Is it possible to define a “reality” behind the quantum world in terms of the classical laws of physics and the spacetime environment defined by Einstein?
In other words can one use our everyday experiences to understand the irrationality behind many of the assumptions made by quantum mechanics and integrate them into the spacetime environment in which we all live

For example the paradoxical wave–particle behavior of energy/mass, one of the fundamental concepts defining Quantum mechanics defies the “reality” of the four dimensional world we live in because of its inability to describe/define how quantumscale 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, secondorder 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 and four dimensional spacetime by redefining Einstein’s spacetime environment to its equivalent four spatial dimension counterpart because it will allow one to directly apply classical concepts of Newtonian space to the wave properties quantum mechanics associates with particles.
(The reasons will become obvious latter.)
Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of spacetime because it allows one to convert a unit of time in his four dimensional spacetime universe to a unit of a space identical to those of our threedimensional space. Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his spacetime universe and one made up of four *spatial* dimensions.
In other words by mathematically defining the geometric properties of time in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions and gave us the ability to redefine the curvature or displacement he associated with energy/mass in a spacetime environment to a spatial displacement in a fourth *spatial* dimension.
This, as mentioned earlier will allow us to understand the reasons behind the paradoxical wave–particle duality of light when it is partially reflected by two surfaces, as outlined on pages 17 thru 23 of Richard P Feynman book “QED The Strange Theory of Light and Matter” in terms of the laws of classical physics.
On those pages 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 this observational paradox can be resolved if particles are, as mentioned earlier are viewed in terms four *spatial* dimension instead of four dimensions spacetime because it shows their behavior can be described in terms of a resonant “structure” generated by a matter wave on a “surface” of a threedimensional space manifold with respect to a fourth *spatial* dimension.
For example in the article “Why is energy/mass quantized?” Oct. 10, 2007 it was shown one can derive both the wave and particle properties of energy/mass and a photon by extrapolating the laws of classical of resonance in a threedimensional environment to a matter wave moving on a “surface” of a threedimensional space manifold with respect to a fourth *spatial* dimension. Additionally it showed that all 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 threedimensional space manifold with respect to a fourth *spatial* dimension.
The existence of four *spatial* dimensions would give the “surface” of threedimensional 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 threedimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.
Therefore if one extrapolates the laws of classical wave mechanics to a fourth *spatial* dimension these oscillations in a “surface” of a threedimensional space manifold 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 wave mechanics to a matter wave on a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.
However, one can also describe the physicality of a particle in terms of the wave properties of its resonant structure.
In classical physics, a point on the twodimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to threedimensional space.
Similarly an object occupying a volume of threedimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.
The confinement of the “upward” and “downward” oscillations of a threedimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article “Why is energy/mass quantized?“
This provides the ability to understand how and why a photon can have the properties of both a wave and a particle because it clearly defines their interdependence in terms of the laws of Classical wave mechanics
However it also defines the physical reality of particlewave duality in terms of the classical of the properties of a matter wave moving on the “surface” of a three dimension space manifold with respect to a fourth *spatial* dimension or four dimensional spacetime environment because remember, as was show earlier they are equivalent
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 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 they will reinforce each other and yield the energy associated with 16 photons.
However, it also tells us the reason the energy variations caused by their interference are quantized and not continuous as wave theory predicts they should 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 the fundamental or harmonic of fundamental frequency of four *spatial* dimensions or spacetime environment they are occupying.
Yet this also defines the reason the wave properties of 8 reflected photons reinforce themselves to create the energy associated with16 photons is because Classical wave mechanics tells us that when two waves of the same frequency interact their frequency will or does not change. Therefore if energy is propagated in discrete quantized values associated with the wavelength or frequency of a resonant system the reinforcement of the wave properties of 8 photons must be carried away in the integral or discreet energies associated with resonant systems of up to 16 photons of the same frequency as those original 8 photons.
This indicates that viewing the quantum mechanical world of wave–particle duality in terms of the geometric properties of a resonant “system” generated by a matter wave moving on a “surface” of a threedimensional space manifold with respect to a fourth *spatial* dimension allows one to derive its “reality” by extrapolating the laws of classical mechanics in threedimensional environment to a fourth *spatial* dimension.
It should be remember Einstein’s genius allows us to chose if we want to resolve all paradoxes between the microscopic world of quantum mechanics and the macroscopic world of Relativity either a spacetime environment or one consisting of four *spatial* dimension when he defined the geometry of spacetime in terms of energy/mass and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe thereby giving us a new perspective on the physical relationship of particles and waves
Later Jeff
Copyright Jeffrey O’Callaghan 2014
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In physics a field is defined as a continuous physical quantity that has a value for each point in space and time while Relativistic Quantum Field Theory (QFT) defines particles as excited states of an underlying physical field.
