This will be a short post, but not because I haven’t been doing a lot of thinking about the latest ideas about twists. Quantum mechanics epitomized by E=hv says that there is a minimum energy in a photon of a specific frequency, and that any emission of light is an integer multiple of this energy. I came to the conclusion that one workable solution that gives quantized states to a scaleless system is to permit the system to have a substance that normally is homogeneous but can have twists embedded within the substance system. These twists have the nice property of having the right number of degrees of freedom to form photons of circular polarization, and if my ring theory is used, electrons/positrons have the right number of degrees of freedom (spin up/down, matter/antimatter). It explains why electrons have antiparticles but photons do not. This line of thought seems like the strongest possibility because a system of twists is the only possible system that can produce waves that have a fixed amplitude (all our known macroscopic wave systems other than EM radiation has waves that have non-quantized amplitude).

It also explains the stability of quantum particles, since a system with a twist in it is not topologically equivalent to a system without twists. There is no morphism from one to the other, so twists have stability over space and time, even when traveling the length of the universe.

A system of twists has some important assumptions, though, and I spent some time trying to figure them out. At first, I was perturbed by the cut requirement–a twist in 3D requires a discontinuity surrounding the length of the twist. As I realized that the discontinuity must be some topological version of a cylinder where the field is only joined to the twisting material at the end of the cylinder, it began to plague me how a homogeneous material could have a discontinuity. Since the twist has no radial dimension (otherwise electrons could not absorb a photon that is many orders of magnitude bigger), and since the quantized nature of twist energy requires that twists must complete one entire turn of 360 degrees, this sheath cannot consist of empty space and still be a valid solution.

I realized the twist substance must not be homogeneous–it must be composed of at least two distinct materials or states. Eeew, how can a scaleless system evolve to produce this condition? Well, that’s where a lot of my thinking is going. Even the solution using an empty space cylinder cut is a solution of two states, material or no material. This solution doesn’t enforce the integer twist state requirement of quantization, so I have come to the point that our universe has to have two possible states or forms of existence. This actually makes sense when considering the macroscopic EM field as having two orthogonal states. Note that special relativity says that E fields become M fields and vice versa depending on the relative frame of reference–the implication being that there is one material here but it can exist in one of two states or some linear combination of both. Special relativity also severely constrains what kinds of systems we can consider–the photon still has to be a photon no matter how our frame of reference moves.

So–how can a scaleless system produce a two state material–and more importantly, for a system that allows twists, this material must be a surface with one state on one side, and the other state on the other side. Only then can a quantized twist occur, because at each end of the cylinder, the material must connect with the same polarity. Can you visualize this scheme? It’s easier if imagining the 2D analog, where the twist has a cut on either side and there is a mobius-like twist between the cuts. You can see that if the material has both ends with the correct polarity of connections, there has to be a full 360 degree turn–nothing else will work. It’s a wonderful way to visualize why our universe has quantization, but how would a scaleless system produce a two-sided surface like this?

I think the answer is actually pretty obvious–it is probably homogeneous, but is a directional material. When the material is pointing within the 3D surface, it is one state, when it is pointing orthogonal to the 3D surface (in a 4th dimension direction) it is another state–and the states have to be common at the ends of the cylinder, but can twist within it. Ahh, ok–that feels pretty good–except there is (in this scaleless model) no 4D direction, so how can something “point” that way? What does it mean to point, anyway??!

More to come.

Agemoz

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