Friday, July 06, 2012

Quantum mechanics with taste of cabbage roll

Yesterday our institute hosted Helen Fay Dowker. She gave a talk at our traditional thursday lunch meetings and the title was something like the path integral interpretation of quantum mechanics.

Fay gave an introduction about Dirac's 1932 paper that the lagrangian approach to classical mechanics was probably more fundamental than the hamiltonian approach because the former is relativistically invariant whereas the latter is "essentially nonrelativistic." This is because in the definition of hamiltonian time is an exceptional dimension and the evolution occurs in that dimension. This breaks the equality between time and space that general relativity is based on.

In a path integral we sum over histories from which the physical world is described directly in terms of events in spacetime. The path integral approach, however,has been championed in more recent times by Jim Hartle in a probabilistic nature and by Raphael Sorkin in non-probabilistic nature.

It was almost half past since I put the last piece of the cabbage rolls in my mouth that Tony Leggett asked whether Sorkin's approach with its zero measure can potentially give rise to Yang's experiment... . I remembered a few years ago when I was at the Perimeter Institute in a talk Raphael gave about his causal set I asked this question in a very shaky way with lots of fears and he gave answers but the end of the story as far as I remember was that he didn't know, but he has thought about that.

This path integral talk would have been tasted better with noodles, of course!

And that is my memo.

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