Quantum mechanics defines a particle only in terms of the probabilistic values associated with SchrÃ¶dinger wave equation and assumes that it exists or is superpositioned in all possible places before a measurement is made.
In other words in a quantum system SchrÃ¶dinger wave equation plays the role of Newtonian laws in that it predicts the future position or momentum of a particle in terms of a probability distribution by assuming that it simultaneously exists everywhere in three-dimensional space.
This accentuates difference between quantum and classical mechanics because it derives the evolution of a particle in terms of it being in one place both before and after a measurement was taken whereas quantum mechanics derives its finial resting place in terms of an infinite number of possible starting points.
However one may be able to reconcile these two conflicting concepts by observing how matter and energy interact in terms of the classical properties of space-time.
But it will be easier if we first transpose or covert Einstein’s space-time universe to one consisting of only four *spatial* dimensions.
This is because it will allow us to define the mechanism responsible for the superpositioning of particles it in terms of a geometry which is directly related their position or spatial properties instead of its non-positional or temporal components.
Einstein gave us the ability to do this when he use the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because that provided a method of converting a unit of space-time associated with energy to unit of space associated with position. 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.
However the fact that one can use Einsteinâ€™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 â€œDefining energy?â€ 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 will allow as the article â€œWhy is energy/mass quantized?â€ Oct. 4, 2007 to understand the physicality of the 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 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 occur in one consisting of 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 to oscillate spatially 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 space.
Therefore, these oscillations in a “surface” of a three-dimensional space manifold would meet the requirements mentioned above for the formation of a resonant system or “structure” in four-dimensional space if one extrapolated them to that environment.
Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency.
Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with the quantum mechanical systems.
Yet it also allows one to define the boundary of a quantum system in terms of the geometric properties of four *spatial* dimensions.
For example 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 â€œupâ€ or â€œdownâ€ with respect to a fourth *spatial* dimension.
The confinement of the â€œupwardâ€ and â€œdownwardâ€ oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article â€œWhy is energy/mass quantized?â€œ
As mentioned earlier in the article â€œDefining energy?â€ Nov 27, 2007 showed 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 assuming its energy is result of a displacement in four *spatial* dimension allows one to derive the the most probable position of a particle in terms of its wave function by extrapolating the observations and classical laws associated with a three-dimensional environment to a fourth *spatial* dimension.
Classical mechanics tell us that due to the continuous properties of waves the energy the article â€œWhy is energy/mass quantized?â€ associated with a quantum system would be distributed throughout the entire “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.
For example Classical mechanics tells us that the energy of a vibrating or oscillating ball on a rubber diaphragm would be disturbed over its entire surface while the magnitude of those vibrations would decease as one move away from the focal point of the oscillations.
Similarly if the assumption that quantum properties of energy/mass are a result of vibration or oscillations in a “surface” of three-dimensional space is correct then classical mechanics tell us that those oscillations would be distributed over the entire “surface” three-dimensional space while the magnitude of those vibrations would be greatest at the focal point of the oscillations and decreases as one moves away from it.
As mentioned earlier the article â€œWhy is energy/mass quantized?â€ shown a quantum mechanical system is a result of a resonant structure formed on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Yet Classical Wave Mechanics tells us resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,
Similarly a particle would most probably be found were the magnitude of the vibrations in a “surface” of a three-dimensional space manifold is greatest and would diminish as one move away from that point.
In other words a particle appears to be superpositioned because its wave energy is distributed in probabilistic manner throughout the entire universe.
This suggests the reason why particles appear to be superpositioned is not due to the mathematical probabilities associated with SchrÃ¶dinger wave equation but due to a classical interaction of the wave properties of a quantum system with the geometry of a universe of a consisting either four dimensional space-time or four *spatial* or time dimension.
It should be remember Einsteinâ€™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
Copyright Jeffrey O’Callaghan 2015