14

Einstein was often quoted as saying “If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless.”

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.

â€œFrom 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 â€” for a â€œunified fieldâ€ theory that would unite electromagnetism and gravity, space and time, all together â€” 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 â€œDefining energy?â€ Nov 27, 2007 that all forms of energy including gravitational and electromagnetism can be derived in terms of a spatial displacement in a â€œsurfaceâ€ 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**

Quantum mechanics defines our observable physical environment only in terms of the probabilistic values associated with SchrÃ¶dingerâ€™s wave equation.

More specifically it defines a particle in terms of the instantaneous collapse of a wave function which it assumes extends form one edge of the universe to the other.

However this definition appears to contradict two very basic properties of our observable reality: the fact that particles appear to have a physical presents and how it can be simultaneously be in many places at the same time. In other words if SchrÃ¶dingerâ€™s wave equation does define our observable environment one should be able to explain how a mathematical probability obtains a physical presents when observed and how that physical presents can exist in different places at the same time.

**Einstein gave us the answer to the second question in his formula for relativistic length contraction L = L0((1 – v2/c2))1/2 because it tells the distance between every point along the trajectory of all forms of energy which are moving at the speed when viewed by an outside observer including that associated with the wavefunction is zero. **** Additionally because time stops for anything traveling at the speed of light it would have enough time to travel from the perspective of an outside observer from one end of the universe to the other. In other words according to Einstein’s theory the particle associated with the wave function when viewed by an outside observer simultaneously exist in many places ***because the distance between its end points when viewed by him or her is zero *

However it is extremely difficult to define a set of statements which explains how those probabilities can be connected to physical properties of particles even though it has held up to rigorous and thorough experimental testing.

This may be the reason most physicists consider quantum mechanics only in terms of its mathematical formalization instead trying to understand the meaning of it in terms of the space-time environment we occupy.

For example in 1924 Louis de Broglie was the first to realize all particles are physically composed of a matter wave as the discovery of electron diffraction by crystals in 1927 by Davisson and Germer) verified. However in his paper, *â€œTheory of the double solutionâ€œ* he could not define a physical interpretation of SchrÃ¶dinger equation in classical terms of space and time.

As is pointed at his biography on the nobleprize.org web site in “1951, he together with some of his younger colleagues made another attempt, one which he abandoned in the face of the almost universal adherence of physicists to the purely probabilistic mathematical interpretation of, Bohr, and Heisenberg.”

However the fact that no has been able to physically connect those probabilities to our environment does not change the fact that there must be one because if there wasn’t they could not interact with it to create the physicality of observable world upon which those probabilities are based.

As mentioned earlier Louis de Broglie and his colleagues tried unsuccessfully to find a physical interpretation of SchrÃ¶dinger equation in classical terms of space and time.

However the reason for their failure may be due to the fact that quantum properties of particles are related to the spatial not a time dependent properties of the wave function.

If so one may be able to establish the connection Louis de Broglie was looking for it in terms of a spatial instead of the time or space-time property of the wave function

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

The fact that one can use Einsteinâ€™s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article â€œDefining energy?â€ 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.

This would have allowed Louis de Broglie to physically connect the probabilities associated SchrÃ¶dinger equation*to the observable properties of particles in terms of a physical or spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension* as was done in the article “Why is energy/mass quantized?” Oct. 4, 2007.

Briefly that article showed that one can do this by assuming they are caused by the formation of a resonant system created by the wave component of particles on a “surface” of a three-dimensional space manifold with respect to fourth “spatial” dimension. This is because it showed the four conditions required for resonance to occur in a three-dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one made up of four.

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

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

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established on a surface of a three-dimensional space manifold.

Yet the classical laws of three-dimensional space tell us the energy of resonant systems can only take on the discontinuous or discreet energies associated with their fundamental or harmonic of their fundamental frequency.

However, these are the similar to the quantum mechanical properties of energy/mass in that they can only take on the discontinuous or discreet energies associated with the formula E=hv where “E” equals the energy of a particle “h” equal Planck’s constant “v” equals the frequency of its wave component.

In other words Louis de Broglie would have been able to physicality connect the quantum mechanical properties of his particle waves to SchrÃ¶dinger equation in terms of the discrete incremental energies associated with a resonant system in four *spatial* dimensions if he had assume space was composed of it instead of four dimensional space-time.

