One can define reality as the world or the state of things as they actually exist, as opposed to an idealistic or notional idea of them.

Currently there are two ways science attempts to explain and define the reality of our universe. The first is Quantum mechanics or the branch of physics defines its evolution in terms of the probabilities associated with the wave function. The other is the deterministic environment of Relativity which defines it in terms of a physical interaction between space and time.

Specifically, Relativity would define the observable positions of particles in terms of where the point defining their center of mass is located.

While quantum mechanics uses the mathematical interpretation of the wave function to define the most probable position of a particle when observed.

Since we all live in the same world you would expect the probabilistic approach of quantum mechanics to be compatible with the deterministic one of Einstein. Unfortunately, they define two different worlds which appear to be incompatible. One defines existence in terms of the probabilities while the other defines it in terms of the deterministic of properties of space and time.

However, to show why those probabilities appear to be incompatible with Relativity’s determinism even though they are NOT it will be necessary to explain the evolution of quantum environment in terms of a deterministic interaction between the components of a space-time environment.

For example, when we role dice in a casino most of us realize the probability of a six appearing is related to or is caused by its physical interaction with properties of the table in the casino where it is rolled. Putting it another way what defines the fact that six appears is NOT the probability of getting one but the interaction of the dice with the table and the casino it occupies.

This suggests to show the “reality” behind the wave function one MUST explain how its environment evolves in terms of how the physical components of space-time interact to define a particles position.

The fact that Relativity defines evolution of space-time in terms of the energy propagated by electromagnetic wave while Quantum Mechanics defines it in terms of the mathematical evolution of the wave function give us a starting point. This is because it suggests the evolution in both is defined in define by a wave.

To define the position of a particle in terms of the deterministic properties of Relativity one can use the science of wave mechanics along with the fact Relativity tells us an electromagnetic wave move continuously through space-time unless it is prevented from doing so by someone observing or something interacting with it. This would result in its energy being confined to three-dimensional space. The science of wave mechanic 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 COLLAPSE and 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 means a particle would occupy an extended volume of space defined by the wavelength of its standing wave.

Putting it another way what defines the fact that a particle appears where it does is NOT determined by the probabilities associated with the wave function but a deterministic interaction of an electromagnetic wave with the physical properties of space-time.

(NOTE We will use a particles position to make the connection between the probabilities of Quantum mechanics and the determinism of Relativity but the same logic will apply to all conjugate pairs.)

However, the probabilistic interpretation of the wave function is defines its reality because it use a mathematical point to represent a position of a particle which it randomly places with respect to the center of a particle. Therefore, the randomness of where that point is with respect to a particle’s center will result in its position, when observed to be randomly distributed in space. This means one must define its position in terms of probabilities to average the deviations that are caused by that random placement.

Yet as was mentioned earlier Reality defines the position of particles in terms of where the point defining their center of mass is located. Therefore, because similar to quantum mechanics Relativity cannot precisely determine where that point is located it would also have to define their exact position in terms of probabilities.

However, the large number of particles in objects such as a moon or planet would result in averaging out the deviation of the position of each their individual particles it appears to be deterministic.

But the same logic would apply to a quantum environment because its probabilistic deviations of a particle’s position would average out making the position of large objects such as the mom and planets appear to be deterministic.

This suggests the reason our universe appears indeterminate on a quantum scale while being deterministic on a macroscopic level is because similar to Relativity those deviations would be averaged out by the large number of particles in objects like the moon and planets.

As was mentioned earlier one can define reality as the world or the state of things as they actually exist, as opposed to an idealistic or notional idea of them.

Therefore, as was shown above one can define the Reality of the probabilistic world of quantum mechanics and the deterministic one of Relativity by assuming actual existence of an electromagnetic wave whose evolution can be defined by the notional idea of the wave function.

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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Quantum mechanics assumes the quantization of energy is what prevents electrons from falling into the nucleus of atoms.   However, Classical Wave Mechanics provides another explanation base the observation that a system which is oscillating at its natural resonant frequency is one the most efficient ways to store and transfer energy between different storage modes.  This combined with the law conservation of energy which tells us it can neither be created or destroyed suggests the reason why electrons do not fall into the nucleus MAY BE because the most efficient way to store their energy is in resonate systems.

