Correlations without joint distributions in quantum mechanics

Leon W. Cohen

Kazimierz Urbanik

Willem M. de Muynck, Peter A. E. M. Janssen, Alexander Santman

Roderick I. Sutherland

It is shown that the uncorrelated joint distribution, when adopted for quantum mechanics, is not (despite initial appearances to the contrary) in conflict with the known correlations between position and momentum in the classical limit. It is therefore not excluded on these grounds as a possible joint distribution expression for quantum mechanics.

Richard Healey

Shasanka Mohan Roy, Virendra Singh

Present quantum theory, which is statistical in nature, does not predict joint probability distribution of position and momentum because they are noncommuting. We propose a deterministic quantum theory which predicts a joint probability distribution such that the separate probability distributions for position and momentum agree with usual quantum theory. Unlike the Wigner distribution the suggested distribution is positive definite. The theory predicts a correlation between position and momentum in individual events.