We have shown throughout "The Imagineer’s Chronicles" and its companion book "The Reality of the Fourth *Spatial* Dimension" there would be many theoretical advantages to space in terms four *spatial* dimensions instead of four-dimensional space-time.

One of them is that it would allow for the understanding of why some particles are stable while others are not in terms of their geometry.

The article "Why is energy/mass quantized?" Oct. 4, 2007 showed it is possible to explain the quantum mechanical properties of a particle by extrapolating the laws classical resonance in a three-dimensional environment to a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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Briefly it 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 be meet by a matter wave in four spatial dimensions.

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.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its resonant or a harmonic of its resonant frequency

Therefore the discrete or quantized energy of resonant systems in a continuous form of energy/mass would be responsible for the discrete quantized quantum mechanical properties of 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 is what defines the geometric boundaries of the resonant system associated with a particle in the article "Why is energy/mass quantized?"

However, it is not possible to define its boundaries in space-time environment 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 resonating system.

It is also possible to derive why some particles are stable while others are not by extrapolating the properties of classical resonance to a fourth *spatial* dimensions.

To be stable a classically resonating system must have the energy associated with the discrete values of its fundamental frequency or an integral multiple of its resonant environment. If it does not it will either lose gain energy from its 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 or harmonic of the resonant 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 a frequency other than the one associated with the energy of its resonant environment. 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 why one can define the stability or instability of a particle in terms of its geometry by extrapolating the properties of a classically resonating system in three-dimensional space to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2009

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