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Richard Feynman the farther of Quantum Electrodynamics believed Thomson’s double slit experiment provided a mechanism for understanding the wave particle duality of energy/mass because it clearly demonstrates their inseparability and provides a mechanisms for understanding how it is propagated through space.

The wave–particle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects.  Standard interpretations of quantum mechanics explain this paradox 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.

The reason the above-mentioned experiment is so important is because it provides a mechanism for understanding how electromagnetic energy is propagated and why the particle wave dually exists purely in terms of Einstein’s Theory of Relativity.

But before we begin, we must first understand how the electromagnetic wave component of a particle’s duality is propagated through space and time.

One of the difficulties involved in doing so is that we define its movement though space in terms Maxwell’s equations which are based on the interaction between its electric and magnetic components with respect to time not space.  This presents a problem because the particle component of its duality must always be defined by its spatial position when observed. Therefore, to understand how they are related we should attempt to define its movement through space and time in term of its spatial properties.

Einstein gave us the ability to do this purely in terms spatial properties of its electromagnetic wave components when he used the constant velocity of light to defined the geometric properties of space-time because it allows one to convert a unit of time in his space-time universe to an equivalent unit of space in an environment consisting of only four *spatial* dimensions.  Additionally, because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words, by mathematically defining the geometric properties of a space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

This gives one the ability to derive the properties of an electromagnetic wave and understand its movement in terms of the spatial displacement that would be created by its observed transverse wave characteristics. 

For example, a transverse wave on the two-dimensional surface of water moves through water because it 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 is 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. This results in a wave to move on the surface of the water.

Similarly, an energy 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.  This would result a wave moving on the "surface" of three-dimensional space.

Therefore, classical wave mechanics, if extrapolated  to four *spatial* dimensions tells us a force will be developed by the differential displacements caused by an energy wave moving on a "surface" of three-dimensional space with respect to a fourth *spatial* dimension that will result in its elevated and depressed portions moving towards or become "attracted" to each other causing it to move through space.

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 charges than it would be for a single charge.

One can also define the directionality of electrical component of electromagnetic energy 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 because classical Mechanics tells us a horizontal force will be developed by that 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 the apex of that displacement.

However, this means that one can define a physical model for the propagation of an electromagnetic field in terms of Einstein’s space-time theory because, as was shown above when he mathematically defined its geometric properties in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his theory in terms of the geometry of four *spatial* dimensions.

Yet, viewing it in terms of its spatial components also allows one to understand the mechanism responsible for the wave particle duality of a photon as observed in the Thomson’s double slit experiment and why electromagnetic energy always presents itself as a particle when it strikes the detector in the that experiment.

For example, the article, "Why is energy/mass quantized?" Oct. 4, 2007 showed that one can use the Einstein’s theories to explain the quantum mechanical properties of an electromagnetic wave by extrapolating the rules of classical resonance in a three-dimensional environment to an energy wave moving on “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 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 an energy wave moving in four *spatial* dimensions.

The existence of four *spatial* dimensions would give the energy wave associated with a photon 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 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.

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.

As was shown in that article these resonant systems in four *spatial* dimensions are responsible for the particle called a photon.

However, one can also use Einstein space-time theories when viewed in their spatial equivalent to explain how the boundaries of the standing wave responsible for creating the resonant system that article indicated was responsible of a particles formation are created.

In classical physics a standing wave is created when the vibrational frequency of a source causes reflected waves from one end of a confined medium to interfere with incident waves from the source.  This interference of the wave energy causes their peaks troughs to be reinforce in the volume they are occupying thereby creating a standing wave.

The confinement required to create a standing wave in space-time or its equivalent in four *spatial* dimensions can be understood by comparing it to the confinement a point on the two-dimensional surface of paper experiences when oscillating with respect to three-dimensional space.  The energy associated with the wave motion of that point would be confined to its two-dimensional surface and would be reflected and interfere with the incident wave when reaches three-dimensional space at its edge. Therefore, a standing would be created by its interaction with three-dimensional space.

