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Einstein, in his General Theory of Relativity derived the force of gravity in terms of the geometry of space and time.  Unfortunately he was unable describe the other forces in nature, above all those of electromagnetism, in same terms, 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“.

However we have shown throughout the this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” there would be many theoretical advantages to defining the universe in term of four *spatial* dimensions instead of four-dimensional space-time.

One is that it would allow for the unification gravity and electromagnetism by extrapolating the laws of a classical three-dimensional environment to a fourth *spatial* dimension.

Einstein gave us the ability to do this when he use the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because that provided a method of converting a unit of time in his space-time universe to unit of space in one consisting of only four *spatial* dimensions .   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up 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 energy 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 many advantages to using this approach is that it, as was shown in  the article Embedded Dimensions” Oct. 22, 2007 allows one to derive all forms of energy including gravity and electromagnetism in terms of a curvature or displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

In other words it showed that one can derive gravity in terms of a differential force caused by a curvature or displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This curvature is analogous to the space-time curvature Einstein associated with gravity.

Similarly the article “What is electromagnetism? Sept, 27 2007 showed one can derive the forces associated with electromagnetism in terms of the differential force caused by the “peaks” and “toughs” of a matter 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 electromagnetic properties of electromagnetism by extrapolating the laws of Classical Wave Mechanics in a three-dimensional environment to a matter 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 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, classical wave mechanics, if extrapolated  to four *spatial* dimensions tells us a force will be 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 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 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, Classical Mechanics tells 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.

However, as was mentioned earlier the gravity can also be explain by in terms of a differential force caused by a curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words the differential force cause buy a curvature in space created by the peaks and valley of an electromagnetic wave is no different than the curvature Einstein associated with gravity.  The only difference is that gravity is unidirectional in terms of a “surface” of a three-dimension space manifold with respect to a fourth *spatial* dimension while that of electromagnetism is bi-directional.

This shows how one can define a common mechanism for the causality of both electromagnetism and gravity in terms of a “unified field” consisting of four *spatial* dimension by extrapolating the laws of classical mechanics in a three-dimensional environment to four *spatial* dimensions. 

Einstein was unable to accomplish this in terms of four-dimensional space-time because time is only observe to move in one direction forwards and therefore could not support the bi-directional spatial movement required to support the electromagnetic component of a wave moving on its “surface”. 

It should be remember Einstein’s genius allows us to choose to define our universe in either a space-time environment or one consisting of four *spatial* dimension when he defined it in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories making them applicable to both the spatial as well as the time properties of our universe.

Later Jeff

Copyright 2008 Jeffrey O’Callaghan

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