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 :-)


Anonymous said...

No no no. You're conflating the unfamiliarity of an abstract mathematical description of natural phenomena with inherent weirdness. Quantum mechanics is no weirder than any other part of physics. Feynman failed to see that eventually people would be educated differently than he was, and that this education would include stuff he didn't have in school. Such a failure of imagination allows room for this quasi-mystical bullshit about quantum being weird, under the mistaken premise that people are intuitively familiar with some of the types of abstract modeling of the world we do. They are not familiar with any type of abstract modeling of any serious sort without the training a scientist gets.

Things have moved on, which is why it shouldn't be weird to your students unless you're not teaching them well enough or they aren't thinking about it enough. So please stop peddling an older generation's bullshit to the world, they already misunderstand what we do enough.

PS. Blogger really needs to start using a recaptcha for verification.

Anonymous said...

"For a long time foundations of quantum mechanics was dismissed by physicists as a fringe activity, suitable only for fuzzy headed philosophers."

Speaking as someone who occasionally does research in this subject, I'd add that it still is dismissed in this way by the vast majority of physicists. Enlightened informationalists are still a minority in the greater scheme of things. Even in quantum information, there are those who would like to distance the subject from any foundational fuzziness, and their numbers will only increase as the subject becomes more practical and experimentally viable. I suppose this is par for the course. As soon as a subject becomes practical, it ceases to be regarded as foundational.

Anonymous said...

It isn't weird. The literature is gradually reconciling classical and quantum ways of thinking.

Seth said...

I can't really express this notion well yet, but increasingly I get the feeling that QM has at least metaphorical bearing on human interactions. In the sense that our behavior has a sort of deterministic "cross section" without being deterministic at an event-by-event level. Also, that direct expression of a point of view can influence someone to oppositional behavior by a sort of "exclusion" principle.

Just an intuition, but I wonder if others can relate to it.

JTankers said...

I enjoyed the article. I find it more than a bit disturbing that most physicists aren't bothered enough by [standard] QM.

With bell's theorem fairly convincingly challenged on mathematical grounds [1][2], I fail to understand why a clear thinking, creative physicist would still prefer "Spooky Interaction at a Distance" over "hidden variables". But then again, physicists chose that infinitely complex and bizarre model over Einstein's simple model even before Bell's arguments decades later.

No one should be too surprised though, as the vast majority of physicists also overtly rejected Einstein's relativity theory, until relativity was clearly proven to be a superior model than what preceded it. I hope some of the physicists working on deterministic QM are correct and a proof can be presented to shed some empirical light on the true nature of QM [3].

But there is I think unfortunately little hope that most physicists will routinely think independently enough to question what they are taught when it appears bizarre. To learn that newly taught physicists do not even tend to find QM bizarre is amazing to me. Don't physicists like the idea of trying to find the simplest model that is at least equally accurate in predicting empirical outcomes? Isn't that still the goal?

[1] Professor Joy Christian, Oxford University Physics (2009/11), Disproofs of Bell, GHZ, and Hardy Type Theorems and the Illusion of Entanglement

[2] Professor Karl Hess, Beckman Institute Engineering/Physics and Professor Walter Philipp Illinois University Statistics/Mathmatics (2003/11) Breakdown of Bell's theorem for certain objective local parameter spaces

[3] New Scientist Magazine, Mark Buchanam (March 22, 2008), Quantum randomness may not be random,

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