In other words, when a wave on the surface of a piece of paper encounters the third *spatial* dimension at its edge it is reflected back allowing a standing wave to be formed on its surface.

Similarly, an electromagnetic wave moving on the surface of three-dimensional space would be confined to it and reflected back to that volume, similar to the surface of the paper if it was prevented from oscillating with respect to a four *spatial* dimensions or four-dimensional space-time.

In other words, the interference caused by the confinement of an electromagnetic wave to three-dimensional space, which is caused by it striking the detection screen in the Thomson’s double slit experiment results in the resonant standing wave to be formed in space called a photon.

That experiment is made up of "A coherent source of photons illuminating a screen after passing through a thin plate with two parallel slits cut in it.  The wave nature of light causes it wave component to interfere after passing through both slits, creating an interference pattern of bright and dark bands on the screen.  However, at the screen, the light "is always found to be absorbed as discrete particles, called photons".

When only one slit is open, the pattern on the screen is a diffraction pattern however, when both slits are open, the pattern is similar but with much more detail.  These facts were elucidated by Thomas Young in a paper entitled "Experiments and Calculations Relative to Physical Optics," published in 1803.  To a very high degree of success, these results could be explained by the method of Huygens–Fresnel principle that is based on the hypothesis that light consists of waves propagated through some medium.  However, discovery of the photoelectric effect made it necessary to go beyond classical physics and take the quantum nature of light into account.

However, the most baffling part of this experiment comes when only one photon at a time impacts a barrier with two opened slits because an interference pattern forms which is similar to what it was when multiple photons were impacting the barrier.   This is a clear implication the particle called a photon has a wave component, which simultaneously passes through both slits and interferes with itself.  (The experiment works with electrons, atoms, and even some molecules too.)"

Even more puzzling is why any attempts to measure which slit that electron passed through cause the interference pattern to disappear.

Yet, as mentioned earlier one can derive the outcome of this experiment by assuming that electromagnetic energy is propagated by a wave on the "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension instead of four-dimensional space-time

For example, the reason why the interference patterns remain when only one photon at a time is fired at the barrier with both slits open or "the most baffling part of this experiment" is because, as was just shown it has an extended spatial volume which is directly related to the wavelength.

This means a portion of its energy can simultaneously pass both slits, if the diameter of its volume exceeds the separation of the slits and recombine on the other side to generate an interference pattern.

Additionally, one can also explain why the interference pattern disappears when a detector is added to determine which slit a photon has passed through.  The energy required to measure which slit it passes through interacts with it causing the wavelength of that portion to change so that it will not have the same resonant characteristics as one that passed through the other slit   Therefore, the energy passing thought that slit will not be able to interact, with the energy passing through the other one to form an interference pattern on the screen.

However, as was shown earlier one can also show the reason the interference pattern appears as a particle when electromagnetic wave contacts a detection screen is because striking it results in it being confined to three-dimensional space instead of four-dimensional space-time or four spatial dimensions, thereby creating a standing wave in either four spatial dimensions or four dimensional space-time to be created.

In other words, it clearly shows the reason all forms of energy exhibit both wave and particle properties are because they are physically made up of waves in terms of Einstein’s Theory of Relativity.

The above discussion shows that Richard Feynman was right in assuming that Thomson’s double slit experiment provided a mechanism for understanding the  wave particle duality of energy/mass because it clearly demonstrates their inseparability.

Additionally, it also provides an explanation how and why energy  is propagated through space because it shows the quantum mechanical and wave properties of energy displayed in the double slit experiment can be understood if one assumes they are made up of a resonant system in a moving in a four dimensional space-time manifold or on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension in terms Einstein theories.  REVIEW BUTTON

It should be remembered that Einstein’s genius allows us to choose whether to define an electromagnetic wave either a space-time environment or one consisting of four *spatial* dimension when he defined its geometry in terms of the constant velocity of light.

Later Jeff

Copyright Jeffrey O’Callaghan 2020

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