On the problem of completeness of QM: von Neumann against Einstein, Podolsky, and Rosen

TL;DR

This paper critically examines the arguments of EPR against quantum mechanics, revealing that their paradoxical conclusion stems from a misuse of von Neumann's projection postulate, which does not align with the formal axioms of QM.

Contribution

The paper clarifies the mismatch between EPR's critique and von Neumann's formalism, highlighting the improper application of the projection postulate in EPR's argument.

Findings

EPR's arguments do not align with von Neumann's formalism.

EPR misapplied the projection postulate to degenerate spectra.

EPR's conclusion on incompleteness is based on a misuse of QM axioms.

Abstract

We performed a comparative analysis of the arguments of Einstein, Podolsky and Rosen -- EPR, 1935 (against the completeness of QM) and the theoretical formalism of QM (due to von Neumann, 1932). We found that the EPR considerations do not match at all with the von Neumann's theory. Thus EPR did not criticize the real theoretical model of QM. The root of EPR's paradoxical conclusion on incompleteness of QM is the misuse of von Neumann's projection postulate. EPR applied this postulate to observables with degenerate spectra (which is totally forbidden by the axiomatics of QM).