Twist? What about div, curl and all of that?

Every college student majoring in science and engineering goes through the EM physics course that teaches about the behavior of electrostatic fields and Maxwell’s field equations. Curl(E)=0, Div(E)=0 unless there’s a charged particle in there. So why do I argue for a twist in the field? Am I not going to get shot down immediately by an eager beaver freshman physics major? Twists, particularly the analytic solution that I propose that encloses it with a magnetic field sheath, are going to have curl non-zero. Why do I persist with this nonsense?

Well, I should have made it clear in previous posts–quantization of a field cannot happen with Maxwell’s field equations. The particle portion is an empirical addition to the field equations but create a magical black box on the particle itself. We know from QFT that the field has to be quantized. What rule do we break, and what do we hold to make this work? Right now, all we have for particles such as photons and electrons is a black box with very precisely defined aggregate or macroscopic behavior.

I have looked at what quantization means geometrically and have concluded that quantization has to result from field twists, and that a degree of freedom is given when we go from macroscopic EM field behavior to the quantum behavior of fields. To enforce quantization, I’ve come up with a modified vector field element that in aggregate will show the macroscopic behavior we observe such as inverse force law, spin and so on. This modified vector field is unitary in order to achieve E=hv quantization (otherwise there is a degree of freedom in field magnitude that will enable the quantization to dissipate), and generates aggregate E and B fields as collections of photons. I form photons from linear twists of this vector field, and electrons from rings of these twists. Doing all this readily derives Planck’s uncertainty relation and the special relativity Lorentz transforms.

But, getting back to the original question–what about div(E), curl(E)? How do we get there from twists?

That is a valid question, and any hypothesis about twists is going to have to answer that. But first, I have to come up with a mathematical model for the twist that doesn’t break some obvious constraint, and all my cavorting and groaning and blogging for the last few years has been to try to come up with something that will hold up. Not there yet, working on it–so far have found a whole bunch of ideas that won’t work, and chewing on one right now that might work. One thought I am having, though–I would expect *any* system that is granular (composed of quantized components) to exhibit macroscopic div(F) = 0, curl(F) = 0 behavior, regardless of the internals of the components–if the granular components don’t interact with each other. Maybe that’s what makes my twists work at the macroscopic scale…



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