The theorem stating that quantum mechanics cannot be explained by local hidden variables is Bell's theorem.
Introduced by physicist John Stewart Bell in 1964, the theorem grew out of the Einstein–Podolsky–Rosen paradox and the puzzling phenomenon of quantum entanglement. Bell showed that any theory combining locality with hidden, pre-existing values for measurement outcomes must obey mathematical limits called Bell inequalities.
Quantum mechanics predicts—and experiments observe—correlations between entangled particles that violate those inequalities. This rules out local hidden-variable theories as complete explanations of quantum phenomena. It does not mean that every hidden-variable theory is impossible: nonlocal theories, such as pilot-wave theory, remain logically possible.
A common mix-up is to treat the EPR paradox as the theorem itself. EPR motivated the question, while Bell supplied the decisive test. The Kochen–Specker theorem addresses contextuality, and the Leggett–Garg inequality concerns macrorealism rather than locality in entangled-particle experiments.