Please click here for a brief summary of the ideas presented in this blog.

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

However, because observations of particles in particle accelerators APPEAR to verify Einstein’s assumption that if they had mass, they COULD NOT move at the speed of light one must assume 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, reduces down to E = p2c2. 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 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 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 because it has no rest mass. However, even though Einstein may have defined Relativistic energy in terms of its components such as rest mass, and momentum he did not make the same distinction regarding their energy. What he DID do was define gravity and therefore mass in terms of a curvature in space-time caused by the energy density of space. This means that we should NOT assume the increase in its energy density caused by the momentum of photon will NOT do the same. Since his equation E=mc^2 defines the energy contained in the curvature in space-time he associated with mass we must assume the added energy density associated with a photon’s momentum will cause it to have mass. This means it is as some have suggested FUNDAMENTALLY WRONG to say the momentum of photon can carry energy because it has no rest mass.”)

Therefore, if electromagnetic energy was propagated by a photon Einstein Theories would be invalidated, because it is impossible to use it to define how a particle could propagate energy at that speed.

While if one can show that electromagnetic energy is NOT propagate by the particle called a photon it would invalidate Quantum mechanics because one of its core principals is that all energy it quantized.

This suggests if one could explain ALL of the observable properties of a photon PURELY in terms of the theoretical structure of either one of these theories it would validate one over the other.

For example, one can use the science of wave mechanics to understand how energy can be propagated faster than the speed of light in terms of the continuous field properties of the space-time environment defined by Einstein because it tells us waves move energy from one location to another without transporting the material they are moving on. For example, a water molecule does not actually travel with the waves but does transmit that movement associated with it to the next unit of water. Putting it another way the molecules that make up the wave remain stationary with respect to the back ground of the water. Additionally, it will continue to do so unless it is obstructed by encountering an object or beach.

Similarly, an electromagnetic wave in space-time COULD move at the speed of light because it does not move the energy associated with its peaks and valleys it creates in space-time but would transmit them to the next unit of space-time. Putting it another way 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 space 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 if it is prevented from moving through space by an interaction with an observer or the “external world”.

For example, wave mechanics tells us an electromagnetic wave would move through the continuously properties of 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 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” of something.

This shows if one assumes that electromagnetic energy is propagated BY a wave NOT a particle one can explain how it can be propagated though space at the speed of light and why when it interacts with the external world of an observer it APPEARS as a photon in a manner that is consistent with the assumptions of Einstein Theory of Relativity.

This mechanism for the creation of a photon from an electromagnetic wave is consistent with the quantum mechanical observation that the wave properties of energy or the wave function as they like to call it only reduces or COLLAPSES to a photon or quantized unit of energy when it is observed or interacts with something.

However, as was mentioned earlier Quantum Mechanism tells us electromagnetic energy MUST be propagated by a particle called a photon however it CANNOT explain how it can move at the speed of light SOLELY in terms of its theoretical structure.

This suggests that Einstein theory provides the best theoretical model for understanding why a photon is what it is because it can explain ALL of its observable properties in terms of its theoretical structure whereas Quantum mechanics CAN NOT.

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Please click here for a brief summary of the ideas presented in this blog.

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.

A fundamental issue in Einstein Theory of Relativity is if all motion is relative how can we measure the inertia of a body? Einstein and many others assumed we must measure it with respect to something else. But what if a particle is the only thing in the universe, how can we measure it.

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.Â 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*Â 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.Â 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 .Â 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.Â 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.Â 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.Â 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.Â 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

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Presently, there is disconnect between our understanding of one of the most mysterious facets of quantum mechanics quantum, 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 stated 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 particles are entangled 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 effect 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.

In quantum physics, it is assumed entangled particles remain connected so that actions performed on one immediately affect the other, even when separated by great distances. The rules of Quantum physics also state that an unobserved photon exists in all possible states simultaneously but, when observed or measured, exhibits only one state.

One of the experiments that many assume verifies that entanglement is a quantum phenomenon uses (This description was obtained from the Live Science web site) 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.

Yet, this tell us (Please see attached graphic) that the separation between the observation points in a laboratory from the perspective of two photons moving at the speed of light would be ZERO no matter how far apart they might be from the perspective of an observer in that laboratory. This is because, as was just mentioned according to the concepts of Relativity one can view the photons as being stationary and the observers as moving at the velocity 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 determining 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 photon which are.

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

Therefore, all photons no matter how far apart they are from the perspective of a lab will be entangled because Einstein tells due to the fact that they are moving at the speed of light that distance will be Zero from their perspective.

However, he also tells us that for particles moving slower than the speed of light the distance between will be greater than zero and how much more would depend on their the relative speed with respect to it. In other words, the slower with respect to the lab they are moving the less that distance will be shortened.

Therefore, if it was found that only photons experience entanglement when the observation points were separated by large distances it would support the idea that it is caused by the relativistic properties of space defined by Einstein.

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 equal due to its wavelength. Therefore, all particles will be entangled if the reduction in length between the endpoints of the observations when adjusted with respect to 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 when 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.

Some have suggested that “There are inertial frames for every speed less than light – speaking informally – but there is no inertial frame for light speed itself. Any attempt to generate one actually generates a degenerate frame which can cover only an infinitesimal fraction of space-time.” However the argument that there are “There are inertial frames for every speed less than light”

because they would create an infinitesimal fraction of space-time is invalid, because Special Relativity WITHOUT EXCEPTION defines an inertial frame reference as one which is not undergoing acceleration. Therefore, even though using a photon as a reference frame may create infinitesimal 2 dimensional fraction of space-time the conceptual foundations formulas for length contractions of reference frames in relative motion define by Einstein tells us that one can exist. One reason that all of the mass which is contained in it is not undergoing acceleration.Therefore, the fact that it may define a degenerate frame would be irrelevant to the conclusion draw above because as that post showed it is the distance between the end points of the observation when viewed from a photon that determines whether or not it will be entangled.

Copyright Jeffrey O’Callaghan 2020

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One cannot deny that Quantum mechanics, the theory that defines the tiny world of particles and Einstein’s theories, the one that defines what we see through a telescope have been the most successful scientific theories of modern times However, attempts to bring these two theories together and define "A Theory of Everything" have been unsuccessful.

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.

*H***owever, 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 SchrÃ¶dinger 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 â€œ__Why is energy/mass quantized?__â€ 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 SchrÃ¶dinger 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**

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