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 space-time.
For example an electric field was a concept develop to explain the action-at-a-distance 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 space-time. However even though we can observe the physicality of the spatial dimensions we cannot do so for a time or space-time 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 space-time field when he used the velocity of light to define its geometric properties because that allows one to convert a unit time in a space-time 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 space-time 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 space-time 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 space-time 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 space-time 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 three-dimensional 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 space-time is it allows one to derive their physical properties those of an electric field in terms of the observable non-abstract properties of space in our three-dimensional environment instead of in the abstract properties of time or a space-time 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 non-abstract spatial properties of a waves in 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.
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 non-abstract properties space in 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.
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 non-abstract resonant properties of a three-dimensional environment to one consisting of four *spatial* dimension.
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 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 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.
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 non-abstract properties space in 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 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 three-dimensional 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 three-dimensional 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 non-zero probability they could be found anywhere in our three-dimensional 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 three-dimensional 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 three-dimensional 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 three-dimensional 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 space-time or four *spatial* dimension.
Later Jeff
Copyright Jeffrey O’Callaghan 2016