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

One of these is that it would allow for the derivation of a physical link between 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.

Einstein gave us the ability to do this when he qualitatively and quantitatively defined the geometric properties of a space-time universe 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 equation E=mc^2 and 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.

However as was just mentioned this would allow one define a link between the physical properties of an electromagnetic wave and gravity in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension because as was just shown that displacement is interchangeable with the one Einstein’s “The General Theory of Relativity” postulated is responsible for gravity.

For example in the article What is electromagnetism?” Oc2007 it was shown one can derive the propagation of electromagnetic energy by extrapolating the laws of classical wave mechanics in three-dimensional environment 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 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.

The reason why electromagnetic energy is quantized is because its energy is propagated through space in quantized resonant systems photons defined in the article “Why is energy/mass quantized?” Sept. 24, 2007.

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 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.

In other words the quantum properties of an electromagnetic wave is a result of a resonant system system formed in environment consisting of either four *spatial* dimensions or four dimensional space-time.

This shows that one can derive a common link between gravity and electromagnetism because it defines both in terms of a displacement in environment consisting of either a fourth *spatial* dimensions or four dimensional space time.

It should be remember Einstein’s genius allows us to choose to define all systems in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on their properties and how they physically connected to our observable universe.

Later Jeff

Copyright Jeffrey O’Callaghan 2007

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