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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.

“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 — occupied more of Einstein’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 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 “Defining energy?” 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 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

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