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1kWe have shown throughout this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” there would be 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 mechanical and wave properties of energy/mass by extrapolating the classical laws of a three-dimensional environment to a fourth *spatial* dimension.
In 1924 Louis de Broglie was the first to theorize that all particles had a transverse matter wave component. 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 time or a space-time dimension can only move in one direction, forward. Therefore, it could not support bidirectional movement required for the propagation of a transverse wave.Â
However Einstein provided a solution to this problem when he use the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because that gave a method of converting a unit of time associated with energy to its equivalent unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.
This may have allowed Louis de Broglie to define the quantum or particle properties, as was done in the article “Why is mass and energy quantized?” Oct. 4, 2007 of the transverse wave he theorized they were made up of in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Briefly that article showed that the four conditions required for resonance to occur in a classical three dimensional 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 be satisfied by a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
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 space.
As was shown in that article these resonant systems in a continuous form of mass/energy are responsible for its quantum mechanical properties.
He then many have been able defined a causal interpretation of the Quantum Mechanical equation for a particles energy or E=hv (where “h” is Planck’s constant “v” is a particles frequency and “E” is the magnitude or its energy) based on the existence of these resonant systems
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.Â
Therefore, he could have interpreted the equation E=hv as defining the quantization of a particle’s energy in terms of the incremental energies “h” associated with the fundamental or harmonic of the resonant frequency of an environment consisting of four *spatial* dimensions..
However, this would have also allowed him to define a casual mechanism responsible for the uncertainty principal and the probability functions of Quantum Mechanics, again by extrapolating the three-dimensional laws of classical resonance to four *spatial* dimensions.
Because he may have realized the causality of the uncertainty in one’s ability to define the exact position or momentum of a particle was due to the fact that the resonant system that the article “Why is mass and energy quantized?” derived was responsible for the quantum mechanical properties of energy/mass is distributed over the finite volume associated with the wavelength of its resonant system. Therefore, one could only define its specific position or momentum in terms of an uncertainty related to where relative to its finite extended volume a measurement is made.
This indicates may have been able to derive a causal interpretation of the quantum mechanical properties of energy/mass in terms of classical properties of a matter wave if he had assumed there were a result of the geometric property 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 the transverse wave properties Louis de Broglie associated with particles.
Later Jeff
Copyright Jeffrey O’Callaghan 2010
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