A theorem stating that no local hidden-variables theory can make predictions in agreement with those of quantum mechanics. Local hidden-variables theories give rise to a result, called Bell’s inequality, which is one of many similar results concerning the probabilities of two events both occurring in well-separated parts of a system. The British physicist John S. Bell (1928–90) showed in 1964 that quantum mechanics predicts a violation of the inequalities, which are consequences of local hidden-variables theories. Experiments are in agreement with quantum mechanics rather than local hidden-variables theories by violating Bell’s inequality, in accordance with Bell’s theorem. See also Leggett’s theorem; Quantum Entanglement (Feature).

http://www.drchinese.com/David/Bell.pdf The original 1964 paper in Physics