One of the core principals of quantum mechanics is that the energy of all electrons is stored in a wave defined by de Broglie’s equation ?dB = h/p.

Therefore, to verify the reason electrons do not fall into the nucleus is the law conservation of energy and not the fact that quantum mechanics tell us it is quantized one must first show how a resonate system can be created in the space around the nucleus in terms of the non-quantized properties of a wave.

Science of wave mechanics tells us the wave energy of an electron would move continuously in the space around the nucleus it is bound to.  However, as mentioned earlier a system which is oscillating at its natural or harmonic of its resonant wavelength is one the most efficient ways to store energy.  Therefore, the most efficient way to store it would be in a wave moving in a path where the circumference is equal to the wavelength or a harmonic of its resonate system.

    However, observations and the science of 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 tell us the energy of the electrons orbiting an atom MAY NOT be quantized just because quantum mechanics say they are but because the most efficient way to store their energy is in a quantized resonant system.

    As was mentioned earlier energy can neither be created or destroyed therefore an electron’s energy could NEVER repeat NEVER disappear by falling into a nucleus and therefore it MUST repeat MUST be stored someplace.

    Yet as was also mentioned earlier classical wave mechanics tells us the most efficient way to store energy is in resonant system such as the standing wave. This tells us the energy in each level would most likely be stored in a resonant system or standing wave that has the energy associated with that level.

Both quantum mechanics and as was shown above classical wave mechanics gives valid reasons why electrons do not fall in the nucleus.  Quantum mechanics assumes they do not because their energy is quantized based ONLY on the assumption it is quantized.  However, as was show above classical wave mechanics and law of conservation of energy gives another reason which are just as valid in terms of the observable properties standing waves and the fact that energy has NEVER been observed to be either created or destroyed.

Putting it another way the reason electrons do no fall into the nucleus MAY NOT be because Quantum mechanics tells us they are quantized but because observations of resonant systems and the law of conservation of energy tell us their energy can NEVER repeat NEVER be destroyed or as mentioned earlier disappear into the nucleus.

Physics is a science based on observation.  Therefore, if two ideas give the same result one should give more creditability to the one which can be verified observationally instead of one that cannot.

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Mach, an Austrian physicist and philosopher developed a principle which some have interpreted as the motion of such a particle’s has no meaning if it was alone in the universe.

In Mach’s words, “the principle is expressed as the investigator must have knowledge of the immediate connections, say, of the masses of the universe. There will hover before him as an ideal insight into the principles of the whole matter, from which accelerated and inertial motions will result in the same way.”

Einstein considered Mach prospective so important to the development of General Relativity that he christened it Mach’s principle and used it to explain why inertia originates in a kind of interaction between bodies.

For example, according to General Relativity, the benchmarks for all motion, and accelerated motion in particular, are freely falling observers who have fully given in to gravity and are being acted on by no other forces. Now, a key point is that the gravitational force to which a freely falling observer acquiesces arises from all the matter (and energy) spread throughout the cosmos. In other words, in general relativity, when an object is said to be accelerating, it means the object is accelerating with respect to a benchmark determined by matter spread throughout the universe. That’s a conclusion which has the feel of what Mach advocated. So, in this sense, general relativity does incorporate some of Mach’s thinking.

However, he provided another way of defining inertia that does not require the existence of any other objects but relies only on the geometric properties of space defined in his General Theory of Relativity. In other words, geometry of space itself provides an absolute baseline for inertia.

In physics inertia is the resistance a physical object to a change in its velocity. Therefore, one can define a baseline for its measurement if one can find a universal starting point for it based on objects velocity.

One of the most logical ways to do that would be to use the observable differences between the two types of motion; velocities and accelerations.

For example, velocities transverse the same space or distance in a given time frame while accelerations transverse an exponentially increasing distance over that same time period.

This tells us the primary difference between them is a component of space not time because if one uses the same time frame for both the only thing that distinguishes them is the distance they transverse.

However, Einstein defined the geometry of space and our universe in terms of time therefore, because space not time is, the variable that distinguishes velocities from accelerations, we should look for a way to define motion and it energy purely in terms of its spatial properties.

Einstein gave us the ability to do this when he defined the mathematical relationship between space, time and energy in terms of the constant velocity of light because in doing so, he provided a method of converting a unit of time in a space-time environment to its equivalent 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.

