The Quandary of Attraction, Part III

I worked quite a bit with figuring out a way to make twists work in the electron-photon case.  I had excluded partial twist bending as a means of propagating the charge field of a remote charged particle, but this really troubles me, because it is a very clean way of representing virtual photons.  Virtual photons actually come from QFT as partial terms of a total expression of interaction probabilities.  They are a mathematical artifact only in the sense that there are constraints on the sum of all virtual interaction probabilities.  Even though they aren’t really “real”, they derive from real field behavior in aggregate, so there must be some physical analog if I’m going to construct an underlying theory.  Partial twists were perfect–since they have to return to the background direction without executing a full twist (otherwise there would be a real photon there), and since they have a linearity property where multiple charge sources can create a sum of bends, there was a good match for the QFT virtual particle artifice.  Such a bend will have an effect on a remote ring (charged particle) caused by the delta bend from one side of the particle to the other.  Here’s a simple picture that illustrates what I am thinking:

Problem with bend solution to Unitary Twist Field theory in a charged particle array

If bends are correct, there’s a whole bunch of problems that show up, the Figure 2 shows one of them–it doesn’t work correctly if a third charged particle is added at an angle to the line of the first and second particles.  In addition, the bends aren’t even correct if the field due to the receiving particle is added in.  It just doesn’t work, and so I decided to throw in the towel and say that bends are not virtual particles and there is no option but to only consider full twists for real photons.  The twist model won’t have a QFT equivalant mapping with virtual photons.  Oh, I really don’t like that.  I also really don’t like the background vector in R3 in order to enforce quantization–I see a large number of problems creating such a system that is gauge invariant (what I mean by that is that the system’s behavior is independent of absolute position, rotation, and Lorentz invariant to frames of reference in space-time).

It occurred to me that all these problems could be solved if we put the background vector direction orthogonal to our R3 space.  Not really a 4th dimension because nothing will exist there, but a 4th dimension direction to point.  I think multi-particle bends will correctly sum to create an electrostatic or magnetic field that QFT would generate with virtual photons, and now there is no preferred angle in R3 that would ruin gauge invariance.

I have to think about this a lot more because now there may be too many degrees of freedom for twists.  The work on circular polarization for photons wont be affected since the background direction just provides a reference for the available twists.  But the ring solution might end up with too many possibilities, I have to figure that out.  But I see a lot of promise in this adjustment to Unitary Twist Field theory–I think it is a closer match to what we know QFT and EM fields will do, yet still preserves the quantization and special relativity behavior that makes the Unitary Twist Field idea so compelling to me.



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