Discontinuity Contradiction

Well, does it or doesn’t it?  If you are one of my readers following my thinking adventure (thank you!),  you’ve seen my stream of thinking where I debate what a unitary field twist solution to the particle zoo would look like.  I’ve come up with the twist idea because every particle must obey E=hv (energy is a quantized multiple of a particle’s frequency times a constant, ie, the discovery that won Einstein his Nobel).  Assuming a continuous field, and assuming that particles emerge from this field,  it is valuable to uncover geometric structures that also have this quantization, and a field twist is definitely one of them.

The cool thing about the field twist is how special relativity falls out of it–there are many derivations, but my favorite is how twist rings exhibit a maximum speed that is constant in any frame of reference, thus providing a geometrical explanation for the speed of light.

But, there’s a fundamental problem, as you’ve seen in my last several posts.  Twists assume a background state, and since the field is unitary, this means that quantization occurs as a result of a local twist in field direction.  In order to enforce an integer number of twists (no partial twists) there must be some kind of attraction to the background state.  I have used continuity as a means to generate this attraction–if the ends of a radial twist are locked to the background state, the twist will become topologically stable and will not dissipate.  All good so far, but EM field experts will point out that div(F) is not zero.  Geometrical analysis appears to show that there is no such Maxwell’s EM field valid solution.  That doesn’t bother me too much since this is not a Maxwell’s field, but is closely related, it is unitary (can’t go to zero) and this is what enables a stable entity such as a twist.

But what does bother me is that I can’t find a valid unitary twist field solution that doesn’t have a discontinuity in it, which contradicts the starting assumption of continuity–the thing that allows a valid tie-down at the ends of the twist.  If I allow discontinuities internally to the twist, what stops it from having discontinuities at the ends, and the model breaks down.

I thought I had proven inductively that there cannot be a twist solution without a discontinuity, but lately I found a flaw in that conclusion.  But one thing I’m pretty sure of now–if I allow discontinuities, I no longer have a tenable twist field solution, because not only is there a loss of the continuous field enforcing tie-down, but now the very definition of the field being unitary doesn’t make sense, you can’t have a magnitude variation.  It simply cannot have a discontinuity, else I no longer have a theory.



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