More Details on the Precursor Field

I’m getting ready to start some detailed analysis work on the proposed precursor field. This effort is intended to show how the quantized particle zoo and the EM and strong forces could emerge given a field with an underlying (“precursor”) set of properties I’ve worked out in previous posts. I am taking the liberty of using this post as a placekeeper for keeping track of the details–this might help a reader understand better what I’m proposing but this particular post is not really intended to be especially profound. If it gets freshly pressed, that would be funny in an ironic way!

This precursor field, as described in previous posts, has unitary magnitude and rotates in R3 + I, or 4 dimensions. This will map to a rotation group (SO(4)) and will embed two types of field connections. I think of the connections as forces, although forces actually are a particle concept (ignoring general relativity for now) and technically this word probably shouldn’t be used here. There’s a semantic issue here which right now I want to ignore as I try to prove the concept, so I’m going to use the word force here to describe the required connections.

The necessity for these two connections is described in previous posts and consist of the quantizing force and the rotation force. The first is a force that attempts to restore an element of the field to the imaginary dimension. It has no effect on neighborhood elements. The second is a true connection from one element rotation velocity to neighborhood element rotation states. I will experiment with various specific functions for each of these forces, but will start with some simple guesses. For the quantizing force, I will use a linear restoring force (to the I dimension) that gets stronger as the angle from the imaginary axis increases.

The rotation force is tricky. It is tempting to use a central force (1/r^2) where the rotation velocity of an element will cause a proportionate weighted delta rotation to neighborhood elements, dropping as 1/r^2. This force must be normalized to a finite value at zero–but 1/r^2 has a pole there, that won’t work. A workable solution that avoids renormalization would be to use a Gaussian, but doesn’t have as good a physical justification.

The central force approach can easily be justified as linearly proportional to the number of elements present at the function’s radius, which grows as r^2 in the R3 space. (Dont let the I dimension fool you–that is only a direction dimension. The real part, which is the only part that the radius value r is dependent on, is what determines the magnitude of the rotation force). Nevertheless, right now I see no way to use this because of the pole at zero, so I will just take the gaussian as a guess for a function that is finite at zero r and declines to zero at infinity. If this guess yields the expected stable particle zoo or something resembling it, then work to exactly derive the rotation force function will need to be done.

There you have it–that is a mathematical definition of the Precursor Field that should yield a particle zoo and the EM and Strong force interactions. I’m setting up a sim and some analysis to see what this construct will yield. I’ve yakked for a long time why this twist field thing makes sense, now it’s time to fish or cut bait…


PS, note that I’m ignoring quantum wave functions for right now and treating the precursor field elements as actual physical states. If the concept pans out, the math will have to be generalized to composite states (wave functions). It will also be necessary to generalize to relativistic speeds. It’s my guess that neither of these are necessary to explain the particle zoo, although once shown, refinement for quantitative analysis would then have to be done.

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