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`In physics, a field is a physical quantity that has a value for each point in space and time.
However Quantum Field Theory or QED mathematically defines the field properties of its environment in terms of the abstract properties of probabilities.
While Einstein mathematically defines the values of gravity in terms of field equations based on the existence of four dimensional spacetime.
However neither of them define what the field is physically made of only its value at a specific point in it.
For example an electric field was a concept develop to explain the actionatadistance of electric forces. All charged objects create an electric field that extends outward into the space that surrounds it. The charge alters that space, causing any other charged object that enters the space to be affected by this field. The the value of it is dependent upon where the charged the object creating the field is and upon the distance of separation from the charged object.
However if one is to accept the definition of a field given above: that is a that is a measure of the value of a physical quantity one should be able to define what that physical quantity is. Yet neither Einstein’s or Quantum Field Theory do.
Granted Einstein did based both his Special and General Theories of Relativity on the existence of four dimension spacetime. However even though we can observe the physicality of the spatial dimensions we cannot do so for a time or spacetime one because we as human perceive time only in the abstract. There are even, as was shown in the article "Defining time" Sept 20, 2007 some who believe it is an invention of the human consciousness that gives us a sense of order, a before and after so to speak.
Therefore it is a bit difficult to understand how it can be a component of the physical quantity physicists call a field.
However Einstein gave us a way to define the physical properties of time mass and energy at each point in a spacetime field when he used the velocity of light to define its geometric properties because that allows one to convert a unit time in a spacetime environment to an equivalent unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant it is possible to define a one to one correspondence between his spacetime universe and one made up of four *spatial* dimensions.
In other words because he defined the geometric displacement responsible for energy and mass in a spacetime environment in terms of the constant velocity of light means that one can quantitatively and qualitatively define a one to one connection between the abstract properties of time in a spacetime universe with physicality most associate with space in one consisting of four spatial dimensions.
The fact that one can use the Einstein’s equations to qualitatively and qualitatively derive the displacement Einstein associated with energy and mass in a spacetime environment in terms of four *spatial* dimensions is one bases for assuming, as was done in the article “Defining energy?” Nov 27, 2007 that all fields and forms of energy can be derived in terms of a physical displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
One of the theoretical advantages of modeling the existence of energy/mass in terms of four *spatial* dimensions instead of four dimension spacetime is it allows one to derive their physical properties those of an electric field in terms of the observable nonabstract properties of space in our threedimensional environment instead of in the abstract properties of time or a spacetime dimension.
For example of the properties of electromagnetism was developed in the article “Electromagnetism in four *spatial* dimensions” Sept 27, 2007 where it was shown they can be explained and predicted in terms of matter wave on a field consisting of four *spatial* dimensions.
Briefly it showed that one can derive its field properties by extrapolating the observable nonabstract spatial properties of a waves in threedimensional environment to a fourth *spatial* dimension.
For example a wave on the twodimensional 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 threedimensional 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 threedimensional 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 threedimensional space manifold with respect to a fourth *spatial* dimension.
However, it also provides a nonabstract 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 threedimensional 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.
In other words one can mathematically derive a physical quantity that has a value for each point in space associated with an electromagnetic field by extrapolating the observable nonabstract properties space in our three dimensional environment to a matter wave moving on a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
This shows how one can understand many of observable properties of electric fields by assuming they are made up physical non abstract properties of space instead of the abstract properties of time.
However, as was shown in the article “The Photon: a matter wave?” Oct. 1, 2007 one can also use the concept outlined above to understand the the physicality of a quantum electrical field and the probability associated it by extrapolating the observable nonabstract resonant properties of a threedimensional environment to one consisting of four *spatial* dimension.
That article showed the four conditions required for resonance to occur in a threedimensional environment an object or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in an environment consisting of only four spatial dimensions.
The existence of four *spatial* dimensions would give the continuous surface or field of a threedimensional 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 threedimensional 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 threedimensional 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.
