Talk:Gleason's theorem

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Gleason's theorem has been listed as one of the Natural sciences good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it.
Review: March 2, 2020. (Reviewed version).

Bohm's theory[edit]

I like this article very much, but I would suggest adding one sentence. Currently, the article says:

"The theorem is often taken to rule out the possibility of hidden variables in quantum mechanics."

If you say this, I think that you need to add a caveat. Gleason's theorem doesn't apply to Bohm's theory, which is the only popular hidden variable theory nowadays. Gleason's theorem assumes that you begin by describing a particle by a state in Hilbert space, but Bohm doesn't do that. (For him, a particle has a definite position at all times.) This is a really big loophole, because other hidden-variable approaches could just dispense with Hilbert space altogether.

Personally, I don't really like Bohm's theory, but it does provide a nice counterexample to most "general" statements about hidden-variable theories (as evidenced here)! Sthinks (talk) 07:39, 9 December 2007 (UTC)[reply]

I agree with this comment. I was quite surprised not to see a mention of Bohm's "pilot wave" model https://en.wikipedia.org/wiki/Pilot_wave_theory. "Bohmian Mechanics" seems perfectly sound, though many would consider its non-locality a flaw. Bohmian Mechanics is based on refactoring the Schrodinger equation, so in a sense offers no new predictions. It's a kind of isomorphism to conventional QM, only with a deterministic, hidden variable interpretation. Wouldn't it therefor be allowed by Gleason's Theorem? 24.5.52.167 (talk) 16:20, 26 July 2022 (UTC)[reply]