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 supported by a continuous non-quantized form of mass.

Source: Maths: Fourth Dimension Videos

Additionally 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.

The suggests the mass of a particle is not the result of its wave properties but the fact that it generates a resonant system in a continuous non-quantized form of mass which would cause the relative density of a continuous non-quantized form of mass to be greater in volumes it occupies relative to the adjacent volumes.  This increase in the relative density of a continuous non-quantized form of mass is the causality of a particle’s mass.

However, it did not explain how the boundaries of a particles 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 a object occupying a volume of three dimensional space would be confined to three-dimensional space 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 mass and energy with respect to a fourth *spatial* dimension to a three-dimension volume is what define the geometric boundaries of resonant system defined in the article "Why is mass and energy quantized?"

The article "Defining energy" Nov. 26, 2007 showed that all forms of energy are definable in terms of a displacement in a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, a stable particle would be definable in terms of the energy associated with the oscillations or displacements, with respect to a fourth *spatial* dimension of a volume containing a continuous non-quantized form of mass at the fundamental or harmonic of the resonant frequency of the volume it is occupying.

An unstable particle would be one in which the continuous non-quantized mass component of a volume is oscillating at frequencies that are not associated with ether the fundamental or harmonic of the resonant frequency of the volume it is occupying.  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 of that volume.

This shows that one can define the stability or instability of a particle in terms of a classically resonating system and the geometry of four *spatial* dimensions whereas one cannot in terms four-dimensional space-time because 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

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