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Presently there is disconnect between our understanding of the probabilistic world of quantum mechanics and the classical one of causality because it can predict with precision the future position of an object while the other cannot.
However this may just be an illusion resulting from a lack of understanding of the quantum environment.
One of the fundament areas where this disconnect appears is in the probabilistic interpretation Schrödinger wave equation
However one could eliminate this disconnect if one could explain the causality of those probabilities in terms of a physical image based on the laws of classical physics similar to how we explain the causality of the movement of the planets around the sun in terms of a physical image of a curvature in spacetime.
Granted this will not change the fact that one cannot use quantum mechanics to make precise predictions of future events but it would give us a physical reason why we cannot in terms of our classical understanding of causality.
One way of accomplishing this would be look at the physically observable properties of all quantum systems and determine if by applying the laws of causality in a classical environment one can explain the reason for the probabilities associated with Schrödinger’s equation.
For example in 1924 Louis de Broglie theorized that all quantum objects are physically composed of a wave as was verified by 1927 by Davisson and Germer) when he observed electrons diffracted by crystals.
However, the fact that no one has been able to physically connect the causality of those observable properties to the probabilities of all quantum systems does not change the fact that there must be one because if there wasn’t they could not interact with our environment to create the physically observable properties of the world upon which those probabilities are determined.
One reason for this failure may be due to the fact that those probability are related to the spatial not time dependent properties of the wave function.
If so one may be able to establish the connection by looking at it in terms of its spatial properties instead of the spacetime ones associated with Einstein’s theories.
Einstein gave us the ability to do this when defined the geometric properties of spacetime in terms of the constant velocity of light because that provided a method of converting a unit of time in a spacetime environment of unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his spacetime universe and one made up 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 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 manifold with respect to a fourth *spatial* dimension.
However doing so would have allowed Louis de Broglie to physically define the casualty of the quantum properties associated with Schrödinger equation in terms of a physical or spatial displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension as was done in the article "Why is energy/mass quantized?" Oct. 4, 2007.
Briefly, that article showed the quantized properties of energy/mass are the result of a resonant system formed by a matter "wave" on a "surface" of a threedimensional space manifold with respect to fourth "spatial" dimension. This is because it showed the four conditions required for resonance to occur in a threedimensional 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 made up of four.
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* 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.
However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established on a surface of a threedimensional space manifold.
Yet the classical laws of threedimensional space tell us the energy of resonant systems can only take on the discontinuous or discreet energies associated with their fundamental or harmonic of their fundamental frequency.
However, these are the similar to the quantum mechanical properties of energy/mass in that they can only take on the discontinuous or discreet energies associated with the formula E=hv where "E" equals the energy of a particle "h" equal Planck’s constant "v" equals the frequency of its wave component.
In other words Louis de Broglie would have been able to physicality connect the properties of his particle waves to the quantum mechanical properties of Schrödinger equation in terms of the discrete incremental energies associated with a resonant system in four *spatial* dimensions if he had assume space was composed of it instead of four dimensional spacetime.
Yet it also would have allowed him to define the physical boundaries of a quantum system in terms of the geometric properties of four *spatial* dimensions.
For example in classical physics, a point on the twodimensional surface of a piece 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?" Oct. 4, 2007.
As mentioned earlier in the article “Defining energy?” Nov 27, 2007 showed all forms of energy can be derived in terms of a spatial displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
However assuming the energy associated with Louis de Broglie particle wave is result of a displacement in four *spatial* dimension instead of four dimensional spacetime as was done earlier would allow one to define a classical causality for quantum probabilities in terms the observable environment we inhabit.
Classical mechanics tell us that due to the continuous properties of waves the energy the article "Why is energy/mass quantized?" Oct. 4, 2007 associated with a quantum system would be distributed throughout the entire "surface" a threedimensional space manifold with respect to a fourth *spatial* dimension.
For example Classical mechanics tells us the energy of a vibrating or oscillating ball on a rubber diaphragm would be disturbed over its entire surface while the magnitude of those vibrations would decrease as one move away from the focal point of the oscillations.
Similarly if the assumption that quantum properties of energy/mass are a result of vibrations or oscillations in a "surface" of threedimensional space is correct then classical mechanics tell us that those oscillations would be distributed over the entire "surface" threedimensional space while the magnitude of those vibrations would be greatest at the focal point of the oscillations and decreases as one moves away from it.
As mentioned earlier the article “Why is energy/mass quantized?” shown a quantum particle is a result of a resonant structure formed on the "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
Yet Classical Wave Mechanics tells us resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,
Similarly a particle would most probably be found were the magnitude of the vibrations in a "surface" of a threedimensional space manifold is greatest and would diminish as one move away from that point.
This shows that one can define the causality of the probabilities associated Schrödinger wave equation in terms of the laws of causality associated with our observable environment by redefining them in terms of four *spatial* dimensions.
In other words one can eliminate the disconnect between the probabilities associated his equation and a classical environment by defining their causality in terms of the laws of classical physics.
