Von Neumann's Hidden-Parameter Proof

Because the mathematical form of von Neumann's hidden-parameter proof is not well known, its scope has sometimes been unjustifiably narrowed by commentators. The proof is here reproduced in the more familiar Dirac calculus and its precise import made clearer. In particular, it is emphasized that the proof proceeds independently of both the basic statistical assumption of quantum mechanics: 〈R〉av = 〈φ|R|φ〉, and the extension of this assumption to mixtures: 〈R〉av = Tr(UR), where U = Σn|φn〉wn〈φn|. Mention is also made of some recent criticisms of the von Neumann proof.