Towards a Deeper Understanding of the Einstein–Podolsky–Rosen Problem

Abstract

Most of the nearly innumerable attempts to provide for a sound understanding of the gedanken experiment of Einstein, Podolsky, and Rosen (EPR) contain additional ideas, notions or features imposed on pioneer or traditional quantum mechanics (TQM). In the present paper the problem is analyzed without employing any new or philosophically contested concept. We do even without referring to the probability calculus, and we especially avoid any admixture of realistic ideas. Neither entanglement nor special features of “states” are used. Instead, formulating strictly within the framework of TQM and using an ensemble approach, the crucial point is boiled down to the decision between separability and non-separability. The corresponding second-order correlation functions Δs and Δn−s, resp., which predict the experimental outcome, may differ by a factor of 2 if certain operator pairs are maximally non-commuting. Even in the case of commuting pairs, an experimentally relevant difference between the Δ-functions might exist. Taking into account the experimental evidence, it is unavoidable to accept that the sub-ensembles involved in EPR-type experiments are in fact non-separable. This result has been obtained without resort to Bell's inequality.