In 1935, Einstein, Podolsky, and Rosen (EPR) published an important paper in which they claimed that the whole formalism of quantum mechanics together with what they called a "Reality Criterion" imply that quantum mechanics cannot be complete. That is, there must exist some elements of reality that are not described by quantum mechanics. They concluded that there must be a more complete description of physical reality involving some hidden variables that can characterize the state of affairs in the world in more detail than the quantum mechanical state. This conclusion leads to paradoxical results. As Bell proved in 1964, under some further but quite plausible assumptions, this conclusion that there are hidden variables implies that, in some spin-correlation experiments, the measured quantum mechanical probabilities should satisfy particular inequalities (Bell-type inequalities). The paradox consists in the fact that quantum probabilities do not satisfy these inequalities.  And this paradoxical fact has been confirmed by several laboratory experiments since the 1970s. Some researchers have interpreted this result as showing that quantum mechanics is telling us nature is non-local, that is, that particles can affect each other across great distances in a time too brief for the effect to have been due to ordinary causal interaction.  Others object to this interpretation, and the problem is still open and hotly debated among both physicists and philosophers. It has motivated a wide range of research from the most fundamental quantum mechanical experiments through foundations of probability theory to the theory of stochastic causality as well as the metaphysics of free will.   PDF version of the article  Author Information: László E. Szabó Email: leszabo@philosophy.elte.hu Eötvös University Budapest, Hungary © 2008