For 10 points, identify this no-go theorem which asserts that local hidden variable theories are incompatible with quantum mechanics.
A theorem extending this statement concerns the impossibility of embedding a set of non-commuting observables in a commutative algebraic structure; that extension is the Kochen-Specker theorem. In a quip reminiscent of Wolfgang Pauli, this statement's formulator declared a similar but faulty theorem by John von Neumann to be "not merely false but foolish" due to its unphysical assumptions. Aspect, Grangier, and Roger verified the predictions of this statement using two-photon atomic transitions from calcium cascade decay. The bounds that this statement places on the results of a two-channel (*) detector experiment are equivalent to the later-developed CHSH inequality. This theorem, which was introduced in the paper "On the Einstein Podolsky Rosen Paradox," is usually explained in terms of correlations between simultaneous measurements of entangled particles. For 10 points, identify this no-go theorem which asserts that local hidden variable theories are incompatible with quantum mechanics.
A theorem extending this statement concerns the impossibility of embedding a set of non-commuting observables in a commutative algebraic structure; that extension is the Kochen-Specker theorem.
Bell's theorem [or Bell's inequality]