However there is a conceptual discontinuity between QFT and its relativistic component because it is based on the abstract properties mathematics while the Einstein’s Theory of Relativity is based on the continuous physicality of space and time.
For example the Schrödinger wave equation that is used to mathematically define a particle in QFT does so in terms of a nondimensional harmonic oscillator at each point in space but does not define what is physically oscillating while Einstein defines the relativistic properties of space and time in terms of a physical interaction of time with threedimensional space. Additionally it is difficult to understand how nondimensional point oscillation can be responsible for dimensional properties of a particle because by definition it cannot have those properties.

Yet one may be able resolve this issue if one views the relativistic properties of our universe in terms of four *spatial* dimensions instead of four dimensional spacetime.
(The reason will become obvious later.)
Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of spacetime because it allows one to convert a unit of time in his four dimensional spacetime universe to a unit of space identical to those of our threedimensional space. Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his spacetime universe and one made up of four *spatial* dimensions.
In other words by mathematically defining the geometric properties of time in his spacetime universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.
The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in spacetime he associated with energy in terms of the field properties of four *spatial* dimensions is one bases for assuming, as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a threedimensional space field with respect to a fourth *spatial* dimension.
However it also allows one to define the physicality of the harmonic oscillator QFT associates with a particle in terms of physical interaction of the field properties of threedimensional space with a fourth spatial dimensional similar to how Einstein define gravity in terms of a physical interaction of time with threedimensional space.
For example the article, “Why is energy/mass quantized?” Oct. 4, 2007 showed that one can explain and understand the physicality of the harmonic oscillator QFT associates with particles terms of the classical field properties of a wave by extrapolating the laws of resonance in a threedimensional environment to a matter wave moving on “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension. It also explained why all energy must be quantized or exist in these discrete resonant oscillators when observed.
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 a matter wave moving in 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 threedimensional 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 in four *spatial* dimensions.
Observations of a threedimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.
Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.
Therefore these resonant systems in would be responsible incremental or discreet energy associated with quantum mechanical systems.
This allows one to define the physicality of the harmonic oscillators QFT associates with particles in terms field properties of either four dimensional spacetime or four spatial dimensions because as was shown earlier they are equivalent.
However, one can also define its field properties of a particle in terms of the boundaries of its harmonic oscillator.
In classical physics, a point on the twodimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to threedimensional space.
Similarly an object occupying a volume of threedimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.
The confinement of the “upward” and “downward” oscillations of a threedimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries of the harmonic resonator associated with a particle in the article “Why is energy/mass quantized?“
However as mentioned earlier it also defines the physical boundaries of the harmonic oscillator QFT associates with a particle in terms of the properties of a wave moving on a continuous field consisting of four *spatial* dimensions or four dimensional spacetime because remember as was show earlier they are equivalent
This also provides the ability to understand the inseparability of the concepts of a field and particles in QFT because it clearly defines how one is depend on the other.
However it also explains why a field can display either the properties of a particle or the wave properties of a harmonic oscillator when measured because if one wants to measure the total energy contained in a given volume of space one will observe it as a particle while if one want to measure how it is propagated through space one must observe its wave properties.
Additionally it defines a classical reason why particles sometimes behave like oscillators and sometimes like particle and why it is impossible simultaneously observe these two different properties.
As shown earlier the energy contained in a quanta of space associated with a particle would be defined by the wavelength of its harmonic oscillator. In other words to observe or measure the particle properties of a given volume of space one has to sample all of its energy leaving nothing of its wave component to measure. Similarly if one wants to observe or measure fully the wave energy of a quantum of space one would have to sample all of its energy leaving none of its particle properties behind.
(If one does not want to observe all of the energy in a given volume of space then one would expect that the difference would be made up by the emission of the harmonic oscillator QFT associates with photon or other particle.)
The reason why one cannot simultaneously measure both its wave and particle of the harmonic oscillator it is because as mentioned the energy of a particle is defined by its wave properties. Since the energy that defines a particle is the smallest unit of its harmonic oscillator if one measures its particle properties there would be no wave energy left for measuring its wave proprieties while if someone measure its wave energy there would be no energy left to support its particle properties. Therefore making one of these measurements precludes the other.
This shows that one can integrate the abstract mathematical properties of Schrödinger wave equation or the foundation of Quantum field theory with the continuous physical of space and time In Einstein’s theory of relativity.
It should be remember Einstein’s genius allows us to chose whether to solve all problems in either a spacetime environment or one consisting of four *spatial* dimension when he defined the geometry of spacetime in terms of energy/mass and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe and gives us a new perspective on the integration of QFT with the relativistic properties of space and time.
Later Jeff
Copyright Jeffrey O’Callaghan 2014
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