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We have shown throughout “The road to Unification” and its companion book “The Reality of the Fourth *Spatial* Dimension” there are many theoretical advantages to defining space in terms of four *spatial* dimensions instead of four dimensional space time.

One is that it would allow for the integration of the quantum mechanical or photonic with the classical electromagnetic wave properties of light in terms of the relativistic properties of space and time.

In the article “The Photon: a matter wave” Oct. 1, 2007 it was shown that one could explain and predict both the electromagnetic wave and quantum mechanical or photonic properties of light by extrapolating the laws of classical resonance to a matter wave in a continuous non-quantized field of energy/mass moving on a “surface” of a three-dimensional space with respect to a fourth *spatial* dimension.

Einstein gave us the ability to do this when qualitatively and quantitatively derived the relativistic properties of a space-time environment 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 in one consisting of only four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

Briefly that article 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 continuous non-quantized field of energy/mass and four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave 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.  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.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in continuous non-quantized field of energy/mass

Classical mechanics tells us the energy of a resonant system or structure can only take on the discrete quantized values associated with its fundament or a harmonic of its fundamental frequency.

Therefore, these resonant systems in four spatial dimensions define a common mechanism for the wave and photonic properties of light because they derive one in terms of the other.

Additionally it was shown that one can also derive its electromagnetic properties by extrapolating the laws of classical wave mechanics to a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly 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 similar 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 from the apex of that displacement.

This shows how one can theoretically derive the electromagnetic properties of light and define a physical link between it and it quantum mechanical or photonic properties by extrapolating the laws of classical wave mechanics to matter wave in a continuous non-quantized field of energy/mass moving on a surface of a three dimensional space manifold with respect to a fourth *spatial* dimension.

This cannot be done in terms of four dimensional space- time because time is only observed to move in one direction forward and therefore could not support the bi directional or transverse movement of light wave necessary to define a resonant system.

This shows how one can explain the mechanics responsible for both the photonic or quantum mechanical and electromagnetic wave properties of in terms of Einstein theory of relative by reinterpreting it in terms of four *spatial* dimensions.

Later Jeff

Copyright 2008 Jeffrey O’Callaghan

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