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It is possible to understand how and why a photon can have of both the particle and wave properties described by Richard P Feynman in his book "QED The Strange Theory of Light and Matter" by defining it in terms of a resonant "system" in four *spatial* dimension.
On pages 17 thru 23 he discusses what happens when light is partially reflected by two surfaces. He demonstrates 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.
These observations by Mr. Feynman support a wave theory of electromagnetic radiation. Because according to wave theory, the energy associated with the interference of 4 photons with 4 other photons will result in energy variations that corresponds to the energy associated with 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 take on integral or quantum values equal to the energy of the photons that originally struck the surface of the glass. This indicates that a photon's energy is not transmitted by a wave but by a quantum unit or particle of energy.
However, this apparent contraction between the wave and particle properties of a photon can be resolved if a photon is, as mentioned earlier viewed in terms of a resonant "system" generated by the passage of matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Chapter one postulated that space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.
In Chapter two, the particle properties of a photon were derived in terms of discrete resonant "systems" formed in space by oscillations in a continuous non-quantized form of mass.
Chapter three derived the propagation of a photon's energy in terms of a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by oscillations in a continuous non-quantized form of mass.
(Louis de Broglie was the first to theorize that all particles had a wave component. His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer. However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.)
Therefore, Chapters two and three answers the question regarding how and why a photon can behave at times like a wave and at other times like a particle because it defines both its wave and particle properties in terms of a common mechanism related to matter wave in a continuous non-quantized form of mass.
The wave like interference of photons observed by Mr. Feynman would be due to the wave properties of the oscillations responsible for the formation of the resonant "system" of a photon defined in Chapter two.
If the distance between the two glass surfaces in Richard Feynman's experiment is equal to half of the wavelength of the oscillations in the continuous non-quantized mass component of a photon, the interference of the wave properties of those oscillations will yield the energy associated with 0 photons.
If the distance between two glass surfaces is equal to the wavelength of the oscillations in a continuous non-quantized mass component of a photon, the interference of their wave properties of those oscillations will yield the energy associated with 16 photons.
However, this does not explain how and why the energy variations caused by the interference of photons are quantized and not continuous as wave theory predicts they should.
The reason the energy of interfering photons is not continuous is because as, mentioned earlier, the oscillations in a continuous non-quantized form of mass form resonant "systems" that define the energy of a photon.
Since the energy of the resonant "system" of each photon is fixed by its resonant parameters it can only interact or interfere with the wave prosperities of other photon to generate photons with those same resonant parameters.
Therefore, energy variations caused by the interference of the wave properties of a photon can only have the discrete or quantum values associated with the resonant "systems" of the those photons.
This indicates viewing a photon in terms of a resonant "system" formed by oscillations in a continuous non-quantized form of mass can define a mechanism that can explain and predict both the observed particle and wave properties of a photon.
However, defining the energy of a photon in terms of a resonant property of a matter wave also makes it possible to analyze the path of individual photons between two reflective surfaces in terms of their energy amplitudes, as Richard P Feynman did in his book "QED".
In Richard Feynman’s book "QED", he analyzed the process by which 4 photons are reflected from bottom surface of two pieces of glass in terms of the direction of their energy amplitudes. When light is reflected from a single surface, the directions of energy amplitudes of the reflected photons are randomly varying with respect to photons impacting the surface. However, when photons are reflected from two surfaces the timing or direction of the energy amplitude can be synchronize between the top and bottom surfaces so they can be made to cancel or reinforce each other. As a result 4 photons reflected form the bottom surface can cause as few as 0 photons or as many as 8 photons to arrive at the top surface.
When the directional energy amplitudes of the 4 photons reflected from the top surface are opposite to those that are impacting the bottom surface, they will cancel and no photons reflected from the bottom surface will arrive at the top surface. When the directional energy amplitudes of the photons reflected from the bottom surface are the same as to those that are impacting the bottom surface, they will add and 8 photons reflected from the bottom surface will arrive at the top surface.
The vector properties of the energy amplitude or energy component of a matter wave define the mechanism responsible for the synchronization of the energy amplitude of photons.
The direction of energy of the continuous non-quantized mass component of a matter wave varies sinusoidally with respect to distance. This means that it would be possible to synchronize the direction and amplitude of it between the top and bottom reflective surfaces so that as few as 0 photons or as many as 8 photons to arrive at the top surface.
Therefore defining a photon in terms of a matter wave in a continuous non-quantized mass component of space defines a mechanism that allowed Mr. Richard Feynman to analyze the process by which 4 photons are reflected from two surfaces in terms of the direction of their energy amplitudes.
“The
universe's most powerful enabling tool is
not knowledge or understanding
but
imagination"
Jeffrey O'Callaghan