In other words, Einstein’s mathematics actually defines two mathematically equivalent physical models of the universe, one consisting of four-dimensional space-time and one of only four *spatial* dimensions.

This allows one to define the energy associated with both accelerations and velocities, in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as well as one in four-dimensional space-time.

In other words, using the spatially equivalent model of Einstein space-time theories one could define the energy associated with velocities in terms of a linear displacement in the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension because it remains constant as an object moves though space.

While one would define accelerations both gravitational and non gravitational in terms of a non-linear displacement or curvature in that “surface” because, as was mentioned earlier it increases as a object move though space.

In other words, if one defines gravitational accelerations in terms of a positive non-linear displacement or curvature in that “surface” one would define all other forms of accelerations in terms of an oppositely directed displacement or curvature in that “surface”.

Additionally, the magnitude of the linear displacements associated with relative velocities is dependent on the energies associated with their movement or momentum while the degree of the non-linear displacement associated with accelerations would also be dependent on the magnitude of the energy required to cause them.

In other words, the greater the relative velocities or accelerations the greater the displacement or curvature in the “surface” of the three dimensional space manifold with respect to fourth *spatial* dimension associated with their motion.

What makes accelerated motion different from velocities is that they do not create an energy gradient in space necessary to activate the human senses or measuring instruments because, as was just mentioned the displacement they create is linear with respect to the “surface” of the three dimensional space manifold with respect to a fourth *spatial* dimension

Therefore, the reason it only makes sense to say that this is moving with respect something is because referencing it to that something provides an energy gradient or differential which can activate measuring equipment or human senses.

However, because Einstein tells us the displacement in the “surface” of a three-dimensional space manifold with respect to fourth *spatial *dimension associated with accelerated motion is non-linear it will intrinsically create an energy gradient between two points space.

This also allows one to define a universal baseline for the measurement of inertia in terms of the linear displacement in that “surface” because as mentioned earlier it defines the energy level of all constant motion.Â

As was mentioned earlier, in physics inertia is a measure of the resistance or force (over a given time period) required to the change the velocity of a physical object. Therefore, to define an absolute benchmark for measuring it one must first define a starting point for the energy gradient that, as mentioned earlier is responsible for acceleration. Additionally to make it universal benchmark that point must be the same of all objects and particles.

Therefore, a universal baseline for the measurement of the inertia in all objects is the linear displacement in that “surface” with respect to a fourth spatial dimension associated with their velocity before a measurement was taken . In other words, one can measure the inertia of all objects by measuring the energy difference (in a given time frame) between its starting displacement in space and its displacement at the end points. In other words, it defines a universal starting point or baseline the measurement of inertia for all objects.

Some have said that one cannot measure the inertia of a particle or object that exists alone in the universe because one cannot reference its movements to anything.  However, referencing its velocity with respect to the universe is not relevant to its measurement because Einstein tells us that the energy of velocity is made up of two parts.  One is the energy of associated with its velocity and the other is that of the energy of it’s rest mass defined by the equation E=mc^2.  Therefore, because the displacement that defines a object is made up of two parts the energy of its rest mass and that of its velocity does not need to be reference to any other object or particle. In other words the mass of the object provides the displacement or baseline for measuring the inertia of a particle or object at rest. Therefore, its movement or velocity or lack of it with respect to the entire universe will not effect that measurement because it is determined only by the energy required to produce a change in its velocity or the displacement the “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension that is responsible for that change.

This shows how one can derive a universal baseline for measuring the inertia of all particles and objects in terms of the physical geometry of space as defined by Einstein.

It should be remembered that Einstein, by defining the universe’s geometry in terms of the constant velocity of light allows us to choose whether to define inertia either a space-time environment or one consisting of four *spatial* dimension.

Latter Jeff

Copyright Jeffrey O’Callaghan 2020

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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Presently, there is disconnect between our understanding of one of the most mysterious facets of quantum mechanics, that of quantum entanglement and the classical one of separation.

Entanglement occurs when two particles are linked together no matter their separation from one another. Quantum mechanics assumes even though these entangled particles are not physically connected, they still are able to interact or share information with each other instantaneously.

Many believe this means the universe does not live by the law’s classical laws of separation or those derived by Einstein which state that no information can be transmitted faster than the speed of light.

