Both Einstein’s General and Special Theories of Relativity define macroscopic properties of energy/mass in terms of the continuous properties of four dimensional space-time while quantum mechanics defines its microscopic properties in terms of its discontinuous properties of three-dimensional space. 

This fact makes it extremely difficult to conceptually integrate them because something that is discontinuous cannot by definition be continuous.

However it is possible to define a mechanism responsible for creating a discontinuous or quantum unit of space-time if one redefines Einstein’s space-time universe into one consisting of only four *spatial* dimensions.

Einstein gave us the ability to do this when he used he used the velocity of light to defined the geometric properties of space-time and energy/mass because it allows one to convert a unit of time in his space-time universe to a unit of space.  Additionally because the velocity of light is constant means 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 defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

However as mentioned earlier doing so would also allow one to define a physical mechanism responsible for creating a quantum of space-time in terms of the existence of four *spatial* dimensions.

For example the article "Why is energy/mass quantized?" Oct. 4, 2007 showed it is possible to explain the quantum properties of energy/mass by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave on the continuous "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

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

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

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

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

Therefore the discrete or quantized energy of resonant systems in a continuous four dimensional environment would be responsible for the discrete quantized energy quantum mechanics associated with energy/mass.

However, it did not explain the mechanism responsible for quantizing the space containing energy/mass

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

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

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is responsible for the quantization of four-dimensional space because it would result in the formation of discrete or quantized volumes associated with the observed quantum properties of energy/mass.

In other words defining space in terms of four *spatial* dimensions allows one to conceptually the integrate the discontinuous quantum mechanical properties of energy/mass into the continuous field properties four-dimensional space in terms of a resonant system created by the wave properties of energy/mass.

However also allows one to integrate the quantum mechanical properties of energy/mass into the continuous field properties of Einstein’s space-time universe because as mentioned earlier by defining those properties in terms of energy/mass and the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions. 

Additionally it demonstrates it is not necessary to assume the fundamental component of energy/mass is composed of a quantum of space-time or any other field as is assumed quantum field theory because it provides a valid and verifiable mechanism for creating it out of the field properties of space-time.

Physicists should remember it is impossible to derive a mechanism to explain and predict the continuous properties of four dimensional space-time in terms of quantum mechanics because something that is discontinuous cannot by definition be continuous.  However one can understand the quantum in terms of the continuous properties of space-time because something that is continuous by definition can be divided  into smaller units.

Copyright Jeffrey O’Callaghan 2013

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Is it possible to define the physical "reality" of a Quantum field?

We think so.

Many including Albert Einstein and Erin Schrödinger, had difficulty accepting the "reality" of quantum mechanics because many of its concepts appear to contradict those of our observable universe.

For example in a quantum system Schrödinger’s wave equation defines the field properties of its environment and predicts the future distribution of a particle’s position only in terms of the abstract properties of probabilities.

However many including Einstein and Schrödinger define reality in terms of what they see or touch.

For example, Einstein used the observable "reality" of the interactions of electromagnetic energy with a photoelectric material to derive the quantum mechanical properties of energy/mass while using the observable properties of light in our three-dimensional environment to define his space-time universe.

In other words his conclusion that electromagnetic energy is quantized was based on the physical "reality" of the environment sounding the photoelectric material and how electromagnetic energy interacted with it, not on the abstract probabilities associated with quantum fields.

However the abstract properties of probabilities share a common characteristic with Einstein’s space-time universe in that time or a space-time dimension have never be seen or touched and therefore they like the probability functions of quantum field theory are, by definition abstract quantities.

Fortunately they also have a common element, as mentioned earlier in the physically observable non-abstract properties of the *spatial* dimensions because the probabilities associated with Schrödinger’s wave equation are expressed in terms of the spatial properties of position.

Therefore because they share a common connection to the observable "reality" of our three-dimensional spatial environment one should be able to define the physical "reality" of both Einstein space-time dimension and the field properties of quantum mechanics in terms of their non-abstract spatial components.

Einstein gave us the ability to do this when he used the constant velocity of light in the equation E=mc^2 to define how energy/mass effects a space-time environment.  Additionally because the velocity of light is constant it also allows one to defined a one to one qualitative and quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

For example he told us the energy associated with mass causes a curvature or contraction in the "surface" of space-time and when mass is converted to energy it causes the three-dimensional properties of space-time to expand because of a decrease in its curvature he associated with that event.

This expansion and contraction would be analogous to how the two dimensional "surface" of a balloon either expands of contract when air (energy) is added or taken away from it.

However observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein one must assume that energy also has a spatial component.  However, because the equation E=mc^2 uniquely defines the geometric properties of a space-time universe in terms of both energy and mass one can use it to convert or transpose the space-time curvature Einstein’s associated with energy to one that would define it terms of a spatial curvature in a four *spatial* dimensions.

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

The fact that one can use the Einstein’s equations to qualitatively and qualitatively derive the spatial properties of energy in a space-time universe 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 can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

One of the theoretical advantages of a modeling the existence of energy/mass on four *spatial* dimensions instead of four dimension space-time is it allows one to derive the "reality" of a quantum fields in terms of the observable non-abstract properties of our three-dimensional environment.

The physical "reality" of the field properties energy/mass in four *spatial* dimension was developed in the article “Electromagnetism in four *spatial* dimensions” Sept 27, 2007 where it was shown the forces associated with an electromagnetic field can be explained and predicted in terms of matter wave on field consisting of four *spatial* dimensions.

Briefly it showed that one can derive its field properties by extrapolating the observable non-abstract properties of a three-dimensional environment to a fourth *spatial* dimension.

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

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

Therefore observations  of our three dimensional "reality", if extrapolated  to four *spatial* dimensions tells us the force developed by the differential displacements caused by a matter wave moving on a "surface" of three-dimensional space with respect to a fourth *spatial* dimension 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 non-abstract mechanism for understanding why similar charges repel each other because observations of wave on the surface of water tell us that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

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

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

However, observations of our three dimensional environment tell us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

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

This shows how one can explain and predict the continuous field properties of electromagnetism by extrapolating the observable non-abstract properties of our three dimensional environment to a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, as was shown in the article “The Photon: a matter wave?” Oct. 1, 2007 the quantum field properties of four *spatial* dimension can also be derived by extrapolating the observable non-abstract resonant properties of a three-dimensional environment to one consisting of four *spatial* dimension.

There are 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.

The existence of four *spatial* dimensions would give the continuous surface or field of three-dimensional space manifold (the substance) the ability to oscillate spatially with respect to a 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.

Therefore, these oscillations in four *spatial* dimensions, would meet 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 four *spatial* dimensions are responsible for the incremental or discreet field energies associated quantum and electromagnetic field theories

This shows how one can define the "reality" of the continuous field associated with Schrödinger’s wave equation and a physical mechanism responsible for the creation of particles in that field in terms of the observable non-abstract "reality" of our three-dimensional environment.

Latter Jeff

Copyright 2013 Jeffrey O’Callaghan

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