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Simple proof of Bell theorem. Top: assuming any probability distribution among 8 possibilities for values of 3 binary variables ABC, we always get the above inequality. Bottom: example of its violation using quantum Born rule: probability is normalized square of amplitude.
New explanation of Bell's theorem added recently by Joseph Boone is nice, but I have a terminological objection. The mathematical proposition as formulated is but a special case of Boole–Fréchet inequalities (as noted in the article), well-known long ago before Bell, rather trivial, and unrelated to quanta. I feel it rather humiliating for Bell, to say that this trivial remark IS his great achievement. If THIS is called Bell theorem, then, what is the name for "No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics"? Boris Tsirelson (talk) 06:22, 29 August 2017 (UTC)
Bell's corollary? YohanN7 (talk) 10:16, 29 August 2017 (UTC)
I also struggle with this terminology, and decided Bell's theorem is "No physical theory of local hidden variables can ever reproduce ...", and Bell's inequality is what everyone seems to understand. And, I refer to a "Bell's theorem experiment" as any effort to investigate this spookiness (regardless of whether the experimentalists even know that a local hidden variable is). I for one, would be hard pressed to define "local hidden variable", but have no great desire to do so. This is all just my opinion--I am no expert on this junction between physics and philosophy.--Guy vandegrift (talk) 16:06, 30 August 2017 (UTC)