However, we must be careful not to jump to conclusions because Einstein gave us the definitive answer as to how and why some particles, such as photons are entangled while others are NOT in terms of the physical properties of space-time.

Quantum mechanics assumes that entanglement occurs when two particles or molecules share on a quantum level one or more properties such as spin, polarization, or momentum. This connection persists even if you move one of the entangled objects far away from the other. Therefore, when an observer interacts with one the other is instantly affected.

There is irrefutable experimental evidence the act of measuring the state of one of a pair of particles can instantaneously affect another even though they are physically separated from each other.

However, before we come to the conclusion it is a result of their quantum mechanical properties, we should first examine the experimental setup and any variables that may allow us to come to a different conclusion.

(This description was obtained from the Live Science web site) One of the experiments many assume verifies that entanglement is a quantum phenomenon uses a laser beam fired through a certain type of crystal which causes individual photons to be split into pairs of entangled photons. The photons can be separated by a large distance, hundreds of miles or even more. 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 (or information) 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. Scientists have successfully demonstrated quantum entanglement with photos, electrons, molecules of various sizes, and even very small diamonds).

However, Einstein told us there are no preferred reference frames by which one can measure distance.

Therefore, he tells the distance between the observational points in a laboratory, can also be defined from the perspective of the photons in the above experiment.

    However, from that perspective his Theory of Special Relativity tells us the distance separating the end points of ALL observations made in a laboratory would contract along the direction of motion relative to a photon. Yet, it also tells us that the separation between those two points would be zero form the perspective of all photons moving at the speed of light.

    (Some have suggested that if you have two photons moving in opposite directions, you can only treat one as being stationary at a time, not both simultaneously” However that directly contradicts relativity because it means that from the perspective of the stationary one the lab where a measurement is made is moving at the speed of light away from it while the other one is moving at the speed of light in the opposite direction from the lab. However, that means the second photon is moving at twice the speed of light from the perspective of the first one. That is a direct contradiction of relativity because it would mean that they could transmit information between themselves at twice the speed of light.  The only way to resolve this issue is to view the relativistic properties of each photon individually.

For example, Einstein’s math and observations tell us the time moves slower when an object is in relative motion and stops if it is moving at the velocity of light. Therefore each photon because it is moving at the speed of light would view time to have stopped at the point were they were entanglement even though they are moving in opposite directions.  Therefore, because from their perspective time has stop the information they carry would not change no matter how far apart they might be.  I think this is the definition of entanglement.   The same would be true if you looked at it from the perspective of length contraction.  Einstein’s math tells us that the length contracts to zero from the perspective of anything moving at the speed of light.  This means each photon even thought they are moving in the opposite direction would view the distance between the endpoints of the measurements as being zero.  Therefore, all photons which originate from the same point will be entangled because from their perspective the distance between the end point of the measurement will be zero.

One would come to the same conclusion if they are viewed in terms of their light cones because the base of the cone expands at the same velocity as the photons are moving away from their point of origin.  Therefore, they will always be casually connected or entangled no matter how far apart they might be from that point.

    Some have also suggested that entanglement means information can be communicated faster than the speed of light in a quantum environment.   However, because the information that photons are entangled can ONLY repeat ONLY be communicated from their origin to an observer in the future by photons means the information they contain can only move at the speed of light and NO repeat NO faster.  This means even in a quantum environment information including that contained in entangled photons cannot be communicated faster than the speed of light.)

Therefore, according to Einstein’s theory all photons which are traveling at the speed of light are entangled no matter how far they may appear to be from the perspective of an observer who is looking at them.

In other words, entanglement of photons can be explained and predicted terms of the relativistic properties of space-time as defined by Einstein as well as by Quantum Mechanics.

One way of verifying if this is correct would be to determine if particles which were NOT moving at the speed of light experience entanglement over the same distances as photons do.

This is because, the degree of relativistic shortening between the end points of the observations of two particle is dependent on their velocity with respect to the laboratory where they are being observed.

Therefore, if it was found that only photons experience entanglement when the observation points were separated by large distances while others that are not moving at the speed of light do not it would support the idea that it is a result of the relativistic properties of space defined by Einstein and not by their Quantum mechanical properties.

