Why Einstein, Podolsky and Rosen did not prove that quantum mechanics is `incomplete'

TL;DR

This paper argues that the EPR argument claiming quantum mechanics is incomplete is flawed due to logical errors, and that the proposed experiment cannot definitively establish the theory's completeness.

Contribution

It identifies logical errors in the EPR argument and clarifies why the proposed experiment cannot prove quantum mechanics is incomplete.

Findings

EPR's conclusion is invalidated by logical errors

The proposed experiment cannot determine the completeness of quantum mechanics

Wave function properties lead to vanishing measurement probabilities

Abstract

It is shown that the Einstein-Podolsky-Rosen conclusion concerning the `incompleteness' of Quantum Mechanics is invalidated by two logical errors in their argument. If it were possible to perform the proposed gedanken experiment it would, in fact, show that Quantum Mechanics is `complete' for the observables discussed. Because, however, of the non square-integrable nature of the wave function, the proposed experiment gives vanishing probabilities for measurements performed in finite intervals of configuration or momentum space. Hence no conclusion as to the `completeness', or otherwise, of Quantum Mechanics can be drawn from the experiment.