Let me go to another thread of thought that comes from the group wave thinking I have done. You may recall, this is the attempt to explain quantum behavior by stating that particles in our existence, both massive and massless, are formed by a Fourier composition of all possible unitary magnitude wave frequencies. The waves have no intrinsic causality such that a change in phase at a given frequency affects the whole wave instantaneously (providing the mechanism for various quantum paradoxes such as the two-slit experiment and quantum entanglement). If this collection of waves is completely random, there are no particles (do an inverse Fourier transform of a constant value, this will give nothing in physical space). But if the waves have phase such that (for example, in 1D space) the wave phase is equal to e^(Pi I freq), then a delta function, that is, a particle, will exist in physical space. The particle moves if the wave phases have a constant e^ (Pi I x0) applied to it over an interval of time. Using the same analysis you can also create or annihilate more particles on the same collection of unitary waves. You can re-state laws of conservation of energy, charge, and other properties in terms of allowable changes in the phase behavior of these waves.

With such a system you can create finite causality of a group wave construction such as a delta function and its movement (that is, a speed limit c) by limiting how quickly the phases can shift. I explained all of this previously, but now I have new thoughts on this. One of them came when trying to envision just what a photon is–in such a system the photon emerges as a Fourier decomposition along a straight line. But what is the mathematical structure of this photon, and how could such a construction emerge from a scaleless system? Well, one very important result of this model is that the construction must result from an infinite range of wave frequencies *all with the same magnitude*. This magnitude is important, it is an unconstrained parameter of the system but must be constant across all frequencies (otherwise the emergence of group causality is very problematic).

This is profoundly important because of Einstein’s discovery that photon reception in a photomultiplier tube is quantized. What does it mean to be quantized? It means that at a given frequency, there is a minimum amount of energy possible in a photon, and it means that the amount of energy that any set quantity of photons can have is an integer multiple of this minimum. This means that there is something about the nature of a photon that has only so much energy and no more or less. In my model, the amplitude is constant (and could be considered a cosmological constant) for all waves composing the photon, so the only possible variable is the number of cycles of a single photon. If there is more than one cycle to a photon, it seems that the photon would be divisible, and that higher energy collections of photons would yield fractional photons, so I conclude that the photon must compose of exactly one cycle.

In the Fourier decomposition of unitary waves, the delta function that emerges would be due to one or more *twists* of the field in 3D space. This twist is topologically stable and accounts for the enduring stability of the photon as it travels through the universe–only the interception of the photon by a ring of twists (a massive particle) can deconstruct the twists.

Why is the twist such an important answer? Because it provides a solid and believable mechanism for the most important question in quantum theory–Why is there quantization? Why does a discretization appear in a continuous scale-less system? Photons can have an infinite range of frequencies, but only discrete energies: Twists provide an answer–it is not possible to have a partial twist in a 3D spatial system, the twist must return the field to its starting state. Thus there is either no twist, or a complete 360 degree twist, thus causing the observed quantization.

There is no possible field construction other than a twist that can topologically reside in 3D space without having a dimension normal to the direction of travel. But–is it one twist or two? If it is one twist, it is difficult to assign a frequency (energy) to the photon because the model assumes a unitary set of waves of varying frequency. If it is two twists, then a new degree of freedom is added based on the separation in time and distance of the twists. The longer the separation, the lower the energy of the photon. But how can the photon not vary in energy by changing the separation distance? I don’t know, but now I think that two twists is not workable–instead, there is another way to add the necessary degree of freedom if one assumes a momentum of twisting. The faster the twist, the greater the energy.

What’s interesting about twists is considering the zoo of massive particles and how to explain the proliferation of particle types (in a constant effort to bring physics down to the One Rule). It’s conceivable that the various particles are various geometrical permutations of sets of twists. The ring of two twists, my hypothesis for the electron and positron) is one of the simplest. The direction of the twist about the ring spin determines whether the particle is matter or antimatter. I can imagine that protons composed of three quarks might actually be a stable three way configuration of twists of the spacetime field. Muons might be some other geometrical combination of twists.

An unanswered question that is getting some of my thinking is why does a ring of two twists only have one possible stable state? For a given frequency, the field wave magnitude defines the quantized energy, but there are a continuous infinite number of frequencies available–why does the electron have just one of those?

More thinking on this idea to come..

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