Quantum mechanics as a nonergodic classical statistical theory

Abstract

Another interpretation of ψ, the quantum-mechanical wave function, is presented. The nonergodic statistical interpretation is a statistical interpretation, and differs from the statistical interpretation presented by Ballentine only in its ergodic properties (that is in its predictions for time and ensemble averages). The conceptual advantages and disadvantages of this interpretation are analysed from the viewpoint of local hidden-variable theories. The advantages are the following. The nonergodic statistical interpretation is consistent with the local hidden-variable theories that agree with quantum mechanics in the polarization correlation experiments. A corollary of this result is that the statistical interpretation is not neutral to the question of the existence of local hidden-variable theories but is inconsistent with such theories. In this interpretation there is no joint-probability distribution problem as in the statistical interpretation. This interpretation opens up local hidden-variable explanations of interference effects hitherto not considered. This interpretation has the seemingly contradictory properties that it always agrees with the numerical predictions of quantum mechanics and yet is experimentally distinguishable from both the statistical and Copenhagen interpretations. The disadvantages are that this view depends physically on assigning certain radical properties to space. Mainly, the local hidden-variable theories which motivate this view must presuppose the existence of a field or medium with stable states or memory in empty space.