However, one must remember the wave particle duality of existence as defined by Quantum mechanics tell us that before a particle is observed it has an extended length due to its wavelength. Therefore, all particles will be entangled if the reduction in length between the endpoints of the observations when adjusted for their relative velocity is less their wave length as defined by quantum mechanics.

    A more conclusive argument could be made for the idea that entanglement is a result of the relativistic properties of space if it was found that entanglement ceased if the relativistic distance between the end points of observation when viewed from the perspective of particle moving slower than the speed of light was greater than its wavelength as defined by quantum mechanics.

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However, the fact that we have been unable to do so suggests that one or both of these theoretical models does not describe the true nature of reality because the world we see through a telescope must have its foundations in the world of the very small therefore they must be connected.

There can be many reasons for this.  One is that foundational assumptions of either or both of them is incorrect.  In other words, the world of the tiny may not be governed by probabilities as quantum theory suggests or the world, we see though a telescope may not be ruled by relativistic properties of four dimensional space-time.

However, there is another possibility that many have over looked is that even though their mathematics makes very accurate perditions of experimental observations they do not accurately define reality of their operating environments.

For example, Einstein mathematically defined the physical structure of the universe in terms of the geometry four dimensional space-time.

However, when using the constant velocity of light and the velocity of objects that do not move at that speed to define its geometric properties he provided a way of mathematical converting a unit of time in a space-time universe to unit of space in one physically consisting of only four *spatial* dimensions.

In other words, their is an equally valid interpretation of his mathematics in terms of only four spatial dimensions.

Since both of these solutions that of four dimensional space-time and four spatial dimensions would yield the same numerical results it gives one a different way of connecting his theories to those of Quantum mechanics based on the physical properties of four spatial dimensions instead of four dimensional space-time.

Quantum Theory on the other hand defines tiny world of particles in terms of the non physical probabilities associated with Schrödinger wave equation which as mentioned earlier no one has been able to physical connect to the space-time universe define by Einstein.

However, the fact that Einstein provided an alternative solution to his mathematics in terms of four spatial dimensions suggests it may be possible to make that connection and therefore define a Theory of Everything by using the alternative solution of four spatial dimension that his theory provides instead of one based on four dimensional space-time.

For example the article "Why is mass quantized?" Oct. 4, 2007 showed one could derive the quantum mechanical properties of energy in terms of a resonant "system" or structure formed by a energy wave on the surface of a three-dimensional spatial manifold with respect to a fourth *spatial* dimension.

Briefly that article showed the four conditions required for resonance to occur in a three-dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate can be meet in one consisting of terms of four spatial dimension.

Its continuous properties would allow an energy wave on a "surface’ of a three-dimensional space manifold to oscillate with respect to a fourth *spatial* dimension thereby fulfilling one of the requirements for 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.

Therefore, these oscillations in a continuous non-quantized field of energy would meet one of the requirements mentioned above for the formation of a resonant system or "structure" in space.

Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

These resonant systems in a space-time environment would be responsible for the incremental or discreet energy associated with quantum mechanical systems.

Another requirement for a resonate system to be formed is that the wave must be confined to specific volume of space.

However, one can also define the confinement of the resonant component of a particle and therefore establish a physical connection to the wave particle duality quantum mechanics associates with energy in terms of the relativistic properties of four *spatial* dimensions.

In 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 a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article "Why is energy/mass quantized?".

In other words, an energy wave in four *spatial* dimensions will maintain its wave properties unless it is confined to three by an observation, therefore it it always be view as a particle when an observation is made and any energy left over from the formation of its resonate structure will be radiating from the point of observation in the form of light or an energy wave.

The physics of wave mechanics also tells us that due to their continuous properties the energy waves the article "Why is energy/mass quantized?" Oct. 4, 2007 associated with a quantum system would be distributed throughout the entire "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

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

(Some may question the fact that the energy wave associated with particle would be distributed over the entire universe.  However, the relativistic properties of space-time and four spatial dimensions tell that distance perceived by objects or particles in relative motion is dependent on their velocity which become zero at the speed of light.  Therefore, from the perspective of an energy wave moving at the speed of light, the distance between all points in the universe along it velocity vector is zero.  In other words, it’s energy is distributed or simultaneous exists at every point in the universe along its velocity vector.  There can be not other conclusion if one accept the validity of Einstein’s theories.)

