No. No. No…. No discontinuities.

In the previous post, I talked about how special relativity might allow a twist to exist without creating a causally connected discontinuity–indeed, it may be possible for a point discontinuity to exist if it is moving at speed c because a discontinuity can form between the time and spatial regions of a light cone loci from a point. But continuing to think about this, I don’t think this is the answer for twists. First, a twist must exist over a length that is the wavelength of the particle, not a point–and thus appears to require a discontinuity that is at least a line and I think actually has to be a surface. Second–any discontinuity that satisfies a light cone boundary in one frame of reference will be time-like in another, a no-no. If the light-cone boundary is what enables the discontinuity, then it must be valid in every frame of reference, an intersection of all light-cone boundaries available within the time-like region of the particle–a geometric impossibility, that forms the null set. When I added special relativity to the twist problem, I did not end up with a solution due to light-cone boundaries permitting discontinuities.

However, after thrashing this out, I suddenly realized that special relativity does allow one of my old solutions to work–the sheathed twist. Recall that there is a solution for an E field twist if the sheath around a twist points radially. I discarded this previously because I could show that a static solution dissipates–but special relativity does some interesting things here. This solution surrounds the twist (bicycle wheel or radial) with orthogonal field vectors, pointing along the axis of the twist. Statically, this just dissipates–but when the whole twist plus sheath assembly is moving at c along the axis, the sheath becomes a field vector pointing in the direction of velocity c, and special relativity will make the vector go to zero–effectively removing any discontinuity boundary yet maintaining the unitary characteristic required for a twist to be quantized. The vector doesn’t vanish, though–it’s still there but invisible in any frame of reference except that which is moving at c along with the particle. I have hypothesized that field elements pointing in the direction of travel become a B field. Such a system clearly could exist–does special relativity keep this system from dissipating?

More thinking and analysis to come..



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