Yet it also would have allowed him to define the physical boundaries of a quantum system in terms of the geometric properties of four *spatial* dimensions.

For example in classical physics, a point on the two-dimensional surface of a piece 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 â€œupâ€ or â€œdownâ€ with respect to a fourth *spatial* dimension.

The confinement of the â€œupwardâ€ and â€œdownwardâ€ 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?” Oct. 4, 2007

As mentioned earlier the article â€œDefining energy?â€ Nov 27, 2007 showed 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.

*However assuming *the energy associated with Louis de Broglie particle wave *is result of a displacement in four *spatial* dimension instead of four dimensional space-time as was done earlier allows one to connect the probabilities associated with *SchrÃ¶dinger equation* to the observable properties of particles. In other words it can explain how one can be observed at a specific point in space even though its wave energy is distributed throughout a relatively large volume of space. *

For example Classical mechanics tell us that due to the continuous properties of waves the energy 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.

It also tells us that 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/mass are a result of vibrations or oscillations in a “surface” of three-dimensional space is correct then classical mechanics tell us that 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.

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

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

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

Additionally it also gives us a classical expiation of how a particle can simultaneously exist in many different place and why the probability of finding it in a give volume of space is what it is because as mentioned earlier** according to Einstein’s theory**** the distance between end points of the particle wave when viewed by an outside observer is zero even though it may extend from one end of the universe to the other because it is traveling at the speed of light. **** In other words according to Einstein’s theory the wave function when viewed by an outside observer simultaneously exist in many places ***therefore there is a probability of finding the resonant structure associated with its particle properties any where in that space. *

This shows how one can connect the properties with SchrÃ¶dingerâ€™s equation to our observable environment by assuming that space is quantized by the resonate system created by a physical wave in either space-time dimension or a “surface” of a three-dimension space manifold with respect to fourth “spatial” dimension and observing it causes it to collapse into the smaller volume of a resonant structure Quantum Mechanics associates with a particle.

It should be remember Einsteinâ€™s genius allows us to choose to define a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the probabilistic properties of a quantum environment and how they are physically connected to our observable universe.

Later Jeff

Copyright Jeffrey O’Callaghan 2017

Why many physicists chose to define the universe in terms of the physical properties of a time or space-time dimension instead of four *spatial* dimensions is puzzling because, as was shown in the earlier article “Defining time” Sept 20, 2007 there is no observational evidence supporting it having physical properties.

But even more damaging is that assuming it is composed of four *spatial* dimensions instead of four-dimensional space-time, would allow physicists more logical and consistent explanation **based on physical observations** or our environment for time dilation, length foreshortening, the mass increases associated with relative velocities, gravitational and kinetic energy than can be provided by space-time concepts of the Special and General Theories of Relativity.

Einstein himself defined a universe composed of four *spatial* dimension * and* one of four-dimensional space-time when he mathematically defined its geometric properties in terms of the constant velocity of light. This is because it allows one to redefine a unit of time he associated with energy in his space-time universe to unit of space in a one consisting of only four *spatial* dimensions.

However as was mentioned earlier viewing the universe in terms of four *spatial* dimensions instead of four-dimensional space-time, would allow one to define the mechanism responsible for time dilation, length foreshortening, the mass increases associated with relative velocities, and gravity **based on the physical observations instead of the abstract mathematical properties of the Special and General Theories of Relativity.**

One of the advantages of deriving all forms of energy in terms of their spatial instead of their time or space time properties is that it allows one to form a physical image of the opposing nature of kinetic and gravitational forces in terms of our observable properties of our environment

For example we observe that the kinetic energy associated a satellite opposes the gravitational energy of the object it is orbiting.

*However because of observations of our three-dimensional environment tell us one can move in two directions upward or downwards in a *spatial* dimension one can form a clearer image of opposing properties of these forces by defining gravity in terms of a “downward directed” displacement in a surface of a three-dimensional space manifold with respect to a fourth spatial dimension while define kinetic energy in terms of oppositely or upward directed or up displacement in that surface. Granted the one can do the same using the properties of a space-time dimension however it is much more difficult to understand the opposing nature of these force because we only observe time to move in one direction forward. *

This is the observational basis for defining, as was done in the article “Defining potential and kinetic energy?” gravitational and kinetic energy in terms of oppositely directed movements or displacements in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words if one defined the energy/mass in a volume associated with mass in terms of downward directed displacement in a “surface” of a three-dimensional space manifold with respect to a four *spatial* dimension one would define the energy associated with its relative motion in terms of an oppositely or upward displacement in that “surface”.

