of the two-dimensional planes which earlier were defined as being responsible for them.

This is because for a proton or neutron to be stable in three-dimension space the orientation of the xy, yz, and xz dimensional planes must perpendicular to each other

If they are not, they will be unstable.

For examine the two up quarks of proton each with a color charge of two would contain 4 two-dimensional planes (one for each charge).  However, according to Einstein each dimensional plane has the flexibility to orient itself to oppose or cancel the charge of another one.  Therefore, when up quark combines with a down quark the two-dimensional plane that define its charge can orient itself to oppose or cancel one of the charges of the up quarks.  This means it will have forces only 3 of 4 dimensional planes associated with the 2 up quarks

This will form a stable structure in three-dimensional space because it contains the (xy, yz, xz) planes which can be perpendicular to each other.

Neutrons on the other hand contains one up quark and two down quarks.  It is neutral because the 1/3 charge on each of the two down quarks cancel the 2/3 charge of the up quark.

But it also consists four two dimensional planes which means it cannot exist in three-dimensional space.

However, when close enough to a proton it can borrow enough binding energy required to cause its two down quarks to line up along the same two-dimensional plane of three-dimension space. This will result in that plane having the opposite color charge of two down quarks which will result in a neutron having no charge when it interacts with the two charges of the up quark This also means the xy, yz, xz planes would define the three-dimensional volume of a neutron it because they do not have any of the forces that define it color charge. This is true even though one may have twice the color charge of the other two. This will result in it being stable when near enough to borrow some binding energy from proton

However. when a neutron it is not the two two-dimensional planes that define the color charges of the down quarks will not line up resulting in it having 4 dimensional planes resulting in it being unstable and decaying in a proton electron and neutrino.

As was mentioned earlier a stable electric charge is the result of a static spatial displacement in a two-dimensional plain of the three-dimensional space.

This suggests one could describe their geometry in terms of how those planes are oriented.

For example, if a proton is made up two up quarks each with a positive charge of 2/3 and its charge is the result of a displacement in dimensional plane of three-dimensional space each one would contain 2 and combined would contain 4.

However, this means a proton would consist of four spatial dimensions which could not exist in our three-dimensional universe.  Therefore, to correct that it attracts a down quark which has a negative or opposite spatial displacement with respect to one of those dimensional planes.  This would reduce its spatial properties to three allowing it to exist in our universe.

However, it also would change their orientation with respect each other. Instead of being perpendicular it would be 60-degree. This is because as was just mentioned the 2 up quarks of a proton would contain 4 dimensional planes creating four-dimensional spatial object which cannot exist in three-dimensional space.  However, when it combines with the negative dimensional energy Einstein would have associated a down quark it cancels out one of the four dimensional planes associated with the 2 up quarks of a proton leaving only three which can exist in three-dimensional space.

But when one removes one side of a square it allows one of three sides to connect to one of the others to form an equilateral triangle This suggest the energy associated with the rearraigning the orientation of dimensional planes from 90 degrees to 60 creating the object which is responsible for both the positive charge and stability of a proton. I believe Einstein would have come to this conclusion if he as was mentioned earlier, he had known protons had an internal structure.

Einstein’s Explanation of the Unexplainable https://www.theimagineershome.com/Einstein%E2%80%99s-Explanation2.html

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Additionally, it assumes it exists in a superposition of several eigenstates and only reduces or COLLAPSES to a particle when it interacts with the external world.

While Einstein defined gravity in terms of how energy density of space effects the geometry of space-time.

THEREFORE ONE CAN PROVIDE A BRIDGE BETWEEN QUANTUM MECHANICS AND RELATIVITY  DEFINITION OF GRAVITY IF ONE CAN SHOW HOW AND WHY ENERGY DENSITY OF SPACE IS CONCENTRATED IN QUANTIZED UNITS OF SPACE TIME IN TERMS A GEOMETRY OF SPACE TIME.

But before we can understand how to do this we need to establish a connection between the mathematical evolution of the wave function, its collapse and the physical evolution of both electromagnetic and gravity waves. This can be accomplished because as was mentioned earlier in Relativity evolution of space-time is the result of an electromagnetic wave while, as was also mentioned earlier the wave function represents how a Quantum environment evolves to create a particle.