It should be remember Einstein’s genius allows us to choose to define a quantum system in either a spacetime environment or one consisting of four *spatial* dimension when he defined the geometry of spacetime in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the probabilistic properties of a quantum environment and how they physically connected to our observable universe.
Later Jeff
Copyright Jeffrey O’Callaghan 2016
Can one integrate the quantum mechanical interpretation of electromagnetism with the classical concepts of a particle and wave? We think so.
One of the most troubling aspects of its interpretation at least to classical or relativistic physicists is how the role of an observer defines the system under observation.
For example many of the proponents quantum mechanics assume that light and all other objects in our universe simultaneously exist as a particle and wave and only decides which one it want to be when an conscience being measures or observer it.
The standard interpretation of quantum mechanics explains this paradox as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent or a secondorder consequence of various limitations of the observer. This treatment focuses on explaining the behavior from the perspective of the widely used Copenhagen interpretation, in which wave–particle duality serves as one aspect of the concept of complementarily, that one can view phenomena in one way or in another, but not both simultaneously.
Some have even gone so far as to say that some form of intelligent being must observe light before it makes a decision as to whether or not it what’s to be a particle or a wave.
However, assuming that a light has the ability or intellectual capability to decide what it wants to be is, at least in my opinion is a bit bizarre.
Even so one could find a solution to how quantum systems "decides" if they want to be a particle or wave by looking at the effects an observation has on them in classical terms.
But first, we must first show how and why we can apply the laws of a classical environment to them.
Einstein gave us the ability to do this when he use the equation E=mc^2 and the constant velocity of light to define the geometric properties of spacetime because that provided a method of converting a unit of time he associated with energy to unit of space quantum mechanics associates with particle. Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his spacetime universe and one made up 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 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 manifold with respect to a fourth *spatial* dimension.
However, redefining the physical properties of quantum system in terms of its spatial instead of its time components would allow understand how quantum system "decides" if wants to be a particle or wave in terms of the currently accepts classical laws of our observable environment.
For example in the article "Why is energy/mass quantized?" it was shown one can predict the quantum properties of a photon of electromagnetic energy by extrapolating the laws of classical resonance in threedimensional space to a wave on a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
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 the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one consisting of four *spatial* dimensions. .
The existence of four *spatial* dimensions would give a continuous nonquantized field of energy/mass (the substance) 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.
Therefore, these oscillations in a continuous nonquantized field of energy/mass, would meet the requirements mentioned above for the formation of a resonant system in space.
Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with it fundamental or a harmonic of its fundamental frequency.
Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with quantum mechanical systems.
Yet it also allowed one to derive the physical boundaries responsible for a particle in terms of the geometric properties of four *spatial* dimensions.
For example 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 resonant system associated with the particle component of its wave properties in the article “Why is energy/mass quantized?“.
In other words, what determines if one observes a wave or particle would be dependent on if its wave component was allowed to move freely, or if it was confined to a specific volume.
This also explains in terms of the classical laws of our observable environment why particles and waves simultaneously exist and only "decide" which one it wants to be when it is observed.
For example a system always present its particle properties when being observed because the act of observing it restricts its energy to a specific volume and as was shown in the article “Why is energy/mass quantized?" the act of confining its wave component to specific volume results in it presenting its particle properties.
However, when a quantum system it is allowed to move freely though space as when it moves unobserved through the slits in the Thompson double slit experiment its wave properties to become predominate as is demonstrated by a diffraction pattern on a screen placed behind the slits because its energy has not restricted to a specific volume.
Yet one can also use those same concepts to explain the electromagnetic properties of both its wave and particle or photonic components.
For example one could explain and predict that the incremental or discrete energies associated with a photon as was done in the article “Why is energy/mass quantized?“ in terms of the resonant properties of wave on a "surface" of a three dimensional space manifold or with respect to a fourth spatial dimension.
Yet one can also use the wave properties of a quantum system to explain its electromagnetic characteristics if one views them in terms of four spatial dimensions instead of four dimensional spacetime because as was shown in the article “Defining energy?” Nov 27, 2007 its energy can be derived terms of a spatial displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
For example, a wave on the twodimensional 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 wave on the "surface" of a threedimensional 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 it 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 threedimensional 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 threedimensional 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.
In other words the one can explain the electromagnetic prosperities wave and quantum properties of light by assuming it is a wave moving on a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension.
However, also explains how and why the reality of a quantum system is determined by observation because as was shown above one can use classical understanding of waves to explain why when no one is looking it has the properties of wave however when they are observed they always are appear as a particles.
In other words one of the most troubling aspects of quantum mechanics that of how an observer defines the reality of all systems including electromagnetic energy can be easily understood by redefining Einstein’s spacetime universe in terms of four spatial dimensional and applying the laws of a classical environment to it.
It should be remember that Einstein’s genius allows us to choose whether to define the reality of a quantum system in either a spacetime environment or one consisting of four *spatial* dimension when he derived its physical geometry in terms of the constant velocity of light.
Later Jeff
Copyright Jeffrey O’Callaghan 2016
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