This would allow one to form a physical image of the relative mass increase due to relative velocities based on observation of our three-dimensional world because according to the concepts contained in that article the total energy/mass of an object would be equal to the sum of the displacements of a “surface” of a three-dimensional space manifold caused by its rest mass and that caused by their relative velocities.

However defining space in terms of four spatial dimension not only provides observational basis for causality of the gravity and kinetic energy but it also provides an explanation for the casualty of time dilation and the length foreshortening in gravitational environments and moving reference frames based on physical observations made in a three-dimensional environment.

The following analogy can be used to understand and define the relativistic properties length and time based on observations made in a three-dimensional environment.

Assume that two “2 dimensional creaturesâ€ are living on the surface of two pieces of paper resting on a desktop.

Also, assume the two creatures can view the surfaces of the other piece of paper, which are separated a pencil.

If the diameter of the pencil is increased, the curvature between the surfaces of the two pieces of paper will increase.

Each of these creatures, when viewing the other piece of paper will only perceive the two-dimensional translation of the three-dimensional curvature generated by the pencil.

Therefore, each will view the distance between two points on the surface of the other as shorter since they will view that distance as a two-dimensional translation of a three-dimensional curvature in the surface of the paper. Therefore each will measure the distance between them on their piece of paper as being longer as the diameter of the pencil increases then they would if they viewed it on the other piece.

Similarly, because three-dimensional beings could only “view” a three-dimensional translation of a “curvature” or displacement in four *spatial* dimension caused by the relative motion of a reference frame they will measure distance or length in them as being longer than they would be if viewed as an observer who is in relative motion to it.

This is the mechanism responsible for the relativistic properties of length in terms of the geometry of four *spatial* dimensions.

The two-dimensional creatures in the earlier example will also notice that time is effected by a curvature in the surface of their paper.

Each of them will view the others â€œtimeâ€ as moving slower because the three-dimensional curvature in the paper makes the distance between events longer than the two dimensional translation of that curvature. Therefore, it will take longer for events “move” through a curvature in three-dimensional space on the surface of the others piece of paper relative to the time it would take for it to move thought the two-dimensional translation of that curvature.

Earlier it was mentioned that time can be defined as only being the measure or the “distance between” the sequential ordering of the causality of an event.

Therefore time would be dilated with respect to a reference frame that is external to a gravitational field or was in motion because as mentioned earlier the length of the arc generated in three-dimensional space by a gravitational field or the kinetic energy of relative motion to be longer than the cord of that arc. Therefore, the distance between events would be greater for an observer in those reference frames than for one who is outside of it. However, this means an observer outside of those reference frames would measure the time between those events as being dilated with respect to an observer who is inside because the time required for objects to move between events in that reference frame will be longer.

As mentioned earlier article both â€œGravityâ€ and kinetic energy can be define 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 a space-time manifold.

However, this means that one can define the foreshortening of the length of an object in relative motion or in a gravitational field in terms of the cord to the arc generated by that curvature. This is because the cord of an arc created by that displacement is always shorter than the arc itself and since three-dimensional beings can only observe the three-dimensional cord of an arc in four-dimensional space they would view the length of the objects to be shorter when viewed in relative motion or in a gravitational field.

However it would also provide a mechanism for the time dilatational associated with gravity and motion that is consistent with our observations of three-dimensional space.

This shows one the benefits of viewing Einstein relativistic theories in terms of four *spatial* dimension is that it allows one to form a more logical and consistent explanation **based on physical observations** or our environment for time dilation, length foreshortening, the mass increases associated with relative velocities, gravitational and kinetic energy than can be provided by the space-time concepts of the Special and General Theories of Relativity.

As was shown earlier Einsteinâ€™s mathematics allows us to choose to define our universe in terms of either a space-time environment or one consisting of only four *spatial* dimension when he defined its geometry in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on its relativistic properties.

