Precursor Field Constraints

I’m continuing to work through details on the Precursor Field, so called because it is the foundation for emergent concepts such as quantized particles and the EM field/Strong force. I mentioned previously that this field has a number of constraints that will help define what it is. Here is what I had from previous work: the precursor field must be unitary to satisfy the quantization implied by E=hv (no magnitude degree of freedom possible). It must be orientable to R3 + I, that is, SO(4) to allow field twists, which are necessary for particle formation under this theory. It must have a preferred background orientation state in the I direction to enable particle quantization. Rotations must complete a twist to the background state, no intermediate stopping point in rotation–this quantizes the twist and hence the resulting particle. This field must not necessarily be differentiable (to enable twists required for particle formation). There must be two types of field connections which I am calling forces in this field–field elements must have a lowest energy direction in the imaginary axis, such that there is a force that will rotate the field element in that direction. Secondly, it must have a neighborhood force whenever the field element changes its own rotation. I’ll call the first force the restoring force, and the second force the neighborhood force.

These constraints all result from a basic set of axioms resulting from the Twist Theory’s assumption that a precursor field is needed to form quantized stable particles (solitons).

Since then, I’ve uncovered more necessary constraints having to do with the two precursor field forces. Conservation of energy means that there cannot be any damping effect, which has the consequence that the twist cannot spread out. The only way this can occur is if the quantized twist propagates at the speed of light. This introduces a whole new set of constraints on the geometry of twists. I’m postulating that photons are linear twists which will reside on the light cone of Minkowski space, and that all other particles are closed loops. A closed loop on Minkowski space must also lie on a light cone for each delta on its twist path, which means that the closed loop as a whole cannot reach the speed of light. This can easily be seen because closed loops must have a spacelike component as well as a timelike component such that the sum of squares lies on the twist path elements light cone. This limits the timelike component to less than the speed of light (the delta path element has to end up inside the light cone, not on it).

One interesting side consequence is that a particle like the electron cannot be pointlike. The current collider experiments appear to show it is pointlike, but this should be impossible both because the Heisenberg uncertainty relation would imply an infinite energy to a pointlike particle but also because if an electron cannot be accelerated to exactly the speed of light, this forces its internal composition to have a spacelike component and thus cannot be pointlike. Ignoring my scientific responsibility to be skeptical (for example, another explanation would be massive particles are forced to interact within an EM field via exchange particles, thus slowing it down for reasons independent of the particle’s size–but if this were true, why doesn’t this also apply to photons), I have a strong instinct that says this confirms my hypothesis that particles other than the photon are closed loops with a physical size. This also makes sense since mass would then be associated with physical size since closed loops confine particle twist momentum to a finite volume, whereas a photon distributes its momentum over an infinite distance and thus has zero mass. Since collision scattering angles implies a point size, the standard interpretation is to assume that the electron is pointlike–but I think there may be another explanation that collider acceleration distorts the actual closed loop of the electron to approach a line (pointlike cross section).

Anyway, to get back on topic, my big focus is on how to precisely define the two forces required by the precursor field. I realized that the restoring force is the much harder force to describe–the neighborhood force merely has to translate the field elements change of rotation to a neighborhoods change of rotation such that the sum of all neighborhood force changes equals the elements neighborhood force. This gives a natural rise to a central force distribution and is easy to calculate.

The restoring force is harder. As I mentioned, conservation of energy requires that it cannot just dissipate into the field, and a quantum particle must consist of exactly one twist (otherwise the geometrical quantization would permit two or more particles). I’m thinking this means that a change in rotation due to the restoring force must be confined to a delta function and that the rotation twist must propagate at the speed of light, whether linearly (photons) or in a closed loop (massive particles). I suspect we can’t think of the restoring force as an actual force, but then how to describe it as a field property? I’ll have to do more thinking on this…

Agemoz

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