In 1964, he wrote a paper entitled "On the Einstein-Podolsky-Rosen Paradox". There is some disagreement regarding what Bell's inequality—in conjunction with the EPR analysis—can be said to imply. Bell held that not only local hidden variables, but any and all local theoretical explanations must conflict with the predictions of quantum theory: "It is known that with Bohm's example of EPR correlations, involving particles with spin, there is an irreducible e nonlocality." According to an alternative interpretation, not all local theories in general, but only local hidden variables theories (or "local realist" theories) have shown to be incompatible with the predictions of quantum theory.
The theorem was first published as an arXiv preprint with Pusey as the principal author, a subsequent version published in Nature Physics, that states the theorem that either the quantum state corresponds to a physically real object and is not merely a statistical tool, or else all quantum states, including non-entangled ones, can communicate by action at a distance. This preliminary result has been referred to as Pusey's theorem or the PBR theorem, and has been cited by theoretical physicist Antony Valentini as "the most important general theorem relating to the foundations of quantum mechanics since Bell's theorem".