This commonality suggests the wave function MAY BE a mathematical representation of an electromagnetic wave in space-time. This means to derive the reason for its collapse in terms of space-time one must physically connect its evolution to it.

This can be done by using the science of wave mechanics and the fact that an electromagnetic wave moves continuously through space-time unless it is prevented from moving through time by its energy interacting with objects or an observer in three-dimensional space, resulting in its energy confined to it. The science of wave mechanics also tells us the three-dimensional “walls” of this confinement will result in its energy being reflected back on itself thereby creating a resonant or standing wave in three-dimensional space. This would cause the energy of an electromagnetic wave to be concentrated at the point in space were a particle would be found. Additionally, wave mechanics also tells us the energy of a resonant system such as a standing wave can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency that the wave function associates with a particle. Putting it another way one can explain how and why the wave function reduces or COLLAPSES to a particle when it interacts with the external world if one assumes it is mathematical representation of an electromagnetic wave in space-time.

The boundaries or “walls” of its confinement would be defined by its wave properties. If an electromagnetic wave is prevented from moving through time it will be reflected back on itself. However, that reflected wave still cannot move through time therefore it will be reflected back creating a standing wave. The wave itself defines its boundaries because if it cannot move though time it MUST STAND in place in the form of a standing wave called a photon. Putting it another way a particle is a wave that is moving ONLY IN time and NOT THROUGH time and space.

In other words, if an electromagnetic or any energy wave is prevented from moving through space time either by being observed or encountering an object it is reduced or “Collapses” to a form a standing wave that would define the quantized energy quantum mechanics associates with a particle.

As was mentioned earlier Einstein defined gravity in terms of how energy density of space effects the geometry of space-time.

Therefore, one can define why gravity is quantized in terms of the how relativity defines the energy density of space in terms of the presence of a quantized unit of energy or a particle ofmatter.

This provides a bridge between quantum mechanics and relativity in terms of how it CAN define the quantization of the mass associated with a particle and therefore its gravitational potential

Einstein’s Explanation of the Unexplainable https://www.theimagineershome.com/Einstein%E2%80%99s-Explanation2.html

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Antimatter is a material composed of antiparticles and every particle we know of has an antimatter companion that is virtually identical to itself with opposite electric charge. Physics predicts that matter and antimatter must be created in almost equal quantities, and that this would have been the case during the Big Bang. What’s more, it is predicted that the laws of physics should be the same if a particle is interchanged with its antiparticle – a relationship known as CP symmetry. However, the universe we see doesn’t seem to obey these rules. It is almost entirely made of matter, so where did all the antimatter go? It is one of the biggest mysteries in physics to date.

    Therefore, to define ALL the properties of antimatter in terms of the field properties of space-time one must first define how it evolves to produce both particles and antiparticles and then explain why our universe is made ALMOST ENTIRELY OF MATTER.

    Einstein defined the evolution of a space-time environment in terms of an electromagnetic wave moving through its field properties and derived a particle and its mass in terms of a curvature caused by local increase in its energy density.  This means to define antiparticles one must first explain how electromagnetic energy evolves in a space-time environment to create a local increase in its energy density and why it is responsible for particle creation.

One can accomplish that by using the science of wave mechanics along with the fact that Relatively tells us an electromagnetic wave moves continuously through space-time unless it is prevented from doing so by someone or something interacting with it. This would result in its energy being confined to three-dimensional space. The science of wave mechanics also tells us the three-dimensional “walls” of this confinement will result in its energy being reflected back on itself thereby creating a resonant or standing wave in three-dimensional space. This would cause its energy to be concentrated at the point in space were a particle would be found. Putting it another way this defines how electromagnetic energy evolves in a space-time environment to create a local increase in its energy density and why it is responsible for the creation of particles.

The next step in defining the properties of antimatter is to show why every particle we know of has an antimatter companion that is virtually identical to itself.

One can understand this by using an analogy of how water reacts when an object is either added to or removed from it.

For example, if one depresses an empty cup in water its surface will become elevated to exactly make up for the quantity of water displaced while if some removes a cup of water its surface will become depressed enough to make up for the water that was removed.