In other words one can mathematically derive a physical quantity that has a value for each point in space associated quantum mechanical properties of energy/mass by extrapolating the observable nonabstract properties space in our three dimensional environment to a matter wave moving on a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
However it true one should also be able to define the probabilities associated with Quantum Field Theory in the same terms.
Classical mechanics tells us that because of 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 threedimensional space manifold with respect to a fourth *spatial* dimension similar to how the wave generated by a vibrating ball on a surface of a rubber diaphragm are disturbed over its entire surface while the magnitude of the displacement it causes will decrease as one moves away from the point of contact.
However, this means if one extrapolates the mechanics of the rubber diaphragm to a "surface" of threedimensional space one must assume the oscillations associated with each individual quantum system must be disturbed thought the entire universe while the spatial displacement associated with its energy defined in the in the article “Defining energy?” Nov 27, 2007 would decrease as one moves away from its position. This means there would be a nonzero probability they could be found anywhere in our threedimensional environment because, as mentioned earlier the article "Why is energy/mass quantized?" Oct, 4 2007 showed that a quantum mechanical system is a result of a resonant structure formed by the oscillations on the "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
Classical Wave Mechanics tells us a 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 an observer would most probably find a quantum system were the magnitude of the vibrations in a "surface" of a threedimensional space manifold is greatest and would diminish as one move away from that point.
However as mentioned earlier this is exactly what is predicted by Quantum mechanics in that one can define a particle’s exact position or momentum only in terms of the probabilistic values associated with vibrations of its wave function.
One could verify or falsify the above theoretical model by deriving a physical constant for interaction of a fourth *spatial* dimension with threedimensional space for electromagnetism and quantum probabilities and compare them. If they agree then it would have a tendency to verify it if they do not it would rule it it out.
It should be remember Einstein’s genius and the symmetry of his mathematics allows us to choose whether to define the reality of our environment in either a spacetime or four *spatial* dimension.
Later Jeff
Copyright Jeffrey O’Callaghan 2016
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Quantum Chromodynamics a subset of the Standard Model of Particle Physics gives a very accurate mathematical description of the strong force that hold quarks together in protons and neutrons in terms of a gauge theory with the symmetry group of SU(3).
However it does not define how that force physically interacts with them to do that. In other words it mathematically defines a SU(3) group but it does not define how it interacts with our observable environment to create that force.
Despite this shortfall some feel that a physical connection must exist between the math defining Quantum Chromodynamics, the Standard Model of Particle Physics and the physical reality of the observable environment humans occupy because their quantitative predictions so accurately describes the properties and forces associated with quarks. This is true even though gravity which is part of that environment has yet to be incorporated into it.
However the fact that one can mathematically describe properties of an environment does not necessary mean that it accurately depicts its reality.
For example there are many ways to mathematically define why there are five apples on a table. One could say that originally there were six and one was taken away or that there were four and one was added. Both accurately described the observed number of apples on the table. However if originally there were four apples the one that assumed there were six does not define the reality of their environment that produced them.
Similarly there may be several ways to describe the existence quarks.
If so how can we determine which one not only describes what we observe but also defines the reality of the environment that created them?
One way to increasing the possibility of getting it right would to define their environment based on what we observe and then derive its mathematical properties instead of defining them only in terms of its mathematical ones which is what Quantum Chromodynamics does.
For example, observations of the neutron and proton indicate they are made up of distinct components called quarks of which there are six types, the UP/Down, Charm/Strange and Top/Bottom. The Up, Charm and Top have a fractional charge of 2/3. The Down, Strange and Bottom have a fractional charge of 1/3. Scientists have also determined that quarks can take on one of three different configurations they have designated by the colors red, blue, and green. Additionally they tell us the binding energy associated with the strong force is only depended on the distance between them. In other words it does not vary with time
This suggests, because that forces remain constant through time their existence is related to the spatial not the time properties of their environment.
This may be also be the reason why as was mentioned earlier gravity is has not yet been incorporated in it the Standard Model because presently the only viable theory we have; Einstein’s General Theory of Relativity defines it in term of the temporal properties of a spacetime dimension.
