Quantum mechanics assumes that a particle is in a superposition of several states or positions based on the mathematical properties of SchrÃ¶dinger’s wave equation before an observation is made. It also assumes that when it is observed it collapses resulting the particle it represents having a single or unique position.
When the Copenhagen interpretation was first introduced Neils Bohr found it was necessary to assume the collapse of wave function to distinguish the quantum from the classical world. This allowed it to develop without distractions from interpretational worries. Nevertheless since then that it meaning has be hotly debated because if it is a fundamental properties of nature as many have assumed it would contradict the classical or Newton assumption that the world is deterministic.
However the science of physics is devoted to understanding the physical process responsible for creating the “reality” of our observable environment based on observing the physical interaction of its real not imagined components.
One of the reason it has been so difficult to understand what happens to the position component of a quantum system when it is observed may be because too much attention has been focused on the mathematical aspects of the wave function and not enough on its physical meaning in a space-time environment. This is made even more difficult because the concept of superposition is defined in terms of the spatial properties of a quantum system instead of its space-time properties.
This suggest one be able to obtain a better understanding of what happens to it if one could view it in terms its spatial instead of it time or space-time properties.
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 it provided a method of converting a unit of time he associated with energy to unit of space associate 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.
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.
However defining the dimensional properties of quantum system in terms of its spatial instead of its time components would allow one to derive the physicality of the wave functioned associated with SchrÃ¶dingerâ€™s equation by extrapolating the observable properties of our reality to the quantum world it describes.
For example the article â€œWhy is energy/mass quantized?â€ Oct. 4, 2007 showed one can derive its physicality 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 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 it 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.
(In the article “The geometry of quarks” Mar. 15, 2009 the internal structure of quarks, a fundament component of particles was derived in terms of a similar resonant interaction between three and four dimensional space.)
However assuming its energy is result of a displacement in four *spatial* dimension instead of four dimensional space-time as was done in the article â€œDefining energy?â€ Nov 27, 2007 allows one to not only derive the physicality of SchrÃ¶dingerâ€™s equation as was just done but also the physical reason why its particle components would be in superpositioned state before an observation is made.
Classical mechanics tell us that because of 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 similar to how the wave generated by a vibrating ball on a surface of a rubber diaphragm are disturbed over its entire surface while the magnitude of the displacement it causes will decrease as one moves away from the point of contact.
However, this means if one extrapolates the mechanics of the rubber diaphragm to a “surface” of three-dimensional space one must assume the oscillations associated with each individual quantum system must be disturbed thought the entire universe while the spatial displacement associated with its energy defined in the in the article â€œDefining energy?â€ Nov 27, 2007 would decrease as one moves away from its position. This means there would be a non-zero probability they could be found anywhere in our three-dimensional environment because, as mentioned earlier the article â€œWhy is energy/mass quantized?â€ shows that a quantum mechanical system is a result of a resonant structure formed by the oscillations on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Classical Wave Mechanics tells us a 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 an observer would most probably find a quantum system 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.
However as mentioned earlier this is exactly what is predicted by Quantum mechanics in that one can define a particle’s exact position or momentum only in terms of the probabilistic values associated with vibrations of its wave function
Additionally this tells us that the wave function does not collapse but its energy is redirected towards the observer and as was shown in the article Why is energy/mass quantized? he would record its redirected energy in term of discrete quantized properties associated with a particle.
As mentioned earlier the science of physics is devoted to understanding the physical process responsible for creating the “reality” of our observable environment based on observing the physical interaction of its real not imagined components.
Yet even though we may never be able to directly observe the fourth *spatial* dimension we can verify its existence by observing the effects it has on our observable three-dimensional environment similar to how Einstein was able to conclude that gravity was a result of a curvature in a space time environment.
Copyright Jeffrey O’Callaghan 2015