Well, it looked promising–qualitatively, it all added up, and everything behaved as expected. But it’s a “close, but no cigar”. The acceleration at each point should be proportional to 1/r^2, but after a large number of runs, it’s pretty clearly some other proportionality factor. I’ve got some more checking to do, but looks like I don’t have the right animal here. One thing is clear though–this model, which attracts and repels, is the first one that shows qualitatively correct behavior. If twist rings have mass due to the twist distortion, this is the first model that shows it, even if the mass can’t be right.

So, I stepped back and ran through the list of assumptions, and see some flaws that might guide me to a better solution. Many theories die in the real world because of the glossy effect, as in, I glossed over that and will deal with it later, it’s not a major problem. I unintentially glossed over some problems with the model, and in retrospect I should have addressed them from the get-go.

First, twist rings (as modelled in my simulation) have a real planar component, but twist through an imaginary axis. The twist acts as an E field in the real space and as a magnetic field in the imaginary space. The current hypothesis is that the loop experiences different field magnitudes from the source particle, and this causes a curvature change that varies around the loop. The part of the loop that is further away will experience less curvature, the closer part more curvature (curvature is a function of the strength of the magnetic field from the source particle). This simulation shows that if that is the model, you do indeed get an acceleration of the ring proportionate to the distance from the source particle–and the acceleration is toward the source particle–attraction! If you switch the field to the negative, you get the same acceleration away–repulsion. So far, so good, and the sim results made me think–I’m on the right track! I still think I might be on the right track, but the destination is further away than I thought.

First, as I mentioned, the sim results seem to show pretty clearly that the acceleration is not the right proportionality (1/r^2). That might just be a computational problem or just indicate the model needs some adjustments. But there are some things being glossed over here. First, while the model works regardless of how many particles act as a source, there is always one orientation where every point on the ring is equadistant from the source particle–in this case, there is no variation in curvature. The particle would have to act differently depending on orientation. It could be argued that the particle ring will always have its moment line up with the source field, and so this orientation will never happen–fine, but what happens when you have two source particles at different locations? The line-up becomes impossible. OK, let’s suppose some sort of quantum dual-state for the ring–and I say, I suppose that is possible, some kind of sum of all twist rings, or maybe a coherence emerges depending on where the source particles are, but then we no longer have a twist ring. In addition, the theory fixes and patches are building up on patches, and I’d rather try some simpler solutions before coming back to this one. The orientation problem is a familiar one–it shoots down a lot of geometrical solutions, including the old charge-loop idea.

Here’s another issue: I make the assumption that there is a “near side” and a “far side”, which has the orientation problem I just mentioned–a corollary to that is that it also could get us in trouble as soon as relativity comes in play since near and far are not absolute properties in a relativistic situation). I then get an attraction by assuming the field is weaker on the far side and thus there is less curvature. The sim shows clearly the repulsion acceleration away from the source when this is done. Then I cavalierly negated the field and Lo! I got attraction, just like I expected. But I thought about this, and realized this doesn’t make physical sense–a case of applying a mathematical variation without thinking. This would mean that the field caused *greater* curvature when the twist point is further away (the far side). Uhh, that does not compute…

While not completely conclusive, this analysis points out first, that a solution cannot depend on source field magnitude variation alone within the path of the ring. The equidistant ring orientation requires (more correctly, “just about” requires, notwithstanding some of the alternatives I just mentioned) that the solution work even if all neighborhood points on the ring have exactly the same source field magnitude. In addition, there’s another more subtle implication. The direction a particle is going to move has to come from a field vector–this motion cannot result from a potential function (a scalar) because within the neighborhood of the ring, the correct acceleration must occur even if the potential function appears constant over the range of the twist ring.

This is actually a pretty severe constraint. In order for a twist ring to move according to multiple source particles, a vector sum has to be available in the neighborhood of the twist ring and has to be constant in that neighborhood. The twist ring must move either toward or away from this vector sum direction, and the acceleration must be proportionate to the magnitude of the vector sum. Our only saving grace is the fact that this vector sum is not necessarily required to lie in R3, possible I3–but a common scalar imaginary field of the current version of the twist theory is unlikely to hold up.

Is the twist field theory in danger of going extinct even in my mind? Well, yes, there’s always that possibility. For one thing, I am assuming there will be a geometrical solution, and ignoring some evidence that the twist ring and other particles have to have a more ghostly (coherent linear sum of probabilities type of solution we see in quantum mechanics). For another, my old arguments about field discontinuities pop up whenever you have a twist field, there’s still an unresolved issue there.

But, the driving force behind the twist field theory is E=hv. A full twist in a background state is the only geometrical way to get this quantization in R3 without adding more dimensions–dimensions that we have zero evidence for. Partial twists, reverting back to the background state, are a nice mechanism for virtual particle summations. We do get the Lorentz transform equations for any closed loop solution such as the twist theory if the time to traverse the loop is a clock for the particle. And–the sim did show qualitative behavior. Fine tuning may still get me where I want to go.

Agemoz

Tags: charge loop em ring, quantization, quantum theory, simulation, twist, twist ring, twist theory, twists quantization, vector field

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