The Perimeter Institute has a talk on the Feynman chessboard / checkerboard model scheduled for a few days from now. This will be recorded and you can play it back, sometime after November 18th. Links:(adsbygoogle = window.adsbygoogle || []).push({});

Speaker(s): Garnet Ord - Ryerson University

Ord's website: http://www.scs.ryerson.ca/~gord/

Abstract: Conventional quantum mechanics answers this question by specifying the required mathematical properties of wavefunctions and invoking the Born postulate. The ontological question remains unanswered. There is one exception to this. A variation of the Feynman chessboard model allows a classical stochastic process to assemble a wavefunction, based solely on the geometry of spacetime paths. A direct comparison of how a related process assembles a Probability Density Function reveals both how and why PDFs and wavefunctions differ from the perspective of an underlying kinetic theory. If the fine-scale motion of a particle through spacetime is continuous and position is a single valued function of time, then we are able to describe ensembles of paths directly by PDFs. However, should paths have time reversed portions so that position is not a single-valued function of time, a simple Bernoulli counting of paths fails, breaking the link to PDF's! Under certain circumstances, correcting the path-counting to accommodate time-reversed sections results in wavefunctions not PDFs. The result is that a single `switch' simultaneously turns on both special relativity and quantum propagation. Physically, fine-scale random motion in space alone yields a diffusive process with PDFs governed by the Telegraph equations. If the fine-scale motion includes both directions in time, the result is a wavefunction satisfying the Dirac equation that also provides a detailed answer to the title question.

PI talk link: http://pirsa.org/08110045

A related arXiv paper by Garnet Ord is:

http://arxiv.org/abs/quant-ph/0411005

A problem with the above paper is that it seems to be in 1+1 dimensions in stead of 3+1.

Other Ord articles:

http://arxiv.org/find/quant-ph/1/au:+Ord_G/0/1/0/all/0/1

Peter Plavchan's paper giving the 3+1 version of Feynman's checkerboard:

http://www.brannenworks.com/plavchan_feynmancheckerboard.pdf

As some of you know, I'm a big fan of the Feynman checkerboard model. It can be generalized to 3 dimensions. I wrote up a blog post with a link to an article showing the generalization earlier this year:

http://carlbrannen.wordpress.com/2008/04/21/481/

It discusses the Lorentz violation that comes with taking the idea from 1+1 dimensions to 3+1.

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# PI talk on Feynman Checkerboard Model and the wave function

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