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One of the more paradoxical aspects of the quantum theory is the concept of superposition which refers to its assumption that a particle occupies all of its possible quantum states simultaneously before it is observed.  In other words its says the “reality” of a particles state or position only occurs after it is observed.

This goes against what many call a Classical or “Common sense” Sept 1, 2008 interpretation of our world because most feel that objects or particles must have definite position or state before we observe it.

However, the paradox between quantum theory and a “common sense” understanding of a particle can be resolved by extrapolating the classical laws of a three-dimensional environment as was done in the article  “Why is energy/mass quantized?” Oct 4, 2007 to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Einstein gave us the ability to do this when qualitatively and quantitatively convert the geometric properties of his space-time environment to an equivalent one consisting of only four *spatial* dimensions when he defined the geometric properties of a space-time universe and the dynamic balance between mass and energy in terms of the equation E=mc^2 and the constant velocity of light.  This is because it allows one to redefine a unit of time he associated with energy in his space-time universe to unit of space we believe he would have associated with mass in a universe consisting of only four *spatial* dimensions. 

In other words by defining the geometric properties of a space-time universe in terms of the equation E=mc^2 and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

One can understand why doing this will provide a common sense interpretation of superposition by integrating the results of several experiments outlined in 59 and 60 of Brian Cregg book “The God Effect” involving the transmission of photons through a polarizing filter with the laws of classical physics.
In the first experiment, photons in their natural randomized polarization state are passed through a 45-degree polarizer after passing through a vertical one.  This experimental setup shows that 50 percent of the photons that passed through the vertical polarizer also pass through the 45-degree one.

Brian, in his book says the Quantum mechanical explanation of this is that every photon exists in a superposed state or simultaneously in both a vertical and horizontal polarization.  Therefore, every photon that passed through the vertical polarizer will have an equal or 50 percent probability of passing through the 45-degree polarizer. 

However, as was mentioned the earlier article “Why is energy/mass quantized?” Oct 4, 2007 showed its quantum mechanical properties can be explained and predicted by extrapolating the laws governing classical resonance in a three-dimensional environment to a matter wave moving 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 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 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 four-dimensional space. 

Classical mechanics tells us the energy of a resonant system or structure can only take on the discrete quantized values associated with its fundament or a harmonic of its fundamental frequency.

Therefore these resonant systems in four *spatial* dimension would provide a classical or common sense interpretation of the discrete energies of quantum systems.

However, if a photon were made up of a resonant system generated by a matter wave as is suggested in that article a component of the wave that passed through the vertical polarizer would interact with the non-perpendicular orientation of with the 45-degree one.  The interference cause by that interaction would in result in the shifting or re-randomizing of the photons that passed through the vertical polarizer allowing 50 percent of them pass through the 45-degree one.

This defines the reason why 50 percent of those photons should pass through the 45-degree polarizer after passing through a vertical one in terms of the “common sense” laws of classical physics when extrapolated to four *spatial* dimensions.

The second experiment involves two polarizing screens one vertical and one horizontal.  In this case, 50 percent of the photons that pass through the first vertical polarizer and none pass through the second horizontal one.  This indicates that none of the photons that passed through the vertical polarizer were horizontally polarized because if any of them were some would have passed through that polarizer.

However, these experimental results contradict the quantum mechanical assumption that photons simultaneously exist in both a vertical and horizontal state before being observed because if they did the ones that passed through first polarizer would still exist in both states therefore 50 percent of them should pass through the second one.

But one could resolve this paradox if one assumes that a photon were a resonant structure generated by a matter wave moving on a “surface” of a three-dimensional space manifold. This is because classical mechanics tells none of them should get through because they would all be blocked by their perpendicular orientation of the two slits. 

Another experiment describe in Brain’s book involves placing a third polarizer between a vertical and horizontal one and oriented at 45-degree angle with respect to them.  In this experiment, 50 percent of the photons pass through the vertical polarizer and 50 percent of those will pass through the 45-degree one while 50 percent of those photons pass the horizontal one.

The Quantum mechanical explanation of this is that every photon exists simultaneously in both the vertical and horizontal polarized state.  Therefore, every photon that passes through the 45-degree polarizer will have an equal or 50 percent probability of being vertically or horizontally polarized therefore 50 percent of them will pass through the third horizontal one.

However, the second experiment demonstrates yet another paradox in that the photons that passed through the vertical polarizer in the first experiment were not in a superposed state because if they were 50 percent of them would have passed through the horizontal polarizer.

Therefore, if Quantum theory is valid it should be able to explain, why in context with its theoretical structure all possible states of the photons were superposed over each other after passing through a 45-degree polarizer and were not after passing through the vertical one in the second experiment.

However, one can derive a classical explanation and predict the experimental results in the same terms as the earlier experiment where a 50 percent of the photons pass through a 45-degree polarizer after passing through a vertical one.

If a photon were made up of a classically resonating system or “structure” generated by a matter wave, a component of the wave that passed through the first vertical polarizer would interact with the non-perpendicular orientation of the second 45-degree polarizer.  The interference caused by its interaction would in result in the shifting or re-randomizing of the vertically polarized photons that pass through the 45-degree one for the same reason as it did in the first experiment.  This means that 50 percent of those photons that pass through it should also pass through the third horizontal polarizer.

Some will point to the “Copenhagen Interpretation” of quantum mechanics to resolve this conflict.

It states that the act of observing a particle causes it to lose its superposition.  This could explain why the photons that passed through the vertical polarizer in the second experiment did not pass through the horizontal one because the act of “observing” them caused them to exist only in the vertical state so they would be blocked by the horizontal polarizer. 

However, this exposes another paradox in that the Quantum mechanical explanation of why 50 percent of the photons in the first experiment passed through a vertical polarizer after passed through a 45-degree one is because they were in a superposed state.

But this contradicts the Copenhagen Interpretation these photons would not be in a superposed state because they were “observed” by the first vertical polarizer.

However, as we have just shown these paradoxes between observations and theory could be eliminated if one extrapolates the laws of classical resonance in a three-dimensional environment to a to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to fourth *spatial* dimension to define, as was done in the article “Why is energy/mass quantized?” the quantum mechanical properties of energy/mass.

Later Jeff

Copyright Jeffrey O’Callaghan 2008

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