Thanks for the link; I should make an interesting comment in return.

Carl, if only all people would react this way, I’d only write link-posts from now on…

One of the mysteries of spin-1/2 quantum mechanics is why two eigenstates are sufficient to describe a state. Everyone knows how the math works, but physically, it is difficult to understand especially for those who wish their physics to have a classical interpretation.

In elementary particles, the electron is most naturally described as a combination of left and right handed particles. To get a left / right handed electron, you accelerate a regular electron in the direction / against the direction of its spin vector. How much do you accelerate it? To infinity, but not beyond. You have to get the electron to speed c. The left handed electron interacts weakly; the right handed one does not.

If one considers waves in 3 dimensions, say sound waves or classical light waves, to obtain sufficient degrees of freedom to describe an arbitrary direction wave requires that one begin with three degrees of freedom, say three waves travelling in perpendicular directions. This is one more than the quantum spin 1/2 case even though the electron is apparently built from components that do travel at speed c, and therefore should take 3 degrees of freedom, or maybe 6 (so that the waves can go either way, or you can account for position and momentum rather than just position), but certainly not 2.

When you replace the usual spin-1/2 basis states (spin up and spin down) with a Pauli MUB of 3 basis states, you end up with the classically expected 3 / 6 degrees of freedom. So MUBs are tied up with a more classical way of looking at quantum mechanics. From a preon point of view, this says that classical mechanics may be hiding underneath a quantum facade.

I guess I should admit that I’ve temporarily given up on the d=3 MUB case and am working on d=2 cases. Kea, I should have a post out soon with a new preon model that uses this idea.