Similar to water if a particle causes a portion of “surface” of space-time to become depressed it will result in a portion of it to become elevated enough to exactly make up for that depression. While if a portion of the “surface’ of space-time elevated by an antiparticle it will result in a portion of it to become depressed enough to exactly make up for that elevation.

As was mentioned earlier Einstein defined a particles mass in terms of a curvature cause by increase in its energy density

Putting it another way this defines why every matter particle has an antimatter companion that is virtually identical to itself and why it must be created in almost equal quantities because it shows why the curvatures associated with their energy density are interdependent and oppositely directed each other.

However, it also provides a solution to one of the BIGGEST mysteries in physics or why the universe is made up almost entirely of matter, even though both observation and prediction suggest that matter and antimatter must be created in almost equal quantities.

This is because it takes a little more energy to lift or elevate cup of water above its surface than it does to depress it below it in part because gravity opposes it being lifting while favoring it being depressed

    Similarly, it would take a little more energy to elevate or lift the “surface” of three-dimensional space than it would to depress it due in part to the fact the gravitational component of matter below that “surface” would oppose the lifting associated with antimatter while favoring the depression associated with matter.

    Therefore, some energy associated with matter will be left over after all of the antimatter has been eliminated.

One can also understand why their electrical charge is opposite by comparing it to the energy stored in elastic bands.

For example, if one takes two elastic bands side by side and depress down on one and up on the other a force will be developed that will cause them to be attracted to each other

Similarly classical physics tells us an attractive force will be developed by the differential energy density that exists between a matter and its antimatter counterpart that will result in a force to be developed that will cause them to be attracted to each other.

This explains why matter and antimatter particle have opposite electric charges or are attracted to each other is because of the effects their energy densities have on the fabric of space-time

Additionally, one can understand why the spin properties of neutral particles such as a neutron and an antineutron are opposite directed by comparing them to spin properties of high-and-low-pressure areas in our atmosphere. For example, in a high-pressure area air rotates clockwise while in a low one it does so in a opposite direction or counter clockwise.

For the same reason the energy in high energy volume of space-time that defines a neutral particle would rotate in an opposite direction from the low energy volume that defines its antiparticle.

This shows how one can defining the properties of antimatter in terms of the field properties of space-time and why our universe almost entirely made of matter.

Einstein’s Explanation of the Unexplainable

https://www.theimagineershome.com/Einstein%E2%80%99s-Explanation2.html

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Einstein tells us particles with mass cannot move faster than the speed of light while Quantum Mechanics tells us that all energy including electromagnetic MUST be quantized and therefore it assumes it is propagated by a particle called a photon.

However, because observations of particles in particle accelerators APPEARS to verify Einstein assumption that if photons had mass, they COULD NOT move at the speed of light one must assume that they have no mass.

But if it has no mass, it also has no energy because his equation E=mc^2 tells us energy is equivalent to mass.

(Some have tried to use a mathematical argument the equation E=mc^2 is a special case of the more general equation: E2 = p2c2 + m2c4 which for a particle with no mass (m = 0), reduces down to E = pc. Therefore, because photons (particles of light) have no mass, they must obey E = pc and they get all of their energy from their momentum. However, the “p” in the equation NOT ONLY represents the momentum of a photon it also represents the energy associated with its motion. Thus, according to E=mc^2 that energy MUST also be considered mass.)

Putting it another way Einstein tells us it does NOT MATER how we define the energy of a photon the fact that it has energy means it also has mass and therefore, SHOULD NOT be able move at the speed of light.

Some have also suggested that because “E” is the total relativistic energy, which consists of rest mass (mc^2), and momentum (pc) it is fundamentally wrong to say that anything with energy has mass. Therefore, a photon with momentum can still carry energy even if it has no rest mass.

However, momentum is defined as p = mv in Newtonian physics and in relativity p=mc. Therefore, it is FUNDAMENTALLY WRONG as some have suggested to say that the momentum of a photon can have ZERO mass because if it did the energy value of particle with no or 0 mass define by E = pc would be zero.

Therefore, because observations of particles in particle accelerators APPEAR to verify Einstein assumption that if photons had energy, they COULD NOT move at the speed of light one needs to explain how its energy can be propagated at that speed in terms of his theories.

