Einstein, in his 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 the force 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 â€” for a “unified field” theory that would unite electromagnetism and gravity, space and time, all together â€” occupied more of Einsteinâ€™s years than any other activity“.
Unfortunately, Einstein did not have access to the data concerning the quantum “qualities” of mass and electromagnetic energy when developing his theories as we do today, such as the Louis de Broglieâ€™s observation made in 1924 that all particles have a wave component. If he had he may have chosen to define gravity in terms of four *spatial* dimensions instead of four-dimensional space-time because, as was shown in the article “Gravity in four *spatial* dimensions” Dec. 15, 2007 he could have done it that way.
This is because even the smallest particle, according to Broglie observations must have a wave component. Therefore, a continuous medium must be available to support it. Einstein would have realized this medium would have to be made up of a continuous non-quantized field of energy/mass because by definition a wave can only be propagated on a continuous surface.
He also may have due to the spatial properties of a transverse of the energy/mass wave Louis de Broglie observed chose to define energy in our environment in terms of its spatial not time properties because a transverse wave can only be propagated by a spatial displacement with respect to the surface it is moving on.
However Einstein gave us the option to qualitatively and quantitatively convert the geometric properties of his space-time environment to an equivalent one consisting of only four *spatial* dimensions when he defined the geometric properties of a space-time universe and the dynamic balance between mass and energy in terms of the equation E=mc^2 and the constant velocity of light. This is because it allows one to redefine a unit of time he associated with energy in his space-time universe to unit of space we believe he would have associated with mass in a universe consisting of only four *spatial* dimensions.
In other words by defining the geometric properties of a space-time universe in terms of the equation E=mc^2 and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe and gravity in terms of the geometry of four *spatial* dimensions.
Additionally this would have provided a way to integrate quantum properties of energy/mass into both his Special and General Theories of Relativity using the concepts of classical physics.
For example in the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can explain the quantum mechanical properties of energy/mass by extrapolating the “reality” of a three-dimensional environment to a matter wave moving on a “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 one consisting of four *spatial* dimensions
The existence of four *spatial* dimensions would give the “surface” of a three-dimensional space manifold (the substance) the ability to oscillate spatially with respect to it 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 on a “surface” of three-dimensional space, 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 discreet or incremental values associated a fundamental or a harmonic of the fundamental frequency of its environment.
Additionally it also tells us in terms of the physical properties four dimensional space-time or four *spatial* dimensions the reason an electron cannot fall into the nucleus is because, as was shown in that article all energy is contained in four dimensional resonant systems. In other words the energy released by an electron “falling” into it would have to manifest itself in terms of a resonate system. Since the fundamental or lowest frequency available for a stable resonate system in either four dimensional space-time or four spatial dimension corresponds to the energy of an electron it becomes one of the fundamental energy unit of the universe.
However redefining Einstein’s space time concepts in terms of four *spatial* dimensions would also allow one to integrate electromagnetism into them.
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 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 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
The electrical component of electromagnetic energy is a result of the force associated with the “slope” of a curvature created by the “peaks” and “troughs” of a matter wave that is perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that “vertical” displacement
Classical Mechanics tells us a horizontal force will be developed by a 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.
As was shown above redefining Einstein’s space-time concepts in terms of their spatial equivalent allows one to not only allows one to ingrate the quantum properties of energy/mass into the continuous field properties of his space time universe but also give one classical understanding of how to incorporate electromagnetism into it.
Copyright Jeffrey O’Callaghan 2008