We have shown throughout "The Imagineer’s Chronicles" there would be several theoretical advantages to defining the universe in term of four *spatial* dimensions instead of four-dimensional space-time.

Fourth Spatial Dimension 101

For example, it would enable physicists to define a theoretical model that could explain and predict the uncertainty principal and probability functions of quantum mechanics in terms of the observable properties of a classical Newtonian world.

In 1924, Louis de Broglie theorized 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 for the wave properties of particles 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.

However, his theories still serve as the basis for the development of the general theory known today by the name of wave mechanics.  

One of the difficulties he may have faced in defining a probabilistic quantum interpretation of the wave properties of particles is that their wave properties are not caused by quantum probabilities but that the quantum probabilities are a result of there wave properties.

One can understand why if one views the wave properties theorized by de Broglie in terms of the laws of classical physics and four *spatial* dimensions instead of four dimensional space-time. 

In a classical world, a resonant system or "structure" will be formed when the spatial movements of a wave interact to reinforce themselves.

For example, the three-dimensional the transverse or bi-directional displacements of a two-dimensional surface of the water will form a resonant system when the oscillations of the water interact to reinforce each other.

However, the transverse wave properties Louis de Broglie associated with a particle is difficult to explain in terms of four dimensional space-time because time is only observed to move in one direction forward and therefore a universe of four dimensional time could not support the bi-directional movement of a transverse wave.

But if he had assumed that space was composed of four *spatial* dimensions he may have been able to define a probabilistic interpretation Born, Bohr and Heisenberg associated with particles in terms of a classical resonant "structure" formed by a transverse wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This is because as was shown in the article “Why is mass and energy quantized?” Oct. 4, 2007 a resonant system or "structure" on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension formed by a transverse wave would have many of the properties Born, Bohr and Heisenberg associated with particles.  They would appear to have finite boundaries on a macroscopic level however, on a microscopic level their volume would be defined by the wavelength of the wave responsible for their resonant "structure". 

Classical wave mechanics tells us a wave’s energy is instantaneously constant at its peaks and valleys or the 90 and 270-degree points as its slope changes from positive to negative while it changes most rapidly at the 180 and 360-degree points.

However, if a particle was made up of  resonant "structure" formed by a matter wave on a "surface" of a three-dimensional space manifold its position could only be determined at its peak and valleys. This is because only at those points will all its energy be in the form of mass, which would not be "moving" with respect to four-dimensional space.  Where as its total momentum would only be definable with respect to where the energy change or velocity is maximum at the 180 and 360 degree points of the wave.  All points in between would only be definable in terms of a combination of its momentum and position

Additionally, because of the time vary properties of a wave there would always be an uncertainty related to where a measurement or observation was taken.  In other word if one measured the momentum of a particle one could not be certain that the measurement was taken at the 180 or 360 point of the wave.  If not the measurement would be a combination of its momentum and position.  Similarly if one measured the position of a particle one could not be certain that the measurement was taken at it 90 or 270 degree points.  However, this means there will always be an uncertainty related to the momentum or position of a particle based on the probability of where a measurement was taken relative to its wave function.

This, as mentioned earlier would be very difficult to do if one defines the universe in term four dimensional space-time because the spatial properties of a transverse of the matter wave associated with particles is not compatible with a universe consisting space-time.

In other words, if Louis de Broglie had assumed the existence of four *spatial* dimensions instead of four-dimensional space-time he would have been able to theatrically define the particle properties of mass in terms of a resonant system or "structure" formed by a wave which he then could have used to derive the uncertainties and probabilistic characteristics of their interactions found in Born, Bohr and Heisenberg theories.

Later Jeff

The Shadows of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

(In a PDF format)

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