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Loading...We have shown throughout "The Imagineer’s Chronicle’s" that observations of our environment suggest that space is composed of four *spatial* dimensions instead of four-dimensional space-time.
If true we should be able to define the wave / particle properties of particles as observed in the "The double-slit experiment in terms of the geometry of four *spatial* dimensions.
Wikipedia, describes the double slit experiment as being 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 the light waves passing through both slits to interfere, 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 detailed. 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.
It is a widespread misunderstanding that, when two slits are open but a detector is added to determine which slit a photon has passed through, the interference pattern no longer forms and it yields two simple patterns, one from each slit, without interference. However, there ways to determine which slit a photon passed through in which the interference pattern will be changed but not be completely wiped out. For instance, by placing an atom at the position of each slit and monitoring whether one of these atoms is influenced by a photon passing the interference pattern will be changed but not be completely wiped out.
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.)"
However, one can understand the "The most baffling part of this experiment" or why the interference pattern remains when only one photon at a time impacts a screen with two opened slits in terms of the laws of classical physics if one assumes (as is done in the "The Imagineer’s Chronicle’s") the universe is made up of four *spatial* dimensions instead of four dimensional space-time
The article, "Why is mass and energy quantized?" Oct. 4, 2007 showed it is possible to explain and predict the duality or particle / wave properties of matter and energy in terms of a classically resonating system or "structure" generated by a wave moving on “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension. It also explains why all energy must be quantized or exists in these discrete resonant systems when observed.
The reason why the interference patterns remains when 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 mentioned earlier it is made up of a resonant system or "structure" who’s volume would be directly related to the wavelength of that system.
This means a portion of a photon’s energy could 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.
However, according to the laws of classical wave mechanics the "concentration" of a wave’s energy is maximum at its peaks and troughs. Therefore, one could only observe or "drain" the energy continued in a particle’s wave function at points corresponding to its peaks and valleys because those would be the only points where its energy would be “concentrated” enough to be redirected as a resonant system to the observing instrument. However, as was shown in the article "Why is mass and energy quantized?" its wave properties, which define its energy, can only be observed in terms of its quantized resonant "particle" structure. Additionally, this means when one looks at the interference pattern generated by the wave function of a single or multiple particles, there would be a higher probability observing it at the places where the peaks and trough reinforced and less where they cancelled.
This is analogous to how the energy of water in a sink is release by allowing it to go down the drain. If all we could observe is the water coming out of the drain we would have to assume that it was concentrated in the region of space defined by the diameter of the drain. However, in reality the water occupies a much larger region.
It also explains why the interference pattern disappears, in most cases when a detector is added to determine which slit a photon has passed through. The energy required to measure the portion of its energy that passes through one of the two slits interacts with it causing the wavelength of that portion change so that it will not have the same resonant characteristics as one that passed through the slit were no measurement was taken. Therefore, the energy passing thought each slit will not be able to interact to form an interference pattern on the screen.
However it also explains why, as was mentioned in the Wikipedia article "there are ways to determine which slit a photon passed through in which the interference pattern will be changed but not be completely wiped out"; a direct contraction of the Copenhagen interpretation of quantum mechanics. It demands when a detector is added to the experiment to determine which slit a photon has passed through the interference pattern can no longer form. The experimental apparatus should then yield two simple patterns, one from each slit, without interference.
The fact that the interference pattern can occur even if a measurement is made is because if the energy passing through one of the two slits is altered by a relatively small amount compared to what it was originally classical wave mechanics tells us it will be able to interact to form a slightly different resonant system with a slightly different interference pattern on the other side than would be the case if no measurement was taken.
Therefore, there should be a quantifiable minimum value of interaction between a measuring device and a photon that will permit the interference pattern to be reestablished on the other side after measuring which slit the photon passes through.
Additionally there should be a direct relationship between the energy of a particle and when and if an interference pattern is generated when one tries to measure which slit it moves through in the double slit experiment.
One can also define the reason, in terms classical wave mechanics why the results of this experiment are always in the form of discrete particles such as a photon or electron.
As mentioned earlier, all energy must be quantized so therefore the energy impacting the screen will be observed as having the discrete non-wavelike characteristics of a photon whether or not interference occurs.
However, as mentioned earlier, according to the laws of classical wave mechanics the "concentration" of a wave’s energy is maximum at its peaks and troughs. Therefore, one could only observe or "drain" the energy continued in wave function associated with its resonant system at points corresponding to its peaks and valleys because those would be the only points where its energy would be “concentrated” enough to be redirected to the observing instrument. This means when the wave function of single or multiple particles interact, there would be a higher probability observing it at the places where the peaks and trough reinforced and less where they cancelled.
Richard Feynman the farther of Quantum Electrodynamics or "OED" realized the significance of this experiment because it demonstrates the inseparability of the wave and particle properties of particles and felt a complete understanding of quantum mechanics could be gleaned from carefully thinking through its implications.
The above article demonstrates why.
It shows the quantum and wave properties of mass and energy displayed by the double slit experiment can be understood if one assumes they are made up of a classical resonant system in a moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
This cannot be done if one define the universe in terms of four dimensional space-time because as was shown in the article “Why is mass and energy quantized?" time is only observed to move in one direction forward and therefore could not support the bi-directional movement required to derive classical resonance.
Later Jeff
The "Shadows" of four spatial dimensions
Copyright 2009 Jeffrey O’Callaghan
(In a PDF format)