Homer nodded: von Neumann's surprising oversight

TL;DR

This paper reviews von Neumann's no-hidden-variables theorem, highlighting historical gaps and clarifying misunderstandings about its significance in quantum foundations.

Contribution

It clarifies the historical and conceptual misunderstandings surrounding von Neumann's theorem and discusses the overlooked gap identified by Hermann and Bell.

Findings

Identifies a gap in von Neumann's original proof

Clarifies the historical context of the theorem

Reevaluates the theorem's significance in quantum foundations

Abstract

We review the famous no-hidden-variables theorem in John von Neumann's 1932 book on the mathematical foundations of quantum mechanics. We describe the notorious gap in von Neumann's argument, pointed out by Grete Hermann in 1935 and, more famously, by John Bell in 1966. We disagree with recent papers claiming that Hermann and Bell failed to understand what von Neumann was actually doing.