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 second-order 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 waveâ€“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 space-time 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 space-time universe and one made up of four *spatial* dimensions.
The fact that one can use Einsteinâ€™s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article â€œDefining energy?â€ Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional 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 three-dimensional space to a wave on a “surface” of a three-dimensional 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 non-quantized 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 three-dimensional 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 non-quantized 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.
Additionally it also tells us why in terms of the physical properties four dimensional space-time or four *spatial* dimensions an electron cannot fall into the nucleus is because, as was shown in that article all energy is contained in four dimensional resonant systems. In other words the energy released by an electron “falling” into it would have to manifest itself in terms of a resonate system. Since the fundamental or lowest frequency available for a stable resonate system in either four dimensional space-time or four spatial dimension corresponds to the energy of an electron it becomes one of the fundamental energy units of the universe.
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 two-dimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to three-dimensional space.
Similarly an object occupying a volume of three-dimensional space would be confined to it However, it could, similar to the surface of the paper oscillate â€œupâ€ or â€œdownâ€ with respect to a fourth *spatial* dimension.
The confinement of the â€œupwardâ€ and â€œdownwardâ€ oscillations of a three-dimension 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 â€œWhy is energy/mass quantized?â€œ.
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 â€œWhy 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 â€œWhy is energy/mass quantized?â€œ 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 space-time because as was shown in the article â€œDefining energy?â€ Nov 27, 2007 its energy can be derived terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
For example, 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 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 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 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.
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 space-time universe in terms of four spatial dimensional and applying the laws of a classical environment to it.
It should be remember that Einsteinâ€™s genius allows us to choose whether to define the reality of a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he derived its physical geometry in terms of the constant velocity of light.
Copyright Jeffrey O’Callaghan 2016