The "reality" behind wave—particle duality

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Is it possible to define the “reality” behind the quantum world in terms of the classical laws of physics.

For example the paradoxical wave–particle behavior of energy/mass, one of the fundamental concepts defining Quantum mechanics defies the “reality” of a classical world because of its inability to describe/define how quantum-scale objects can simultaneously exist as waves and particles.  Many have tried to explain it as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent, second-order consequence of various limitations of the observer.

However, it is possible to explain the wave–particle duality of the quantum world in terms of the “reality” of classical concepts if one assumes, as has been done in this blog and our book “The Reality of the Fourth Spatial Dimension” that space is made up of four *spatial* dimensions instead of four dimensional space-time and that the quantum mechanical or particle properties of energy/mass are a result of a resonant structure formed by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

For example on pages 17 thru 23 of Richard P Feynman book “QED The Strange Theory of Light and Matter” he describes the seemingly paradoxical wave–particle duality of light or electromagnetic energy when it is partially reflected by two surfaces.

He writes that by placing two glass surfaces exactly parallel to each other one can observe how the photons of light reflected from the bottom surface interact with those reflected from the top surface.  Depending on the distance between the glass surfaces he can determine, by using a photo detector, that four percent or 4 out of 100 photons reflected from the lower surface of the glass could add up to as many as 16 or none at all when they interact with the photons reflected from the upper surface of the glass because of the reinforcement of the reflected wave energy from the bottom and top surfaces of the glass.

In other words the 4 photons reflected from the surface of the bottom piece of glass would interact with the incident ones to that surface creating from 0 to 8 photons while the 4 photons reflected from the surface of the top piece of glass would interact with the incident ones to it creating 0 to 8 more photons for a total of 0 to 16 photons.

These observations by Mr. Feynman support a wave theory of electromagnetic radiation because according to it, the energy associated with the interference of the 4 photons reflected from the bottom surface with 4 from the top will result in energy variations that corresponds to the energy of 0 to 16 photons.

However, wave theory also predicts the energy variations should be continuous.

In other words, the energy of the reflected photons should be able to take on any value between 0 and the combined energies associated with 16 photons.

Unfortunately, for the wave theory of light, the energy of the reflected photons Richard Feynman observed in the above experiment only took on integral values equal to the energy of the photons that originally struck the surface of the glass.  This indicates that their energy is not transmitted by a wave but by a particle.

However the observational paradox associated with its wave / particle behavior can be resolved if particles are, as mentioned earlier viewed in terms of a resonant “system” generated by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In the article “Why is energy/mass quantized?” Oct. 10, 2007 it was shown one can derive the quantum mechanical particle properties of energy/mass and a photon by extrapolating the  laws of classical of 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.  Additionally it showed why all electromagnetic energy must be propagated in these resonant systems.

Briefly it showed the four conditions required for resonance to occur in a classical Newtonian environment, an object, or substance with a natural frequency, a forcing function at the same frequency as its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The existence of four *spatial* dimensions would give the “surface” of three-dimensional space (the substance) the ability to oscillate spatially with respect to a fourth *spatial* dimension 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.

These oscillations in a “surface” of a three-dimensional space manifold, according to classical mechanics, if one extrapolates them to a fourth *spatial* dimension would generate a resonant system or “structure” in space. 

Classical mechanics tell us resonant system can only have the incremental or discrete energy associated with its fundamental or a harmonic of its fundamental frequency.

Similarly the incremental or discrete energies associated with individual photons in Richard Feynman’s experiment could be explained by assuming that they are a result of the fundamental or a harmonic of the fundamental frequency resonant properties of four *spatial* dimensions.

This shows how one can derive the quantum mechanical properties of energy/mass and a photon by extrapolating the laws of classical physics to a matter wave on a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.

(This cannot be done in a universe consisting of four dimensional space-time because time is only observed to move in one direction forward and therefore could not support the bi-directional movement required for Classical resonance to occur.)

