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Saturday, March 01, 2008

Bell and GHZ: spooky action at a distance

I think it is safe to say that no one understands quantum mechanics. -- Richard Feynman

Recently I've been lecturing on quantum weirdness (in Einstein's terminology, "spooky action at a distance") in my graduate quantum mechanics class. The main result is Bell's theorem:

No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.

Usually this result is proved using the Bell inequalities, which have been tested experimentally. The problem with the Bell inequalities is that they are statistical in nature. I prefer to discuss the so-called GHZ states:

| GHZ > = | 000 > - | 111 >

(after Greenberger, Horne and Zeilinger), with which one can demonstrate a much sharper disagreement between local reality and quantum mechanics.

It's interesting that so much time elapsed between Einstein's 1935 paper with Podolsky and Rosen (EPR) that first discussed spooky action at a distance, and Bell's theorem in 1964. Bell was a particle theorist working at CERN who only did foundations of quantum mechanics on the side (he's also the Bell in the Adler-Bell-Jackiw anomaly in quantum field theory). The GHZ paper didn't appear until 1989. For a long time foundations of quantum mechanics was dismissed by physicists as a fringe activity, suitable only for fuzzy headed philosophers. It's only recently, with the explosion of work in quantum information, that there has been renewed interest in the subject.

I find that the hardest thing about teaching this material in class is that, after half a year of training students' brains to think quantum mechanically, it is extremely difficult to get them to feel the weirdness of Bell's theorem and spooky action. It all seems quite normal to them in the context of the course -- they know how to calculate, and that's just how quantum mechanics works!

For my limited thoughts on quantum foundations (mostly about many worlds or "no collapse" formulations), see this talk (PDF) I gave at the Institute for Quantum Information at Caltech, and these blog posts.

Amazingly, I found almost all the reference links above (to GHZ, Bell's theorem, Bell inequality, EPR) on Wikipedia!

Note added: See Dave Bacon on ScienceBlogs for more discussion and some comments. It appears many younger physicists claim to not find QM weird. However, there may be some selection bias towards researchers in quantum information, who generally work in a non-relativistic setting, and may not have thought as much about causality, the light cone, the intricate spacetime structure of quantum field theory, etc. (i.e., unlike Einstein). Or, it could really be a generational change :-)

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