Editing Hidden-variable theory (section)

=== Von Neumann's proof ===
[[John von Neumann]] in his 1932 book ''[[Mathematical Foundations of Quantum Mechanics]]'' had presented a [[Mathematical Foundations of Quantum Mechanics#No hidden variables proof|proof]] that there could be no "hidden parameters" in quantum mechanics. The validity of von Neumann's proof was questioned by [[Grete Hermann]] in 1935, who found a flaw in the proof. The critical issue concerned averages over ensembles. Von Neumann assumed that a relation between the [[expected value]]s of different observable quantities holds for each possible value of the "hidden parameters", rather than only for a statistical average over them.<ref>{{cite book|first=Max |last=Jammer |author-link=Max Jammer |title=The Philosophy of Quantum Mechanics |pages=265–274 |year=1974 |publisher=John Wiley and Sons |isbn=0-471-43958-4}}</ref><ref>{{Cite journal |last1=Mermin |first1=N. David |author-link1=N. David Mermin |last2=Schack |first2=Rüdiger |date=September 2018 |title=Homer Nodded: Von Neumann's Surprising Oversight |journal=Foundations of Physics |language=en |volume=48 |issue=9 |pages=1007–1020 |arxiv=1805.10311 |bibcode=2018FoPh...48.1007M |doi=10.1007/s10701-018-0197-5 |issn=0015-9018 |doi-access=free}}</ref> However Hermann's work went mostly unnoticed until its rediscovery by John Stewart Bell more than 30 years later.<ref>Hermann, G.: Die naturphilosophischen Grundlagen der Quantenmechanik (Auszug). Abhandlungen
der Fries’schen Schule 6, 75–152 (1935). English translation: Chapter 15 of “Grete Hermann —
Between physics and philosophy”, Elise Crull and Guido Bacciagaluppi, eds., Springer, 2016, 239-
278. [Volume 42 of Studies in History and Philosophy of Science]</ref><ref>{{Cite journal |last=Del Santo |first=Flavio |date=2022-01-02 |title=Beyond Method: The Diatribe Between Feyerabend and Popper Over the Foundations of Quantum Mechanics |journal=International Studies in the Philosophy of Science |language=en |volume=35 |issue=1 |pages=5–22 |arxiv=2108.13121 |doi=10.1080/02698595.2022.2031430}}</ref>

The validity and definitiveness of von Neumann's proof were also questioned by [[Hans Reichenbach]], and possibly in conversation though not in print by Albert Einstein. Reportedly, in a conversation circa 1938 with his assistants [[Peter Bergmann]] and [[Valentine Bargmann]], Einstein pulled von Neumann's book off his shelf, pointed to the same assumption critiqued by Hermann and Bell, and asked why one should believe in it.<ref>{{cite book|first=Hans |last=Reichenbach |author-link=Hans Reichenbach |title=Philosophic Foundations of Quantum Mechanics |year=1944 |publisher=University of California Press |page=14 |oclc=872622725}}</ref><ref>{{cite book|last=Wick|first=David|chapter=Bell's Theorem |year=1995|title=The Infamous Boundary: Seven Decades of Heresy in Quantum Physics |publisher=Springer |location=New York|doi=10.1007/978-1-4612-4030-3_11|isbn=978-0-387-94726-6 |page=286}}</ref> [[Simon B. Kochen|Simon Kochen]] and [[Ernst Specker]] rejected von Neumann's key assumption as early as 1961, but did not publish a criticism of it until 1967.<ref>{{Cite book |author-first1=John |author-last1=Conway |author-link1=John Horton Conway |author-first2=Simon |author-last2=Kochen |author-link2=Simon B. Kochen |chapter=The Geometry of the Quantum Paradoxes |pages=257–269 |title=Quantum [Un]speakables: From Bell to Quantum Information |date=2002 |publisher=Springer |editor-first1=Reinhold A. |editor-last1=Bertlmann |editor-link1=Reinhold Bertlmann |editor-first2=Anton |editor-last2=Zeilinger |editor-link2=Anton Zeilinger |isbn=3-540-42756-2 |location=Berlin |oclc=49404213}}</ref>