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 defining space in terms four *spatial* dimensions instead of four-dimensional space-time.
One of them is that it would allow for deriving of why some particles are stable while others are not in terms of their geometry.
Einstein gave us the ability to do this when he used the equation E=mc^2 and the constant velocity of light to define the geometric properties of mass in a space-time universe because that provided a method of converting a unit of time in a space-time to 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 would allow one to derive the quantum mechanical properties of energy/mass, as was done in the article "Why is energy/mass quantized?" Oct. 4, 2007 by extrapolating the laws governing 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.
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 field 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 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 its is oscillating at that frequency.
Summarily 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 structure associated with either the fundamental or harmonic of the resonant frequency associated with their volume.
This shows how 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.
It should be remember Einstein’s genius allows us to choose to define a particle in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the temporal properties of our universe thereby giving us a new perspective on the causality of particle stability.
Copyright Jeffrey O’Callaghan 2009
Vol. 5 — 2014