Challenging the Gospel: Grete Hermann on von Neumann’s No-Hidden-Variables Proof

Abstract

Von Neumann’s no-go theorem against the possibility of hidden variables in quantum mechanics, as published in his 1932 book Mathematische Grundlagen der Quantenmechanik, soon attained a ‘cult’ status and was considered the last word on the subject, not to be challenged. But in 1935 Grete Hermann did challenge this gospel by criticising the von Neumann proof on a fundamental point. This challenge was not widely known at the time, and her criticism had no impact whatsoever. Thirty years later, John S. Bell provided a critique of von Neumann’s proof quite similar to Hermann’s, but Bell’s work did have great foundational impact. In this chapter, after reviewing the details of von Neumann’s proof and its reception, I shall describe Hermann’s 1935 criticism of von Neumann’s argument, and compare it to Bell’s. Finally, I shall discuss the reception (or lack thereof) of Hermann’s criticism, and speculate about why Hermann’s anticipation of Bell’s argument was not—and continues not to be—widely known.

I wish to thank Guido Bacciagaluppi and especially Elise Crull , without whom this chapter would never have been written.