Later Jeff

Copyright 2017 Jeffrey O’Callaghan

Quantum mechanistic defines our observable environment only in terms of the probabilistic values associated with SchrÃ¶dingerâ€™s wave equation.

Many interpret this as meaning a particle and all other objects exists in a world of probabilities and only become connected to the environment when observed. Additionally it assumes that a particle is distributed or simultaneous exists form one edge of the universe to the other because it tells us there is a probability it can be found anywhere in it.

However it is extremely difficult to define a set of statements which explains how those probabilities can be physically connected to that environment even though it has held up to rigorous and thorough experimental testing.

Yet Einstein gave us a an explanation for this connection in his relativistic formulas for length contraction L = L0((1 – v2/c2))1/2 because it tells us the distance between every point along the trajectory of all forms of energy which are moving at the speed including that associated with the wavefunction is zero for an observer who is outside of its reference frame. In other words since the energy associated with SchrÃ¶dingerâ€™s equation which is moving at the speed of light the distance between the each end of the universe for it relative to an outside observer is zero.

However because the probabilities associated with SchrÃ¶dingerâ€™s equation involve the spatial properties of position, to fully understand the ramifications of that equation to our understanding of quantum mechanics one must transpose it to the spatial equivalent.

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

The fact that one can use Einsteinâ€™s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article â€œDefining energy?â€ 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.

*However this would allow one to physically the connect the probabilities associated SchrÃ¶dinger’s equation **to our observable environment in terms of a physical or spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as was done in the article “**Why is energy/mass quantized?” Oct. 4, 2007. *

Briefly that article showed that the observable properties of particles can be caused by the formation of a resonant system on a “surface” of a three-dimensional space manifold with respect to fourth “spatial” dimension. This is because the four conditions required for resonance to occur in a three-dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one made up of four.

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

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

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established on a surface of a three-dimensional space manifold.

Yet the classical laws of three-dimensional space tell us the energy of resonant systems can only take on the discontinuous or discreet energies associated with their fundamental or harmonic of their fundamental frequency.

However, these are the similar to the quantum mechanical properties of energy/mass in that they can only take on the discontinuous or discreet energies associated with the fundamental resonate frequency of space defined by the equation E=hv where “E” equals the energy of a particle “h” equal Planck’s constant “v” equals the frequency of its wave component.

Yet it also allows one to define the physical boundaries of a quantum system in terms of the geometric properties of four *spatial* dimensions.

For example in classical physics, a point on the two-dimensional surface of a piece 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 â€œupâ€ or â€œdownâ€ with respect to a fourth *spatial* dimension.

The confinement of the â€œupwardâ€ and â€œdownwardâ€ 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?” Oct. 4, 2007

As mentioned earlier in the article â€œDefining energy?â€ Nov 27, 2007 showed 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.

*However as mentioned earlier assuming *the probabilities associated with SchrÃ¶dingerâ€™s equation *are the result of a displacement caused by a matter wave moving on a “surface” of a three-dimension space manifold with respect to a four *spatial* dimension allows one to connect them to the physicality of the observable environment we all live in. *

Classical mechanics tell us that due to the continuous properties of the wave energy 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 Classical mechanics tells us that 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/mass are a result of vibrations or oscillations in a “surface” of three-dimensional space caused by matter wave is correct then classical mechanics tell us that 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 because

*However, as was mentioned earlier Einstein in his formula for length contraction L = L0((1 – v2/c2))1/2 tells us that a particle would simultaneously exist everywhere throughout the entire universe because of the fact that wave energy is continuous it would extend to each end of the universe. Therefore the distance between the each end of the universe relative to an observer outside of that reference frame would be zero. Additionally because time stops for anything traveling at the speed of light it would appear to exist simultaneously at every point in the universe of an outside observer.*

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

Yet Classical 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.

In others words one can explain how the probabilities associated with SchrÃ¶dingerâ€™s equation are connected to our physical world and the fact that particles *simultaneously *exist everywhere in the universe before it is observed by applying the concepts of Einstein Theory of Relativity to the quantum environment.

It should be remember Einsteinâ€™s genius allows us to choose to define a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the probabilistic properties of a quantum environment and how they physically connected to our observable universe.