However Einstein gave us the ability resolve this conflict when defined his spacetime environment in terms of the constant velocity of light because that allows one to convert a unit of time in it to a unit of space in a one 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 spacetime universe and one made up of four *spatial* dimensions.
In other words the symmetry of his mathematics provides a qualitative and quantitative means of redefining his spacetime universe in terms of the geometry of four *spatial* dimensions.
Doing so may allow one to define an environment which is responsible the forces and the fractional charge of quarks and how they interact to form particles in terms of the geometry four *spatial* dimension.
For example the article Defining energy Nov. 26, 2007 showed it is possible to define all forms of energy including electrical in terms of a physical displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension similar to how Einstein derived gravity in terms of a physical displacement in a spacetime manifold.
However, we as threedimensional beings can only observe three of the four *spatial* dimensions. Therefore, the energy associated with a displacement in its "surface" with respect to a fourth *spatial* dimension will be observed by us as being directed along that "surface". However, because two of the threedimensions we can observe are parallel to that surface we will observe it to have 2/3 of the total energy associated with that displacement and we will observe the other 1/3 as being directed along the signal dimension that is perpendicular to that surface.
This means one could define the environment responsible for the 2/3 fractional charge of the Up, Charm and Top may be related to the energy directed along a "surface" of a displaced threedimensional space manifold with respect to a four *spatial* dimension while the 1/3 charge of The Down, Strange and Bottom may be associated with the energy that is directed perpendicular to that "surface".
The reason why quarks come in three configurations or colors with a fractional charge of 1/3 or 2/3 may be because, as was shown in the article Embedded Dimensions Nov. 22, 2007 there are three ways the individual axis of threedimensional space can be oriented with respect to a fourth *spatial* dimension. Therefore, the configuration or "colors" of each quark may be related to how its energy is distributed in threedimensional space with respect to a fourth *spatial* dimension.
However, it can also explain why it takes three quarks of different "colors" to form a stable particle because, as the article "Why is energy/mass quantized?" Oct, 4 2007 showed one can define one in terms of a resonant system on a "surface" a threedimensional space manifold with respect to a fourth *spatial* dimension. If the colors of each quark represent the central axis associated with its charge then to form a stable resonate system would require three quarks that have different central axis to balance its energy with respect to the axes of threedimensional space. A particle could not exist if two quarks have the same central axis or color because it would cause an energy imbalance along that axis. Therefore, a particle consisting of anything but quarks of three different colors would not stable.
(Briefly that article showed the four conditions required for resonance to occur in any 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 available in one consisting of four *spatial* dimensions,
The existence of four *spatial* dimensions would give a continuous nonquantized field of energy/mass (the substance) the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.
These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.
Therefore, these oscillations would meet the requirements mentioned above for the formation of a resonant system or "structure" in space.
Observations of a threedimensional 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.)
Yet this gives us a method of mathematically deriving the strong force in terms of the physical properties of predefined environment that it is a part of because we know two of its parameters; the electrical forces pushing them apart and the distance between them. Therefore we should be able to determine the magnitude strong force required to prevent that from happening using the geometric relationship describe above.
As was shown earlier the symmetry of Einstein’s mathematics provides a qualitative and quantitative means of redefining gravity in his spacetime universe in terms of the geometry of four *spatial* dimensions.
Doing so would allow for the anchoring the mathematics defining both gravity and the strong force in terms of the physical properties a common environment something which Quantum Chromodynamics and the Standard Model of Particle Physics have been unable to do.
It should be remember Einstein’s genius and the fact that he defined the geometry of spacetime in terms of the constant velocity of light allows us to choose to define our universe in either a spacetime environment or one consisting of four *spatial* dimension when. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the temporal properties of our universe giving us a new perspective on how the forces it contains interacts with it.
Later Jeff
Copyright 2016 Jeffrey O’Callaghan
Anthology of 
The Reality of the Fourth Spatial Dimension Paperback $9.77 Ebook $6.24 
The Imagineer’s


The Imagineer’s

The Imagineer’s Chronicles Vol. 4 — 2013 Paperback $13.29 Ebook $7.99 
The Imagineer’s 

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