However the article “The Photon: a matter wave?” Oct 1, 2007 showed that one can also derive electromagnetic wave properties of a photon and other particles by extrapolating the laws of classical wave mechanics in 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 a wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present. A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become “attracted” to each other and the surface of the water.

Similarly a matter wave on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that “surface” to become displaced or rise above and below the equilibrium point that existed before the wave was present.

However, as just mentioned classical wave mechanics, if extrapolated to four *spatial* dimensions tells us the force developed by the differential displacements caused by a matter wave moving on a “surface” of three-dimensional space with respect to a fourth *spatial* dimension will result in its elevated and depressed portions moving towards or become “attracted” to each other.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly the magnitude of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one. Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two similar charges than it would be for a single charge.

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its “peaks” and “troughs” that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it. This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards from the apex of that displacement.

Therefore, these two articles define a common mechanism responsible the wave–particle duality of the quantum world because they derive one in terms of the other.  In other words the resonant properties of a matter wave the article “Why is energy/mass quantized?” associates with particles including the photon would be responsible for the observations associated with the particle properties of energy/mass while the matter wave component of their resonant structure would be responsible for its wave properties.

As mentioned earlier the Copenhagen interpretation, explains the paradox associated with wave–particle duality in terms of it being complementarily or a phenomenon which can only be viewed in one way or in another, but not both simultaneously.

However this is what one would expect if one extrapolated the laws of classical mechanics to the quantum world in which particles were made up of a resonant structure formed by a matter wave because it tells us that 100% of its energy would be contained in its wave responsible for the resonant structure the article “Why is energy/mass quantized?” showed is responsible of its particle properties.

Therefore if one devised an experiment to observe its energy in the form its resonant structure that article associated with the particle properties of energy/mass there will be no energy left to support the viewing of its wave component while if someone choose to measure its wave energy there will be no energy left to support is its resonant particle structure.

Therefore one could only be viewed in one way or in another, but not both simultaneously.

This shows how one can define a physical mechanism or the reality behind wave–particle duality of the quantum world and the complementarily Copenhagen interpretation of it by extrapolating the classical laws of physics in three-dimensional environment to a fourth *spatial* dimension.

However, one can also explain the observations made by Mr. Feynman by associating the wave–particle duality of photon and electromagnetic energy with a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

For example, the wave like interference of photons he observed would be due to the wave properties of the resonant “system” defined in the article “Why is energy/mass quantized?“.

If the distance between the two glass surfaces in Richard Feynman’s experiment is equal to half of the wavelength of the resonant “system” associated with a photon, classical wave mechanics tell us the interference of its wave properties would interfere with each and will, as mentioned earlier yield the energy associated with 0 photons.

If the distance between two glass surfaces is equal to its wavelength of their wave properties will reinforce each other and yield the energy associated with 16 photons.

However, this does not explain how and why the energy variations caused by their interference are quantized and not continuous as wave theory predicts they should.

The reason is because, as was shown in the article “Why is energy/mass quantized?” the resonant properties of four *spatial* dimensions means that their energy would be propagated in the discrete quantized values associated with its fundamental or harmonic of its fundamental frequency.

The reason the reflected photon have the same energy as the incidence one is because observations of resonant systems in three-dimensional environment tell us that they interact more efficiently or reinforce each other when they have identical properties. Therefore, if it is true that electromagnetic energy is propagated by a resonant system created by a matter wave they should interact more efficiently or reinforce each other when they have identical wave properties.

Therefore, energy variations caused by the interference of their wave properties will most probably have the discrete or quantum values associated with the resonant “systems” of the original interfering photons.

This indicates that viewing the quantum mechanical world of wave–particle duality in terms of a resonant “systems” generated by a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension allows one to derive its “reality” in terms of the laws of classical mechanics in three-dimensional environment by extrapolating them a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

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