As mentioned earlier the article “Why is energy/mass quantized?” shown a quantum particle is a result of a resonant structure formed by an energy wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

Similarly a particle would most probably be 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, by interpreting Einstein space-time theories in their equivalent four spatial dimension one can connect the non physical probabilities associated with Schrödinger wave equation to the reality of the world defined by him. 

Additional it shows, by changing our interpretation of Einstein’s theories from four dimensional space-time to it equivalent in four spatial dimensions allows one to clearly understand the physical connection between the probabilistic world of quantum theory and the relativistic world of his theories, thereby allowing one to form a Theory of Everything.

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

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Einstein was able to define the origins of gravity and potential energy associated with rest mass in terms of curvature or the changing geometry of a space-time manifold but he did not tell us anything about the causality of kinetic energy.

For example he told us that gravity is caused by curvature or distortion in a space-time manifold however he did not due the same for kinetic energy associated with constant relative motion.

Yet its casualty is central to our understand of our universe because it along with gravity and Dark Energy are assumed to be responsible for evolution of the universe.

However one reason may be because kinetic energy of relative motion is constant with respect to both distance and time.  In other words the energy of an object in constant motion always moves the same distance in a given time interval.

As was just mentioned one of the difficulties in defining the kinetic energy in terms of the space-time environment defined by Einstein is that its magnitude is determined only by the distance an object moves through space within a constant time interval.  In other words it is only dependent on the spatial not on time parameters of its movement.

However redefining Einstein’s space-time universe in terms of its spatial properties would allow one to define the energy of constant motion in terms of those spatial properties.

Einstein gave us the ability to do this when he define the displacement or curvature he associated with the potential energy of rest mass in terms of the equation E=mc^2 and the constant velocity of light because that gave us the ability to redefine a unit of time in his space-time universe to an equivalent unit of space in a universe consisting of only four *spatial* dimensions.

This fact is the bases for assuming as was done in the article “Defining energy” Nov. 26, 2007 that all forms of 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.

Using those concepts one could define the energy of rest mass in terms of magnitude of a physical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension cause by a objects mass while defining the kinetic energy of two masses in relative motion in terms of the spatial displacements cause by that motion. 

In other words the “surface” of three dimensional space associated with objects in relative motion would exist on different three dimensional plains with respect to a fourth *spatial* dimension.

For example magnitude of kinetic energy of two masses would be defined the relative magnitude of their displacement in “surface’ of three dimensional space with respect to a fourth *spatial* dimension 

In other words it allows one to mathematically derive the causality of relativistic motion in terms of the geometry of either four *spatial* dimensions or four dimensional space-time space because when Einsteinâ€s defined his space-time universe in terms of energy/mass and the constant velocity of light he allow to chose one or the other and get the same end results.

Einstein in his General Theory of Relativity derived the causality of gravity in terms of a curvature or displacement in a space-time manifold however in his Special Theory of Relativity he only told us the effects of relative motion has on an environment not what caused the energy of that motion.  However as was shown above one can use his theoretical concepts to mathematically define its casual in terms physical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension thereby give a more complete understanding of the relativistic environment encompassed by his theories.

This is significant because understanding the spatial properties of relative motion is the first step in understanding how Newton’s laws of motion are physically connected to Einstein’s space-time environment.

Later Jeff

Copyright 2018 Jeffrey Oâ€Callaghan

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For example in his General Theory of Relativity he derived the causality of gravity in terms of a curvature in the geometry of space and time.

One can understand how in terms of the physical image of a marble on a curved surface of a rubber diaphragm.  The marble follows a circular pattern around the deformity in its surface. Similarly planets revolve around the sun because they follow a curved path in the deformed “surface” of space-time.

In other words he was able to integrate the physicality of gravity into our consciousness in terms of a physical image based on observing a marble moving on a curved surface.

However he was unable to do the same for electrical forces as was documented by the American Institute of Physics.

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

In other words because time is only observed to move in one direction forward, a space-time universe can only support a force that cause movement in one direction towards an object such as gravity. 

However, it would be easier to form a physical image of electrical forces if one converts or transposes Einstein’s space-time universe to one of only four *spatial* dimensions the because of the bidirectional symmetry of the spatial dimension.

