On n Tuesday, July 16, 2002, at 11:02 Tim May wrote: >On Tuesday, July 16, 2002, at 10:39 AM, Peter Fairbrother wrote: >> 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.