One of the conceptual problems that has been largely ignored in modern quantum theory is what defines the boundaries of a quantum system after an observation is made.
Quantum theories define a particle’s position before one is made in terms of the probabilities associated with Schrödinger’s wave equation. In other words there is a non zero probability that it can be found any where in the universe while after one is made its location can be determined with a 100 percent probability as being in a very well defined region of space.
However what defines the physical boundaries of that space.
We have shown throughout this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” there would be numerous theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.
One of them is that it would allow for the theoretical definition of the “boundaries” of a quantum system after an observation is made by extrapolating the laws of a classical three-dimensional environment to a fourth *spatial* dimension.
Einstein gave us this ability when he used the velocity of light to define the geometric properties of time in a space-time environment because it allows one to convert a unit of time in it to a unit of a space identical to those of our three-dimensional space. Additionally because the velocity of light is constant it is possible to defined a universe made up of four *spatial* dimensions that makes predictions identical to those he had attributed to four dimensional space-time.
The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming, as was done in the article “Defining energy?†Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
This allows one, as was shown in the article “Why is energy/mass quantized?†Oct. 4, 2007 to understand the of physicality of the wavefunction and quantum properties energy/mass by extrapolating the laws of classical wave mechanics 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 was shown 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 could be extended 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 a continuous form of energy/mass.Â
These resonant systems in four *spatial* dimensions are responsible for the quantum mechanical properties of energy/mass.
In other words if one assumes that the wavefunction is physically a result of resonate system in four *spatial* dimension one can understand how and why it can be interpreted as a wave and at other times a particle.Â
However, it did not explain how this change takes place or why its particle properties only become predominate when it is observed.
As was mentioned earlier the article “Defining energy?†Nov 27, 2007 showed that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
However when one observers a quantum system one is making a measurement of it energy which as that article showed can be defined as a spatial displacement of the wavefunction or the matter wave described in the article “Why is energy/mass quantized?†Oct. 4, 2007 with respect to a fourth *spatial* dimension.
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.Â
Similarly an object occupying a three-dimensional volume would be confined to it however, similar to the surface of the paper it could, 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 the resonant systems associated with the quantum mechanical properties energy/mass in the article “Why is energy/mass quantized?“
However it also tells us the reason why all observations of a quantum system take a particle format is because the energy of the wavefunction is confirmed to a specific volume of space by that observation. .
In other it define the confinement of the wave function when an observation is made in terms of its classical properties.
Yet 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.
As mentioned earlier the article “Why is energy/mass quantized?” derived the quantum mechanical properties of energy/mass in terms of a classically resonating system in fourth *spatial* dimension.
However, to be stable system it must have the energy associated with the 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 or harmonic of the resonant frequency associated with that volume.Â
An unstable particle would be one whose three-dimensional volume is oscillating with respect to a fourth *spatial* dimension at some frequency other than the one associated with the resonant system of a 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 how one can derive the physical boundaries of a quantum system and why the probabilities associated with Schrödinger wave equation become confined to a very specific region of space after an observation is made.
It should be remember Einstein’s genius allows us to choose to define a quantum system 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 time properties of our universe thereby giving us a new perspective on the causality of the quantum mechanical properties of energy/mass
Later Jeff
Copyright Jeffrey O’Callaghan 2010