Well. A lot of work on the simulator and a whole lot more thinking, and I began to realize that within the constraints I had set, **there is no solution**. I thought I’d come up with a workable field solution that had no field discontinuities, and I was wrong. After more thinking, I realized that a unitary Maxwell’s field will never produce a stable solution–unless the twist is moving at the speed of light. This is a good thing, because if I had found a solution, I would then have to answer why single, non-moving twists in real EM field never occur. I have taken the long way around showing myself that even if a Maxwell’s field is unitary (thus giving us the required E=hv quantization), it cannot hold a twist in a non-relativistic situation. I had had a hunch for a while that since photons always move at c, I would have to include velocity in my search for a solution.

A few posts ago, I said something about a solution cannot rely on special relativity because different frames of reference will produce variations in the twist solution–but actually, after thinking it through, this will work, I think. The observed circular polarization of light means that the twist has two dimensions to work with–this, combined with the realization that a discontinuity can be avoided if the twist is moving at c (the wave front of the twist moves in such a way that no stable discontinuity will form), made me realize several things all at once. First, the twist must occur such that its axis is normal to the direction of movement, that is, the direction arrow of movement lies on a diameter line of the circle. Second, and this was a breakthrough realization–any object moving at c, according to special relativity, will have its axial dimension of components in the object reduced to zero in **all** frames of reference except that of the object itself. Oh ho, I thought!! I have constrained the field to be unitary, but when the twist moves at relativistic speed, the E field vector spins around and diminishes in magnitude–to the point where it goes to zero! The danger, of course, is thinking that our drawing of a vector arrow has a physical constituent–it doesn’t, it’s just a pointer for the direction of the twist within an epsilon neighborhood–but it’s not the vector that effectively disappears, it’s the spacetime dimension of the object. In **every** observers frame of reference except its own, the E field component in the direction of travel varies as the twist circles about its axis.

How does that help us avoid the discontinuity! Oh boy, I see it now–special relativity requires that the twist be confined to an infinitesimal neighborhood along the direction of travel. It is the only possible solution where a discontinuity cannot have a finite length. Zero times Infinity, we’ve been here before (see my posts on “something from nothing” quite a ways back). The background field direction is preserved–we get our E=hv quantization and a solution without a (finite) discontinuity. The astonishing thing about this is how it points to how the concepts of distance, time, and energy could emerge from a nascent universe–this infinitesimal space holds varying speeds of rotation. It also begins to answer the question of how to reconcile the unitary E field universe (required for E=hv quantization) with the observed non-unitary E fields we see in real life. A whole bunch of interesting insights seem to arise from this model.

More details to come, but it’s time to update the simulator for relativistic solutions. This could be a challenge…

Agemoz

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