In other words because time is only observed to move in one direction forward, a space-time universe can only support a force that cause movement in one direction towards an object such as gravity while one made up four *spatial* dimensions could support the towards and away or bi-directional movement associated with electromagnetism. Therefore because of the bidirectional symmetry of a spatial dimension it would be easier to form a physical image of electrical forces if one converts or transposes Einstein’s space-time universe to one of only four *spatial* dimensions.

Einstein gave us the ability to do this when he used the velocity of light and the equation E=mc^2 to define geometric properties of forces in space-time environment because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of space in a universe consisting of only four *spatial* dimensions.   Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

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

The fact that one can use Einsteinâ€s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with gravitational forces 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 energy including gravitational and electromagnetism can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This allows one to form a physical image of electrical force as was done in the article “What is electromagnetism?“ Sept, 27 2007 in terms of the differential force caused by the “peaks” and “toughs” of a energy wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed it is possible to derive the electrical properties of electromagnetism by extrapolating the laws of Classical Wave Mechanics in a three-dimensional environment to a wave moving on a “surface” of three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

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

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

This shows how one can define a physician image for the causality electromagnetic forces in terms of the existence of four spatial dimensions.

Einstein was unable to accomplish this in terms of four-dimensional space-time because as mentioned earlier time is only observe to move in one direction forwards and therefore could not support the bi-directional component of electromagnetic forces.

However this also shows that Einstein was right, as was mentioned above in the  American Institute of Physics article that electromagnetism and gravity can both be explained as aspects of some broader mathematical structure because as was shown above using only valid mathematical rules one can transform his space-time equations to four *spatial* dimensions thereby allowing one to form a clear physical image explaining the causality electromagnetic forces.

It should be remember that Einstein’s genius allows us to choose whether to create physical images of an unseen “reality” in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in choose terms of energy/mass and the constant velocity of light.

Later Jeff

Copyright 2018 Jeffrey O’Callaghan

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Additionally defining or describing what time is extremely difficult. Some define it only in the abstract saying that is an invention of the human consciousness that gives us a sense of order, a before and after so to speak of the changes that occur in our environment.  However one can define or describe space in terms of the void we can see between objects that it contains.
In other words time and space do not appear to share any physical qualities.

Even so physicists have derived the physical structure of the universe in terms of a mathematical model that combines space and time into a single interwoven space-time continuum.

However it is difficult to understand how in a space-time environment they can physically interact when, as was just mentioned neither of them have any common properties.

Granted using mathematics one can explain how they do in terms of abstract concepts but it does not explain how and why they do in physical terms.

Yet one can use the fact that the one of the primary functions of time is to define change to form a physical image of how it interacts with space to create it.

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

In other words he tells the physical properties of space and time are relative to an observer’s interpretation similar to how the measurements of their magnitudes are relative to an observer’s velocity because, as was show above one can reinterpret the mathematics associated with the space-time environment of both the General and Special Theories of Relativity purely in terms of its spatial components to create an identical one in only four *spatial* dimensions.  However one must be careful not to think of this as the physical replacement of the time dimension in Einstein’s space-time universe with a spatial one because according to his mathematics they simultaneously coexist in the same geometric plain.

However the fact that one can use Einsteinâ€s theories to qualitatively and quantitatively define the displacement he associated with energy in a space-time universe in terms of four *spatial* dimensions is bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy 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.

Doing would also allow one to form a physical image of how the geometric properties of space or time interact to create change because as mentioned earlier we can form a clear physical image of how a void in four spatial dimensions created by that displacement would cause change.

For example we can physically observe how the energy stored in the displacement of water in dam causes change in an environment when it is released or allowed to flow over it.  In other words we can form a physical image of the causality of the changing level of water in the dam in terms of its movement through the spatial void between the top and bottom of the dam.

Similarly one can form a clear physical image of how and why change would occur in  our three dimensional environment by assuming the energy stored in a spatial displacement in a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension is released though the void that displacement creates in four dimensional space.

As was mentioned earlier it is difficult to form physical image of how time can interact with space because of its abstract properties.

However one can from a very clear image of how it does when one realizes that according Einstein theories the physical properties of space and time which as was shown above are relative to an observer coexist on in the same dimensional plain.  Therefore an observer who looks at his theories form a spatial perspective can easily understand how change occurs in a space time-environment in terms of the physical example of water flowing over a dam.

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

Later Jeff

Copyright Jeffrey O’Callaghan 2016

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