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:(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Spin and position and mutually unbiased bases

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