We have shown throughout The Imagineer’s Chronicles there are many theoretically advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.

One is that it would allow for the integration of the quantum and wave properties of matter and energy into a single theoretical model. 

In 1924 Louis de Broglie was the first to theorize that all particles are, in part composed of a transverse wave.  In his paper, “Theory of the double solution“ he attempted to define a causal interpretation of their wave properties in the classical terms of space and time.  He later abandoned it in the face of the almost universal adherence of physicists to the theories presented by Born, Bohr, and Heisenberg regarding the uncertainties and probabilistic interpretation of quantum particles.

One of the difficulties he may have faced in this endeavor is that he assume along with most other scientists of his day the universe was composed of four-dimensional space-time.

This presented a problem because observations of a space-time environment indicate that a time dimension can only move in one direction, forward.  Therefore, it could not support bidirectional movement required for the propagation of a transverse wave. 

However, if he had assumed, as we have done in The Imagineer’s Chronicles the universe was composed of four *spatial* dimensions he may have been able to define the transverse wave properties of particles in terms of sinusoidal oscillations or displacements in a "surface" of three-dimensional space with respect to a fourth *spatial* dimension.

Classical mechanics tells us transverse oscillations in a surface of water will form resonant systems or structures that when view from distance would appear to be made up of discrete units of water with finite boundaries.

Summarily if the microscopic transverse waves theorized by de Broglie were a result of oscillations in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension they would, as was shown in the article "Why is mass and energy quantized?" Oct. 4, 2007 form resonant systems which when viewed from a macroscopic perspective would have the finite discrete boundaries associated with particles. 

He then could have defined a causal interpretation of the Quantum Mechanical equation for a particles energy; E=hv (where "h" is Planck’s constant "v" is a particles frequency and "E" is the magnitude or its energy) in terms of the classical properties of waves.

Classical mechanics tells us that the energy of a resonant system is quantized in terms of multiples of the harmonics of the fundamental frequency of its environment. 

Therefore, he could have interpreted the equation E=hv as defining the quantization of a particle’s energy in terms of a resonant system with a fundamental harmonic "h" of an environment consisting of four *spatial* dimensions..

However, this would have also allowed him to define a casual mechanism responsible for Planck’s constant, the uncertainty principal and the probability functions of Quantum Mechanics in terms of classical mechanics.

As mentioned earlier, classical interpretation of Planck’s constant would be that it defines magnitude of the incremental energy deference between harmonics of a resonant frequency of four *spatial* dimensions.

Additionally there would be an inherent uncertainty in one’s ability to define the exact position or momentum of a particle because it would be distributed over the finite volume associated with the wavelength of its resonant frequency.  Therefore, one could only define its specific position or momentum in terms of an uncertainty related to where relative to its wavelength an observation is made.

The reason why quantum mechanics must rely on probably functions to define particle interaction is because they are composed of waves that do not have a ridged structure.  Therefore, because their wave components vary with time one can only define their interactions in terms of a probably function related to how their time varying wave components would interact.

This shows that one can explain and predict all of the quantum mechanical properties of particle if one assumes they are made up of transverse waves in the classical terms of the geometry of four *spatial* dimensions.

However, as mentioned earlier this cannot be done if one assumes space it made up of four-dimensional space-time because its geometry cannot support a transverse wave properties Louis de Broglie associated with particles.

Later Jeff

The "Shadows" of four *spatial* dimensions

Copyright 2009 Jeffrey O’Callaghan

(In a PDF format)

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