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1kThe measurement problem in quantum mechanics is the unresolved problem of how (or if) wavefunction collapse occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer. The wavefunction in quantum mechanics evolves according to the Schrödinger equation into a linear superposition of different states, but actual measurements always find the physical system in a definite state. Any future evolution must be based on the state the system was discovered to be in when the measurement was made and not on its history, meaning that the measurement “did something” to the process under examination. Whatever that “something” may be does is very difficult to explain in terms of the current accepted theories of space-time.
However, this may be because the wavefunction defines existence in terms of the spatial properties of matter while Einstein defines it terms of its time or space-time properties.
This suggests that one may be able to explain what happens to the wave function when a measurement is made if one could convert or transpose time in Einstein’s space-time universe to its spatial equivalent in four *spatial* dimensions.
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 in 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.
For example the article “Why is energy/mass quantized?
†Oct. 4, 2007 showed one can physical derive the quantum mechanical properties of 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 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.
(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 resonant interaction between a continuous energy/mass component of space and the geometry of four *spatial* dimensions)
However classical mechanics tell us that because of the continuous properties of waves the energy the article “Why is energy/mass quantized?†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 putting a vibrating or oscillating ball on rubber diaphragm will create a displacement which will be disturbed over its entire surface while the magnitude of that displacement 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 a three-dimensional space manifold one must assume the oscillations associated with each individual quantum system must be disturbed thought the entire universe while spatial displacement associated with its energy defined in the in the article “Defining energy?†Nov 27, 2007 would decrease as one move 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 “Why is energy/mass quantized?†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 also 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 its wave function.
Yet it also explains in terms of the observable reality of our environment what happens to the wave function when a measurement is made because to make one energy must be redirected towards the measurement instrument. In other words the wave function does not collapse but is physically redirected towards the observing instrument at the point of observation and would continue on that path until another observation is made.
Later Jeff
Copyright Jeffrey O’Callaghan 2012
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