  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 "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. There must be, they concluded, a more complete
description of physical reality behind quantum mechanics. There must be a
state, a hidden variable, characterizing the state of affairs in the world in
more details than the quantum mechanical state, something that also reflects
the missing elements of reality.
  Under some further but quite plausible assumptions, this conclusion 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 in the last three decades. 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.
