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Maxwell defined the propagation of an electromagnetic wave in terms of a field consisting of both electric and magnetic components which continuously interact with each other, forming an electromagnetic wave.

While Quantum Field Theory defines an electromagnetic field in terms of **discrete parcels of energy **while avoiding the question as to how it moves through space.

A*dditionally, it cannot explain in terms of a physical model and why an electromagnetic wave always without exception becomes a particle when observed. *

*E instein also had a problem of deriving its electromagnetic properties and how they moved through space in terms of a physical model based on his gravitational theories as was documented by the American Institute of Physics .*

*“From 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 ” for a unified field theory that would unite electromagnetism and gravity, space and time, all together â€” occupied more of Einstein’s years than any other activity. *

*However, one of the difficulties in understanding the similarities between electromagnetic forces and gravity is that we define its movement though space in terms of an interaction between its electric and magnetic components with respect to time while we define the magnitude of gravitational forces in terms of the physical distance between two bodies.*

*Therefore, to understand a physical connection between them we should define the interaction of the forces associated with an electromagnetic* wave in in terms of distance as we do with gravity.

Einstein gave us the ability to do this when he used the constant velocity of light and the equation E=mc^2 to define geometric properties of forces in a 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 define 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 define the time-based components of Maxwell’s equations in terms of their spatial counterparts.*

The fact that one can use Einstein’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€œ Defining 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 surface of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This allows one to form a physical image of electromagnetic force and why it moves through space 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 an 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 and magnetic properties of an electromagnetic field 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.

For example, a wave on the two-dimensional surface of water causes a point on that surface to become displaced or rise above or below the equilibrium point that existed before the wave was present. A force is developed by that 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, an 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 an 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 resulting as the wave moves through space.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic field component of a photon in terms of a force developed as the wave moves through four *spatial* dimensions 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 magnitude 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 also derive the magnetic component of an electromagnetic wave in terms of the horizontal force developed by the displacement caused by its peaks and troughs. This would be analogous to how the perpendicular displacement of a mountain generates a horizontal force on the surface of the earth, which pulls matter horizontally towards the apex of that displacement.

Additionally, one can derive 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.

In other words, it allows one to define a physical model for the propagation of an electromagnetic field in terms of Einstein’s space-time theory.

Additionally, the above conceptual model can be quantified, as was mentioned earlier by using the valid laws of mathematics to transform his space-time equations to their equivalent in four *spatial* dimensions. This equivalence also allows one to explain both electromagnetism and gravity "as aspects of some broader mathematical structure" in terms of the geometry of four *spatial* dimensions or four-dimensional space-time.

Yet, it also explains why electromagnetic energy when observed always presents itself as the particle called a photon in terms of Einstein’s space-time model.

For example, the article, " Why is energy/mass quantized? " Oct. 4, 2007 showed that one can use the Einstein’s theories to explain the quantum mechanical properties of an electromagnetic wave by extrapolating the rules of classical resonance in a three-dimensional environment to an energy wave moving on 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 occur in an energy wave moving in four *spatial* dimensions.

The existence of four *spatial* dimensions would give the energy wave associated with a photon 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 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 in four spatial dimensions.

As was shown in that article these resonant systems in four *spatial* dimensions are responsible for the particle called a photon.

However, one can also use Einstein space-time theories to explain how the boundaries of the standing wave responsible for creating the resonant system that article indicated was responsible of a particles formation.

In classical physics a standing wave is created when the vibrational frequency of a source causes reflected waves from one end of a confined medium to interfere with incident waves from the source. This interference of the wave energy causes their peaks troughs to be reinforce in the volume they are occupying thereby creating a standing wave.

The confinement required to create a standing wave in space-time or its equivalent in four *spatial* dimensions can be understood by comparing it to the confinement a point on the two-dimensional surface of paper experiences when oscillating with respect to three-dimensional space. The energy associated with the wave motion of that point would be confined to its two-dimensional surface and would be reflected and interfere with the incident wave when reaches three-dimensional space at its edge. Therefore, a standing would be created by its interaction with three-dimensional space.

In other words when a wave on the surface of a piece of paper encounters the third spatial dimension at its edge it is reflected back allowing a standing wave to be formed on its surface.

*Similarly, an electromagnetic wave moving on the surface of three-dimensional space would be confined to it and reflected back to that volume, similar to the surface of the paper if it was prevented from oscillating with respect to a four spatial dimensions or four-dimensional space-time by an observation*.

In other words, when an electromagnetic wave is confined to three-dimensional space by an observation or an interaction with particle like a proton or electron the interference caused by that confinement sets up a resonant standing wave in space which is called a photon.

Additionally, it tells us that *the reason the energy of electromagnetic wave always without exception becomes a particle when observed is because of the fact that all observations or interactions with other particles will confine its motion to three-dimensional space thereby creating the resonate system that defined a particle that was shown to be responsible for a particle in the article *" Why is energy/mass quantized? " Oct. 4, 2007

**As mentioned early, the above conceptual model can be quantified by using the valid laws of mathematics to transform his space-time equations to their equivalent in four *spatial* dimensions. This equivalence as was shown above allows one to explain both particle and wave properties of electromagnetisms and gravity "as aspects of some broader mathematical structure" in terms of the geometry of four *spatial* dimensions or four-dimensional space-time. **

**It should be remembered that Einstein’s genius allows us to choose whether to define an electromagnetic wave either a space-time environment or one consisting of four *spatial* dimension when he defined its geometry in terms of the constant velocity of light. **

**Later Jeff **

**Copyright Jeffrey O’Callaghan 2020**

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