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Quantum mechanics derives the results of particle in terms of a probabilistic interaction of its wave and particle components by assuming they must exist in all possible states simultaneously before a measurement it taken.

This contradicts the assumptions of classical physics that objects cannot exist in simultaneously  in two different states at the same time.
However, one can define a mechanism for responsible for their separate physical existence by as we have done in the article “Why is energy/mass quantized?” Oct 4, 2007 quantum mechanical properties of particles are a result of resonant system or “structure” generated by a matter wave 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 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.

Briefly that article 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 are responsible for the discrete energies of quantum systems.

One can understand how they cause the results of particle wave interactions to be indeterminate without having to assume they exist simultaneously in all states 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 classical 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, if a photon were made up of a resonant system generated by a matter wave as is suggested in the article “Why is energy/mass quantized?” 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 terms of the laws of classical physics.

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 wave properties of photons simultaneously exist in both a vertical and horizontal state 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 if a photon were a resonant structure generated by a matter wave moving on a “surface” of a three-dimensional space manifold none of them should get through a horizontal polarizer after passing through a vertical one because classical mechanics tells us they would all be blocked by its perpendicular orientation.

In other words assuming that a photon is made up of the wave properties of a resonant system is supported by this observation.

Another experiment describe in Brain’s book involves placing a third polarizer between a vertical and horizontal one and one 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, as the second experiment showed the wave properties of the photons that passed through the vertical polarizer were not in a superposed state with their particle component because if they were 50 percent of them would have passed through the horizontal polarizer.

Therefore, if Quantum theory explanation of particle interaction 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 explain and predict this experimental result in the same classical 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.

Hear again an explanation based on the fact that a photon is made up of the wave properties of a resonant system is more consistent with this observation than the one provided by quantum mechanics.

This shows one can define the why quantum mechanics assumes that particles exist in all possible states simultaneously before a measurement is taken in terms of the laws of classical physics.

Later Jeff

Copyright Jeffrey O’Callaghan 2008

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