Interesting. I spent a lot of time studying geometrical combinations of twists to see if there are other solutions besides the linear twist and the ring. I’ve found good connections there for photons and electron/positrons, but there are many other particles, most of which are not stable. I realized that a stable particle in a unitary twist field would have to be a restoring configuration of twists, such as the twist ring. Metastable solutions could yield all kinds of possibilities that wouldn’t necessarily have any geometrical or topological significance–a local minimum of restoring force, for example. However, a stable particle such as a proton or neutron would have to have a significant equilibrium geometrically. Forces have to balance and be restoring, and this knocks out the vast majority of combinations of twists. You can’t have overlapping but different twists without having two unitary field directions in the same place. You can’t have two twists with different curvature in the same local neighborhood (the twist force is a single value). You can have twists intersect provided the intersect neighborhood has a field direction that is constant. Field twists can only move at speed c. Twist forces have to be constant even as the twist moves (otherwise stability fails).

I went through a list of all kinds of possibilities, and only have two candidates right now–and these match the up-down quark configurations of the proton and neutron. You can have a pair of twist rings with a common center, lying in orthogonal planes, with a third twist ring lying in a plane orthogonal to both of the first two. The third twist ring must have a radius half or twice as big as the other. I ruled out any solution that has two rings in one plane because the 1/r^3 force cannot be made constant, and I ruled out any solution of three rings where the radius is the same for all, because there is no possible solution where the intersections have the same field direction–unless the twist rate is different for one of them. But if the twist rate is different, the resulting 1/r^3 force is different and the curvature thus has to be different, meaning that the radius has to be different.

In summary, I’ve only found two workable solutions (so far) for stable solutions of three twists. There are only two known stable particles, the positron and neutron, (the neutrino is currently unknown for stability, I’m putting that one aside) and these two three-ring solutions show an intriguing potential as representing the quark structure of these particles. Since quarks are only stable in combination with other quarks, I’m treating the triplet combinations as a set of three twists that are unstable when pulled apart (that is, it’s not possible to create a stable single quark, and in the same way, the three twist rings that make up a proton or neutron cannot exist on their own–the only stable single twist ring is the one representing the electron).

An interesting side track to this thinking is that there may be a twist ring pair solution–two electron rings with a common center and lying on orthogonal planes. Bose condensate? This type of solution, whether quarks or electrons, needs to be studied before giving it any credibility. I need to look at the internal forces according to what I’ve set forth for the twist ring for the electron and see if there is any level of consistency or if there are showstoppers to the extension of the twist ring concept to quarks. For example, if true, would the three ring solution yield the observed masses, or is this just a circus? Ha ha, get it? That was funny… uh, I guess it’s time to quit for now and do more analysis…

Agemoz

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