Agemoz's Physics Blog

I did more work with my Schroedinger solver on the various quark charge configurations and ran into a dead-end–this approach does not seem to lead to any valid science.

So, I went back to the study of a 4 spatial dimensional rotation vector field (R4) with a preferred background state that enables twists without discontinuities.

Why add a fourth spatial dimension? For similar reasons that physicists add dimensions to try to make the math work for both general relativity and quantum theory–I claim that having four spatial dimensions plus time has a sufficient number of degrees of freedom to cover the observed states of matter.

Why twists (I use this word to mean a complete vector rotation cycle at a given point)? Because we know that particles such as photons are quantized (E = hv for a quantum of light), and the only way to quantize rotations geometrically is to have a preferred (lowest energy state) rotation direction. A complete rotation defines a real particle–partial rotations are off-shell (that is, temporarily violate energy/momentum conservation) and must return to the background state without completing a rotation.

There is no way in three spatial dimensions (R3) to create a twist without creating a rotation discontinuity, but four dimensions can form continuous field twists. Discontinuities are bad because all kinds of conservation issues (for example, energy potentials) break at the discontinuities. Such discontinuities will have real-world consequences that should be, but never have been, observed.

In addition, quantization requires a background state, a direction that enforces an integer number of rotation twists. In three dimensions, that background state would have to point in some direction that lies in R3, which would violate one of the most important principles of physics–gauge invariance, that is, the premise that all observations are independent of spatial rotation, displacement, and so on. Having the background state rotation point to a fourth dimension. I call it I, imaginary, since a field of that rotation state will have no detectable particles. Any complete or partial rotation away from I into R3 forms a particle–either real or virtual.

Now with that backstory of my research, we finally get to the meat of this post.

For a very long time, I tried to use this R3 + I rotation vector field to model particles. Photons are self evident since linearly propagating quantized twists were the motivator and basis of the theory. Trying to extend this idea to electrons ran into trouble, however. For a long time I believed that the electron set, the four identical variations: spin up e-, spin down e+, spin up p+, and spin down p-, forced the corresponding R3+I models to be dipoles. This runs into conflict with the experimental observation that electrons are point particles. I tried for years to work around this but in the end concluded that a Compton radius dipole cannot represent an electron–it’s too big, and predicting scattering would have to fail to match experimental observation. Whatever model I come up with has to be a point particle model, and for a while I could see no way to get the four electron variations.

I just discovered that there is a point particle solution in R3 + I that gives us four variations. The tricky part that makes this hard is that the solution has to be gauge or frame of reference invariant. You cannot have a frame of reference rotation convert a spin-up electron to a spin-down electron, which is what happens if you reposition yourself about a globe where the South to North pole direction points to a “spin-up” electron–to an upside-down observer, the pole direction then looks like a “spin-down” electron (this is why physics texts emphasize that electron spin is not to be imagined as a classically spinning particle).

In R3, you cannot create a model that gives the four variations, but I discovered that in R3 + I, you can. And better yet, no variation will overlap the photon model, thus giving five independent models. Let’s stop this (long) post here, and I will describe my solution with pictures in my next post.

Agemoz

Tags: physics, quantization, quantum, quantum theory, special relativity

This entry was posted on September 24, 2022 at 3:10 pm and is filed under Physics. You can follow any responses to this entry through the RSS 2.0 feed. You can skip to the end and leave a response. Pinging is currently not allowed.