Monday, March 12, 2007

Bell's theorem: My reading of it (at last)

It was a supercilious Wired magazine article from earlier this year that inspired me update my 27 you QM knowledge.
Ultimately, the answer is bound to be unnerving: According to a famous doctrine called Bell’s Inequality, for entanglement to square with relativity, either we have no free will or reality is an illusion. Some choice.
- Lucas Graves, New York City-based writer
I turned to the Wikipedia article, but I couldn't make sense of it. Now that I've read a bit more, I think the article is actually quite a mess. It feels like the battleground of a religious conflict, a not implausible scenario. I didn't dare edit it, but I added this as a comment:
I'm not a physicist, so I'm loathe to edit the original article. Based on my slow reading of Gribbin (Schrodinger's Kittens, 1994), however, this comes across as a particularly messy article.

For example, the article refers to von Neumann's proof against local variables, but Gribbin claims that proof was demolished by Bell. If that is true, it should not be mentioned here as it would be of only historic significance.

I'll paraphrase below how Gribbin describes Bell's Theorem and its modern consequences. If this makes sense I suggest it be incorporated with a citation to Gribbin (Schrodinger's Kitten). I think I can see pieces of Gribbin's lucid summary in the article, but the message is fragmented and expressed in unnecessarily formal language.

Bell's Theorem showed that if non-locality ("spooky action at a distance", instaneous correlation of polarization states, etc) were found to occur, irregardless of any interpretation of quantum mechanics, then physics had to abandon one of two cherished beliefs:

1. That the world exists independently of our observations of it.
2. That there is no communication faster than the speed of light.

Subsequently non-locality has been shown, several times, to occur. That means we have to give up on either the "persistent world" or faster than light communications. Not surprisingly, physicists have decided the lesser evil is to accept a faster than light communication -- as long as that communication carries no "meaning". In other words, "meaning" cannot travel faster than light.
How does this translate to Lucas Grave's choice between free will and "reality is an illusion"? The illusion part is easy, that's the #1 choice.

I think the "free will" issues comes as a consequence of "faster than light" communication. In physics "faster than light" has usually been thought to be the equivalent of "traveling backwards in time". If a message is sent from the future and measured in the past, then it seems the future is predestined. The message cannot fail to be sent.

My sense is most physicists have opted for choice #2, but since nobody's figured out a way to send a meaningful or actionable message faster than light, #2 has been expressed (my words) as "Meaning cannot travel faster than light".

I don't know if this gives any options for "free will", but I think that is how the Wired quote came about. A predestined universe seems a bit claustrophobic, so maybe physicists will figure out a way that a meaningless (infinite entropy) message can travel faster than light without implying a retro-temporal signal.

Yech. We need some more options.

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