Later Jeff

Copyright 2017

Quantum mechanistic defines our observable environment only in terms of the probabilistic values associated with SchrÃ¶dingerâ€™s wave equation.

Many interpret this as meaning a particle and all other objects exists in a world of probabilities and only become connected to the environment when observed. Additionally it assumes that a particle is distributed or simultaneous exists form one edge of the universe to the other because it tells us there is a probability it can be found anywhere in it.

However it is extremely difficult to define a set of statements which explains how those probabilities can be physically connected to that environment even though it has held up to rigorous and thorough experimental testing.

Yet Einstein gave us a an explanation for this connection in his relativistic formulas for length contraction L = L0((1 – v2/c2))1/2 because it tells us the distance between every point along the trajectory of all forms of energy which are moving at the speed including that associated with the wavefunction is zero for an observer who is outside of its reference frame. In other words since the energy associated with SchrÃ¶dingerâ€™s equation which is moving at the speed of light the distance between the each end of the universe for it relative to an outside observer is zero.

However because the probabilities associated with SchrÃ¶dingerâ€™s equation involve the spatial properties of position, to fully understand the ramifications of that equation to our understanding of quantum mechanics one must transpose it to the spatial equivalent.

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

The fact that one can use Einsteinâ€™s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article â€œDefining energy?â€ 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.

*However this would allow one to physically the connect the probabilities associated SchrÃ¶dinger’s equation **to our observable environment in terms of a physical or spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as was done in the article “**Why is energy/mass quantized?” Oct. 4, 2007. *

Briefly that article showed that the observable properties of particles can be caused by the formation of a resonant system on a “surface” of a three-dimensional space manifold with respect to fourth “spatial” dimension. This is because the four conditions required for resonance to occur in a three-dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one made up of four.

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

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

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established on a surface of a three-dimensional space manifold.

Yet the classical laws of three-dimensional space tell us the energy of resonant systems can only take on the discontinuous or discreet energies associated with their fundamental or harmonic of their fundamental frequency.

However, these are the similar to the quantum mechanical properties of energy/mass in that they can only take on the discontinuous or discreet energies associated with the fundamental resonate frequency of space defined by the equation E=hv where “E” equals the energy of a particle “h” equal Planck’s constant “v” equals the frequency of its wave component.

Yet it also allows one to define the physical boundaries of a quantum system in terms of the geometric properties of four *spatial* dimensions.

For example in classical physics, a point on the two-dimensional surface of a piece 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 â€œupâ€ or â€œdownâ€ with respect to a fourth *spatial* dimension.

The confinement of the â€œupwardâ€ and â€œdownwardâ€ 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?” Oct. 4, 2007

As mentioned earlier in the article â€œDefining energy?â€ Nov 27, 2007 showed 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.

*However as mentioned earlier assuming *the probabilities associated with SchrÃ¶dingerâ€™s equation *are the result of a displacement caused by a matter wave moving on a “surface” of a three-dimension space manifold with respect to a four *spatial* dimension allows one to connect them to the physicality of the observable environment we all live in. *

Classical mechanics tell us that due to the continuous properties of the wave energy 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 Classical mechanics tells us that 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/mass are a result of vibrations or oscillations in a “surface” of three-dimensional space caused by matter wave is correct then classical mechanics tell us that 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 because

*However, as was mentioned earlier Einstein in his formula for length contraction L = L0((1 – v2/c2))1/2 tells us that a particle would simultaneously exist everywhere throughout the entire universe because of the fact that wave energy is continuous it would extend to each end of the universe. Therefore the distance between the each end of the universe relative to an observer outside of that reference frame would be zero. Additionally because time stops for anything traveling at the speed of light it would appear to exist simultaneously at every point in the universe of an outside observer.*

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

Yet Classical 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.

In others words one can explain how the probabilities associated with SchrÃ¶dingerâ€™s equation are connected to our physical world and the fact that particles *simultaneously *exist everywhere in the universe before it is observed by applying the concepts of Einstein Theory of Relativity to the quantum environment.

It should be remember Einsteinâ€™s genius allows us to choose to define a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the probabilistic properties of a quantum environment and how they physically connected to our observable universe.

Later Jeff

Copyright 2017