One can use the science of wave mechanics to understand how this is possible because it tells us waves move energy from one location to another without transporting the material they are moving on. In other words, the molecules that make up the wave remain stationary with respect to the background of the water while its energy is propagated through it.

Similarly, an electromagnetic wave in space-time COULD move at the speed of light because it does not move the “units” of space-time associated with the peaks and valleys it creates but would transmit their energy to the next one. In other words, the units of space-time that make up an electromagnetic wave WOULD remain stationary with respect to the background of space-time while its energy moves through it in the form of a wave.

However, one can also use the science of wave mechanics to understand why an electromagnetic wave ALWAYS takes on the form of a particle called a photon when it interacts with an observer or the its environment.

For example, wave mechanics tells us an electromagnetic wave would move through space-time unless it is prevented from doing so by someone observing or interacting with it. This would result in its energy being confined to three-dimensional space. It also tells us the three-dimensional “walls” of this confinement will result in its energy being reflected back on itself thereby creating a resonant or standing wave in three-dimensional space. This would cause its wave energy to be concentrated at the point in space were a particle would be found. Additionally, wave mechanics also tells us the energy of a resonant system, such as a standing wave can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency. This explains how and why an electromagnetic energy wave becomes quantized in the form of a particle called a photon if it is prevented from moving through space-time by interacting an observer or the “external world”.

Quantum mechanics uses the mathematical properties of the wavefunction to define a quantum environment and states that it maintains its wave properties and becomes quantized ONLY repeat ONLY when it is observed or interacts with its external environment.

Therefore, as was shown above assuming a photons energy is propagated by a electromagnetic wave allows one to understand why it appears as a particle called a photon ONLY when it interacts with its environment or an observer in a manner that is consistent with the assumptions of both of Einstein Theories and Quantum mechanics.

However, it also shows how, if one assumes as was just done that electromagnetic energy is propagated BY a wave NOT by a particle one can explain how its energy can be propagated at the speed of light.

Einstein’s Explanation of the Unexplainable

https://www.theimagineershome.com/Einstein%E2%80%99s-Explanation2.html

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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?â’ 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. 

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

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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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.

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.  

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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The solution was found by Max Planck.  Previously physicists had assumed the microscopic world of an atom’s energy was continuous; that is, the energy of each electron orbital should be able to take on any value.  However, Planck correctly assumed that they could only have the energies that were whole number multiples of some base frequency, which he called “h”. In other words, in the microscopic world of atoms energy appears to be quantized in a manner that corresponded to a whole number of the frequency “h” or Plank’s constant.

However, Einstein, in his General Theory of Relativity defined energy in the macroscopic environment of stars and planets in terms of the continuous field properties of space-time. T

he problem now became how can one integrate the continuous field properties of energy as described by Einstein with the discontinuous properties of an atomic orbital associated with Planck’s constant.

In the past most researchers have attempted to do this without success by attempting to define its continuous field properties in terms of the discontinuous quantum properties associated with Planck’s constant.

However, one may be able to if, instead of attempting to the define those properties in terms of discontinuous properties associated with an atomic orbital, we attempt to derive the discontinuous or quantum properties of an atomic orbital in terms of the continuous field properties of space-time.

One of the difficulties in visualizing and understanding how this would be possible may be because Planck’s constant is defined in terms of the spatial not the time components of a system while Einstein’s theories define energy in terms of time or a space-time dimension.

However, Einstein gave us a way to make it easier when he qualitatively and quantitatively derived the geometric properties of his space-time environment in terms of the constant velocity of light and the velocity of objects that do not move at that speed because it allows one to redefine a unit of time he associated with energy in his space-time universe to its equivalent unit of space in a universe consisting of only four *spatial* dimensions.

In other words, by 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 the geometry pf his space-time universe in terms of its equivalent in four *spatial* dimensions.

The fact that one can use Einstein’s equations to qualitatively and quantitatively to redefine the displacement in space-time he associated with energy in terms of its equivalent in four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy in including that of an electron orbiting the nucleus 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 as well as on in four dimensional space-time.

