Sunday, February 12, 2023

How I Modify Kaluza-Klein

 I sometimes lean towards the Kaluza-Klein theory in order to effectively deal with the problem of electrical charge.  For the shortest possible summary, Kaluza-Klein generalizes relativity to include electrical charge by adding an additional closed dimension, with electrical charge corresponding to something like motion in this additional dimension.  A closed dimension is a direction which, if traveled in for a sufficient distance, will bring you back to the point you started.

I think this dimension is probably what relativity calls "time", which I argue shares only a little bit of resemblance to what we normally think of, when we think of "time" - in particular, it is distinct from "history", which is flying outwards at the speed of light.  Going forwards and backwards in time, then, results in the same outcome: Traveling forward in "history".  That is - I think time is a closed dimension.

Or rather, I think it is a spiral that behaves identically to a closed dimension for our purposes here; specifically, in a relativistic sense, with regard to a particle's perspective, it is more correct to interpret the spiral as rotating, rather than the particle as moving along the spiral.  When using the spiral perspective, history is recovered; distance in history is equivalent to the arclength between two points.  Forwards and backwards in time relate to the direction the spiral is turning; matter versus antimatter corresponds to the chirality of the spiral.

Once viewed in this framework, history is, in a sense, a constant force pushing outward; alternatively, it can be interpreted as the unwinding of the internal metric of each particle.  Imagine a room completely filled with (slightly leaky) balloons, and suppose each balloon is fixed in place.  As the balloons slowly leak air, the distance between the surfaces of the balloons increases, even as the distance between the centers of each balloon remain the same.  In this view, the matter in the universe is constantly, slowly shrinking, such that by the time our known universe is cold and entropically dead, and starting to turn into particles for the next cycle of the universe, galaxies are approximately the size of the, say, electrons they will eventually be.

Either way, once you have history as a force pushing outward, gravity can be seen as pulling inward (for some range of distances, and in particular for the range of distances we observe), and counterbalancing this tendency.  Thus, for a given particle, its "motion" in this dimension is severely constrained; you get an apparently closed dimension of arbitrarily small size.  This constrains the number of effective spacetime dimensions to three (as, from this perspective, time, history, and distance, are all, in a sense, effectively the same dimension) - however, the spiral itself implies two additional (but not independent) complex dimensions, which themselves may be interpreted as the amplitude of the bending of spacetime.

Note that this implies that matter and antimatter, versus positive and negative electrical charge, are the same question, by virtue of the fact that antimatter travels in the opposite direction in "time"; it has reversed chirality of its spiral, and reversed motion, relative to matter.  Why does the antimatter equivalent of an electron, a positron, have a positive charge?  Because it's the same thing.

Then, we should expect no charged particles to be their own antiparticles, and no uncharged particles not to be their own antiparticles, which as far as I am aware is the case.

(With other things, there's also an implication that uncharged particles should all be bosons, that all bosons should be uncharged, that all bosons should travel at the speed of light, and that no bosons should have mass.  This is not the case, and will eventually require explanation here.)

Either way, we have another way of approaching the issue of the electrical force - although it may be interesting to note that the behavior of electricity continues to behave oddly at sufficient distances.