Twist Theory and Electrons

OK, applying this unitary twist field idea to photons seems pretty workable.  We get real photons and virtual photons, and get a good model for how quantization and circular polarization could work.

There are some big questions, though–the biggest of all is that this method of quantizing a continuous system requires a background vector state.  Now, this isn’t as bad as it would seem, because a unitary vector field has to have some direction, and continuity would imply that local neighborhoods would point in the same direction, and the model does not assume that the backround direction has to be absolute throughout, it can change.  Nevertheless, it would seem that a background direction might somehow be detectable with some variation of a Michelson-Morley experiment.  That’s going to get some attention on my part later, but for now I want to go in another direction.

Let’s talk electron models in the Twist Theory.  This is where real physicists have a heyday killing off new theories like this because the electron is so well studied and measured, there is so much that a theory would have to line up with before even beginning to come up with something new.  Don’t know what to say except it’s fun to see what comes out of such a study.

Let’s start with degrees of freedom, just like I just did with the photon, that could kill off the theory in a hurry–and for a long time I knew there was a problem, here it is:  electrons come in four permutations, spin up electron, spin-down electron, spin-up positron, and spin-down positron.  All of these have the same exact mass, charge (+ or -), spin moment, g ratio, and so on.  I have long felt that the electron is effectively modeled with a single unitary field twist ring.   Here’s a picture of the idea.

Twist ring model of an electron in a unitary field with a background state.

The ring has one point where the twist direction matches the background twist state.  The twist curves, unlike the photon, due to internal effects of the ring twist.  I have done math that shows there is a single such solution that is stable, but only in certain circumstances.  I will come back to the math of twist ring solutions, but right now, let’s just see if the degrees of freedom required would shoot this down even before getting to the math.  Sort of like checking to make sure an equation has consistency of units, otherwise the equation is just nonsense.  As I mentioned, there are four variations of the electron that have to have a unique twist field representation.  Are there four unique solutions for the twist ring?

Twist ring degrees of freedom with no background state. Note that two solutions are just mirror images of the other two, we only have one degree of freedom.

Of course, we have our four cases, and no more.  Ooops–wait, two of the four are just mirror images of the first two–we really only have two unique twist ring solutions!  It took me a while to realize there are actually four–in a unitary twist field there would only be two, but in a unitary twist field with a background state, necessary for quantization to work, there are actually four.

The background state required for quantization also provides a reference that prevents the two mirror cases from being identical to the first two cases. There are now two degrees of freedom.

The background state from which the twist must begin acts as a reference vector that keeps the mirror image twist rings from being identical by rotation.  To see this more clearly, look at the two degrees of freedom as a function of the planes they reside in:

The reference vector along with the ring center defines a plane (green) where two possible twist cases result in a unique degree of freedom. The blue plane that the ring resides in defines ring travel direction and is another unique degree of freedom.

One degree of freedom is establised by the ring rotation within the plane that includes the ring.  There are two possibilities, clockwise or counterclockwise.  The second degree of freedom is defined with the plane that the background vector lies in, as well as the center of the twist ring.  The background vector is the starting point for a rotation about the ring circumference.  It should be clear that the background vector creates a reference that makes the two mirror cases unique.  You could argue that it doesn’t matter if the mirror image rotation doesn’t have the same background state, but actually it does–it determines which way the ring will turn if it is moving in a magnetic field–the spin-up electron will move differently than the spin-down electron due to the opposite direction of its starting point vector.  I’ll keep thinking about this but so far, this appears to be valid.

Agemoz

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