For example as the article “Why is energy/mass quantized?” Oct. 4 2007 showed one could derive a model for an atomic orbital by extrapolating the laws of a resonance in our three-dimensional spatial environment to one made up of four.

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 be meet by a matter wave in four *spatial* dimensions.

The existence of four *spatial* dimensions would give space (the substance) 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 to oscillate with the frequency associated with the energy of that event.

However, these oscillations in a continuous non-quantized field of energy caused by such an event would result in a resonant system or “structure” to be formed in space.

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

In other words, value of Planck’s constant can be understood by assuming that it defines the energy of the fundamental resonate frequency of field properties of space-time as defined by Einstein and therefore, the energies all orbits must be multiples of that fundamental frequency.

However, one can also use the above theoretical model to explain the why quantum properties of Planck’s constant must be applied to all stable particles including photons.

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.

Therefore, an energy wave, occupying a volume of three-dimensional space would be confined to it. similar to the surface of the paper when it is forced to oscillate “\”up” or “down” with respect to a fourth *spatial* dimension.

The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension by an observation is what defines the spatial boundaries associated with all particles including photons in the article “Why is energy/mass quantized?”.

Not only that but it can be shown these resonant systems in a continuous field properties of space-time that are responsible for the incremental energies associated with an atomic orbital and Planck’s constant are also responsible for the energy profiles of black body radiation.

The ultraviolet catastrophe is the error at short wavelengths in the Rayleigh–Jeans law (depicted as “classical theory” in the graph) for the energy emitted by an ideal black-body. The error, much more pronounced for short wavelengths, is the difference between the black curve (the wrong curve predicted by the Rayleigh–Jeans law) and the blue curve (the correct curve predicted by Planck’s law).

At room temperature, black bodies emit mostly infrared wavelengths, but as the temperature increases past a few hundred degrees Celsius, black bodies start to emit visible wavelengths, appearing red, orange, yellow, white, and blue with increasing temperature.  By the time an object is white, it is emitting substantial ultraviolet radiation.

The problem is the laws of classical mechanics, specifically the equipartition theorem, states that black-bodies which have achieved thermodynamic equilibrium are mathematically obligated (by classical, pre-quantum, laws) to radiate energy in the form of ultraviolet light, gamma rays and x-rays at a certain level, depending on the frequency of emitted light.

However, observations of black body radiation indicate that there was less and less energy given off at high end of the spectrum.

Einstein pointed out this difficulty could be avoided by making use of a hypothesis put forward five years earlier by Max Planck.  He had hypothesized that electromagnetic energy did not follow classical laws, but could only oscillate or be emitted only in discrete packets of energy proportional to the frequency, as given by Planck’s constant.  In other words, the light waves of each frequency in a black body could not have any energy but are limited to a few discrete values.

However, as mentioned earlier the article “Why is energy/mass quantized?” showed energy of a photon at each frequency could be understood by extrapolating a physical image of a resonant system in three-dimensional space to a fourth *spatial* dimension similar to how Einstein was able to from a physical image of gravity.

For example, as the above theoretical model shows using only the concepts of classical physics and field properties of Einstein’s Theory of Relativity a photon could only have the discrete energies or frequencies that are a fundamental or harmonic of the energy of an environment which would be determined by the temperature of the one it was occupying. Therefore, according to the above theoretical model any frequency other than that would be irregular and non-repeating and would be absorbed into the fundamental or harmonic frequency of that environment.

In other words, it explains in terms of a physical image based on our classical reality why black-bodies which have achieved thermodynamic equilibrium are mathematically obligated by to radiate energy in the form of ultraviolet light, gamma rays and x-rays at  certain discrete levels, depending on the frequency of emitted light because of the field properties of Einstein space-time universe.

As was shown above one can use the resonate field properties of a space-time environment to explain why the energy of a black body is what it is and why all particles AND the electrons orbiting in atoms can only have the energies that are a whole number multiples of the energy associated with Planck’s constant “h”. 

It should be remembered; Einsteinâ€s genius allows us to choose if we want to view the physical properties of Planck’s constant in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the particle and wave properties microscopic quantum world as well as microscopic one of Einstein thereby giving us a new perspective on the physical relationship between particles and waves.

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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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 particleâ€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 waveâ€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.  

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

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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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

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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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

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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