A paradox first enunciated by Einstein et al. (1935), who proposed a thought experiment that appeared to demonstrate quantum mechanics to be an incomplete theory. The usual view of quantum mechanics says that a wave function determines the probabilities of an actual experimental result and that it is the most complete possible specification of the quantum state. Einstein et al. believed the predictions of quantum mechanics to be correct, but only as the result of statistical distributions of other unknown but real properties of the particles.

Bohm (1951) presented a paper in which he described a modified form of the Einstein-Podolsky-Rosen thought experiment which he believed to be conceptually equivalent to that suggested by Einstein et al. (1935), but which was easier to treat mathematically. Bohm suggested using two atoms with a known total spin of zero, separated in a way that the spin of each atom points in a direction exactly opposite to that of the other. In this situation, the angular momentum of one particle can be measured indirectly by measuring the corresponding vector of the other particle. Bell (1964) subsequently formulated Bell's inequalities, which seemed to be a physically reasonable condition of locality which imposed restrictions on the maximum correlations of the measurements of a pair of spin 1/2 particles formed somehow in the singlet state and moving freely in opposite directions. This inequality can be tested in a laboratory experiment because the statistical predictions of quantum mechanics are incompatible with any local hidden variables theory apparently satisfying only the natural assumptions of "locality," as shown by the predictions of Bell's inequalities.

Bell's Inequalities, Hidden Variables