Spin and position and mutually unbiased bases

[CarlB]

If you measure the position of an elementary particle exactly, then its position becomes unknown. So consecutive measurements of position do not give the same result. There's been some recent papers by G. Svetlichny, J. Tolar, and G. Chadzitaskos that show that position measurements move around because the Feynman path integrals can be written in terms of transitions between "mutually unbiased bases", that is, between bases where the transition probabilities from the states in one base to the states in the other are all equal. See:

Feynman's Integral is About Mutually Unbiased Bases
George Svetlichny
http://arxiv.org/abs/0708.3079 and

Feynman's Path Integral and Mutually Unbiased Bases
J Tolar, G Chadzitaskos
http://arxiv.org/abs/0904.0886

On the other hand, the behavior of spin is very stable. If you measure the spin of a free particle once, it stays like that and you get the same result the next time you measure it. But the above author's characterization of the Feynman path integral suggests that it might be useful to make the same analysis of spin. That is, we can assume that spin does move around from mutually unbiased base to mutually unbiased base.

For spin-1/2 there are three mutually unbiased bases at most. They could be any three orthogonal directions. If we think of spin on these bases we can perform Feynman path integrals to see what the long term evolution of spin is (under the assumption that it moves from mutually unbiased base to mutually unbiased base).

I've resummed these path integrals and showed that for spin-1/2 you get three stable solutions. Each can be thought of as a stable spin-1/2 that arises from an unstable spin-1/2 theory. And this seems to be related to the generations. The paper is here:
http://www.brannenworks.com/Gravity/EmergSpin.pdf

I'm planning on submitting it to Foundations of Physics and arXiv after I get some critiques of it. Thanks for any comments,

Carl Brannen

 

[CarlB]

The paper was eventually accepted by Foundations of Physics and given the following DOI, where it can be read, if your institution has Found. of Phys:
http://dx.doi.org/10.1007/s10701-010-9465-8

From the backlog of "on line first" articles, I would guess that it is actually printed about a year from now, say March-April 2011.

 

[MTd2]

Congratulations Carl!

So, can we say that, in terms of Spin Foams, classical gravity is SM-like with N different spin configurations/charges -> infinity?

 

[CarlB]

So, can we say that, in terms of Spin Foams, classical gravity is SM-like with N different spin configurations/charges -> infinity?

Hey, that's wayyyy over my pay grade. I did send a paper into the annual gravitation essay contest but it is a little, uh, crackpotty, and it didn't win anything:
http://brannenworks.com/Gravity/Gravity2010Brannen.pdf

It gives some calculations that relate the "Spin Path Integrals and Generations" paper to gravity. The basic idea is to see how the left and right handed particles interact with gravity. In the first approximation this means a uniform acceleration, so the paper computes how the probability that a particle is left or right handed must change in order for the particle to undergo a uniform acceleration (relativistically).

Carl

P.S. Give me a second and I'll upload the (almost) current copy of the "Spin Path Integrals and Generations" paper. Okay, here it is:
http://brannenworks.com/Gravity/EmergSpin.pdf