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Loading...Although we cannot directly observe particles on a quantum scale, we can use our imagination to extrapolate our experiences in a classical Newtonian world to the quantum world. This may help us to understand some of the more puzzling aspects of quantum theories, like how and why an electron can jump from one atomic orbital to the next without ever moving through the intervening space.
A particle in both quantum mechanics and quantum field theory is defined in terms of resonances similar to those found in classical physics. For example, Nuclear magnetic resonance (NMR) is the name given to a resonance phenomenon involving the quantum mechanical magnetic properties of an atomic nucleus in the presence of an applied, external magnetic field.
This is the basis for assuming in the article "Why is mass and energy quantized?" Oct. 4, 2007 the properties of all particles are a result of a classically resonating system formed in a continuous non-quantized form of mass.
If true, it should be possible to explain why; as Brian Greene points out in his book "The Elegant Universe" "The matter particles neatly fall into three groups, which are often called families in terms of their resonant properties. Each family contains two of the quarks an electron or one of its cousins and one of their neutrino species. The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family."
However, the simplest explanation for why the mass / energy of the corresponding particle types grow larger in each successive "family" is to assume their mass / energy is a result of a classical resonating system. This is because in a classical world, the resonant frequency of each "family" member is determined by the fundamental harmonic of its resonant family.
Therefore, the mass / energy of each particle in the individual families would grow larger because mass component of each successive family is built on a resonant system with a progressively larger or more energetic fundamental resonant frequency.
Additionally it would provide an explanation as to why "The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family".
The energy of the "family" members in each resonant system in a classical world is defined in terms of the harmonics of their fundamental frequencies. This means the energies of the higher harmonics will be proportional to the fundamental frequencies of their respective families. However, their ratios will be the same, which means their physical properties will be proportional to the differences in their fundamental frequencies. Therefore, the reason why the corresponding particle types across the three families will have identical properties except for their mass is that, as was shown in the article "Why is mass and energy quantized?" their energies will be proportional to the fundamental frequency of their resonant "families".
Therefore, the simplest explanation as to why "The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family" is to assume that their mass is a result of a classically resonating system formed in space by oscillations a continuous non-quantized form of mass.
(In a latter article "The geometry of quarks", it will be shown how and why quarks join together to form the resonant systems called the proton and neutron.)
Defining a particle in terms of a resonant system in a continuous non-quantized form of mass can also explain one of its most puzzling aspects: how and why it can generate the interference pattern associated with a wave.
For example, in the double-slit experiment an interference pattern is generated by a single particle when it passed through one of two slits in a screen.
However, one can understand 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.
As mentioned earlier, "Why is mass and energy quantized?" 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.
The reason why the interference patterns remains when one photon at a time is fired at the barrier with both slits open is because, as that article showed 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 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 as a resonant system to the observing instrument. However, as was shown in the article "Why is mass and energy quantized?" a particle is defined by its resonant structure and therefore can only be observed as resonant structure. This means that when one looks at the interference pattern generated by the wave function of a single particle, there would be a higher probability of finding 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.
This 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.
The Copenhagen interpretation of quantum mechanics 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 and the experimental apparatus should yield two simple patterns, one from each slit, without interference.
The reason 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.
This defines a mechanism in terms of classical wave mechanics for the "wave-particle duality" or how a single quantum system can have both the properties of a wave and a particle because it defines its particle properties in terms of a resonant system formed by waves in a continuous non-quantized form of mass.
Defining a particle in terms of a classically resonating system in a continuous non-quantized form of mass can also explain and predict why the energy, momentum, and angular momentum of a quantum system can only take on discrete values that are multiples of Planck’s constant.
As mentioned earlier, observations of resonant systems in a classical world indicate their energy content is not continuous but exists in multiplies or harmonics of their natural frequency.
The reason why the energy, momentum, and angular momenta of a quantum system can only take on discrete values is that the energy of each quantum system is the result of a resonant "structure" generated by oscillations in a continuous non-quantized form of mass. Therefore, the values for the energy, momentum, and angular momenta of a quantum system could only take on the integral values related to the harmonics of its resonant "structure".
Additionally, the reason why energy, mass, and momentum are related to wavelength or frequency is that the energy of a resonant system is depended on the frequency of the oscillations of the components of that system.
Finally defining particles such as an electron in terms of a resonant system in a continuous non-quantized form of mass can explain why particles appear to randomly "move" or "jump" to different positions in space without ever moving though the intervening space.
An electron can "jump" from one atomic orbital to the next without going thought the intervening space because the resonant "system" associated with an electron does not move from one atomic orbital to the next.
Instead, the resonant system associated with an electron collapses in its initial atomic orbital and is then reformed in a new atomic orbital. Because no resonant or "standing" matter wave is generated in the intervening space between the atomic orbital no electrons will be found there.
The fact that it is possible to conceptually define mechanism that can successfully explain and predict the particle and wave properties of mass and energy in terms of a classical Newtonian world indicates that the laws that govern objects on the unobservable quantum scale may not be so different as those that govern the objects we can observe.
Later Jeff
The "Shadows" of four spatial dimensions
Copyright 2007 Jeffrey O’Callaghan
(In a PDF format)