We have shown throughout "The Imagineer’s Chronicles" observations of our environment suggest space is composed of a continuous non-quantized form of mass and four *spatial* dimensions instead of four-dimensional space-time.
The quantum or particle properties of mass and energy is one of them.
The article "Why is mass and energy quantized?" Oct. 4, 2007 showed it is possible to explain the quantum properties of mass and energy in terms of a classically resonating system generated by a wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by extrapolating the classical laws of three-dimensional space to a fourth *spatial* dimension
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It was shown how the existence of a continues non-quantized form of mass and four *spatial* dimensions would satisfied the four conditions required for resonance to occur in a classical Newtonian environment; the first the existence of an object, or substance with a natural frequency, second a forcing function at the same frequency as the natural frequency, thirdly the lack of a damping frequency and finally the ability for the substance to oscillate spatial.
The existence of four *spatial* dimensions would give a continuous non-quantized mass component of space 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, these oscillations in a continuous non-quantized form of mass caused by such an event could generate a resonant system or "structure" to be established in a continuous non-quantized form of mass. These resonant systems are known as particles.
However, it did not explain how the boundaries of a particle’s resonant structure are defined.
In classical physics, a point on the two-dimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to three-dimensional space.
Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.
The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension defines the geometric boundaries of resonant system associated with a particle in the article "Why is mass and energy quantized?"
However, is not possible to define a classical resonant system in terms of space-time dimension because time is only observed to move in one direction forward and therefore could not support the bi-direction movements required to define the boundaries conditions for a classically resonating system.
It is also possible to derive why some particles are stable while others are not by extrapolating the properties of a classically resonance to a fourth *spatial* dimensions.
As mentioned earlier the article "Why is mass and energy quantized?" Oct. 4, 2007 derive the quantum properties of mass and energy in terms of a classically resonating system in fourth *spatial* dimension.
However, to be stable a classically resonating system must have the energy associated with the discrete value of its fundamental frequency or an integral multiple it. If it does not it will either lose gain energy from its environment until it is oscillating at that frequency.
Therefore, a stable particle would be one whose three-dimensional volume is oscillating with respect to a fourth *spatial* dimension at the fundamental frequency associated with that volume.
An unstable particle would be one whose three-dimensional volume is oscillating with respect to a fourth *spatial* dimension at the some frequency other than the fundamental one associated with its volume. Similar to resonant systems in a classical environment, these particles will decay by losing or gaining energy from their environment until they have the stable resonant structure associated with either the fundamental or harmonic of the resonant frequency associated with their volume.
This shows that one can define the stability or instability of a particle extrapolating the properties of a classically resonating system in three-dimensional space to a fourth *spatial* dimension where as one cannot in terms four-dimensional space-time because as mentioned earlier it cannot provide the geometric boundaries required to define a resonant volume.
Later Jeff
The "Shadows" of four *spatial* dimensions
Copyright Jeffrey O’Callaghan 2009
(In a PDF format)

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