On n Tuesday, July 16, 2002, at 11:02 Tim May wrote:

On Tuesday, July 16, 2002, at 10:39 AM, Peter Fairbrother wrote:

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Oh dear. QM does rule out internal states. I didn't think I would have to explain why I capitalised "Bell", but perhaps it was a bit too subtle. Google "Bell" and "inequalities", and go from there.

I disagree. Bell's Inequality is not dependent on QM...it's a mathematical statement about the outcomes of measurements where stochastic processes play a role. The fact that QM is strongly believed to involve stochastic processes is why Bell's inequality shows up prominently in QM. However, we cannot then use B.I. to prove things about QM.

It's a statement about quantum mechanics. Quantum mechanics and the violation of bell's inequality rest on the inseparability of a quantum state. Typically, that means a test using an epr pair, i.e. a pair of S = 1 photons with total J = 0, so that the pair behaves as a single object with J = 0. The pair MUST be originate from the same quantum process, (e.g., a single \pi_{0} decay), not as two arbitrarily selected photons from a stochastic process (e.g., 2 photons selected at random from the 4 produced in the decay of two pions). In short, quantum mechanics is not stat mech.

A more persuasive proof of why hidden variables are not viable in QM is the work done on extending some theorems about Hilbert spaces. Namely, Gleason's theorem from the mid-50s, later extended by Kochen and Specker in the 1960s. The Kochen-Specker Theorem is accepted as the "no go" proof that hidden variables is not viable.

While K-S is an improvement, it's fundamentally the same idea as bell's but eliminates a loop-hole: From: http://plato.stanford.edu/entries/kochen-specker/ "This is the easiest argument against the possibility of an HV interpretation afforded by Gleason's theorem. Bell (1966: 6-8) offers a variant with a particular twist which later is repeated as the crucial step in the KS theorem. (This explains why some authors (like Mermin 1990b) call the KS theorem the Bell-Kochen-Specker theorem; they think that the decisive idea of the KS theorem is due to Bell.[3]) He proves that the mapping dictates that two vectors and mapped into 1 and 0 cannot be arbitrarily close, but must have a minimal angular separation, while the HV mapping, on the other hand, requires that they must be arbitrarily close." In any case, quantum mechanics is well established by a lot of convincing arguments, even without any of the above to rely upon.