Bell's theorem

Bell's theorem shows that no theory satisfying local causality and measurement independence can reproduce every correlation predicted by quantum mechanics.

Bell inequality: A mathematical bound on correlations required by local hidden-variable theories. It makes Bell's assumptions testable through observed correlations.
John Stewart Bell: A Northern Irish physicist whose work established Bell's theorem and shaped foundations of quantum theory. His 1964 argument converted a philosophical dispute into a mathematical one.
Aspect's experiment: A 1982 photon-correlation experiment by Alain Aspect and colleagues that tested Bell inequalities with rapidly switched analyzers. It provided influential evidence against local hidden-variable explanations.
Locality (physics): The principle that physical influences do not propagate faster than light between spatially separated events. Bell's local-causality condition is stronger and more precise than everyday uses of locality.
CHSH inequality: A Bell inequality involving two measurement choices per observer and a bound of 2 on a correlation expression. It is the best-known experimentally practical form of Bell's theorem.
EPR paradox: A 1935 argument that quantum mechanics might be incomplete because it predicts distant correlations. Bell formulated a test of the local-realist reasoning behind this challenge.
Loophole-free Bell test: An experiment designed to close major detection and locality loopholes in tests of Bell inequalities. The 2015 experiments jointly addressed loopholes that weakened earlier tests.
Realism (philosophy of science): The view that physical properties exist independently of observation or measurement. Bell violations alone do not refute realism without additional assumptions.
Local hidden-variable theory: A model in which outcomes depend on shared variables and local measurement settings, without distant influences. Bell's theorem rules out this class as a complete account of quantum predictions.
Bohmian mechanics: A deterministic interpretation of quantum mechanics with particle positions guided by a nonlocal wave function. It preserves hidden variables by abandoning locality, illustrating Bell's constraint.

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