# Homer Nodded: Von Neumann’s Surprising Oversight

@article{Mermin2018HomerNV, title={Homer Nodded: Von Neumann’s Surprising Oversight}, author={N. David Mermin and R{\"u}diger Schack}, journal={Foundations of Physics}, year={2018}, volume={48}, pages={1007-1020} }

We review the famous no-hidden-variables theorem in von Neumann’s 1932 book on the mathematical foundations of quantum mechanics (Mathematische Grundlagen der Quantenmechanik, Springer, Berlin, 1932). We describe the notorious gap in von Neumann’s argument, pointed out by Hermann (Abhandlungen der Fries’schen Schule 6:75–152, 1935) and, more famously, by Bell (Rev Modern Phys 38:447–452, 1966). We disagree with recent papers claiming that Hermann and Bell failed to understand what von Neumann… Expand

#### 14 Citations

von Neumann’s Theorem Revisited

- Philosophy
- Foundations of Physics
- 2021

According to a popular narrative, in 1932 von Neumann introduced a theorem that intended to be a proof of the impossibility of hidden variables in quantum mechanics. However, the narrative goes, Bell… Expand

Must hidden variables theories be contextual? Kochen & Specker meet von Neumann and Gleason

- Mathematics
- 2021

It is a widespread belief that the Kochen-Specker theorem imposes a contextuality constraint on the ontology of beables in quantum hidden variables theories. On the other hand, after Bell’s… Expand

Von Neumann's No Hidden Variable Theorem

- Mathematics, Physics
- 2020

Von Neumann use 4 assumptions to derive the Hilbert space (HS) formulation of quantum mechanics (QM). Within this theory dispersion free ensembles do not exist. To accommodate a theory of quantum… Expand

Bell’s Theorem: A Critical Analysis of an Orthodox View

- 2021

When used to prove the Bell inequality, the widely accepted counterfactual definiteness assumption constitutes an inconsistent hypothesis. It is not equivalent either to realism or determinism, and… Expand

The GHSZ Argument: A Gedankenexperiment Requiring More Denken

- Computer Science, Physics
- Entropy
- 2020

I reassess the gedankenexperiment of Greenberger, Horne, Shimony, and Zeilinger after twenty-five years, finding their influential claim to the discovery of an inconsistency inherent in high… Expand

Ideas Abandoned en Route to QBism

- Philosophy, Physics
- 2019

The interpretation of quantum mechanics known as QBism developed out of efforts to understand the probabilities arising in quantum physics as Bayesian in character. But this development was neither… Expand

From Gender to Gleason : The Case of Adam Becker ’ s What Is Real ?

- Mathematics
- 2019

It is easy to argue that the founders of quantum mechanics made statements which are opaque and confusing. It is fair to say that their philosophical takes on the subject are not infrequently… Expand

Understanding quantum mechanics: a review and synthesis in precise language

- Physics, Computer Science
- Open Physics
- 2019

This review is broad in scope, and aims to reflect enough of the literature to be representative of the current state of the subject, and to contribute to achieving greater consensus on how to understand quantum mechanics. Expand

Is the SIC Outcome There When Nobody Looks

- Computer Science, Physics
- 2018

Close study of three of the "sporadic SICs" reveals an illuminating relation between different ways of quantifying the extent to which quantum theory deviates from classical expectations. Expand

SICs and Bell Inequalities

- Psychology
- 2021

Close study of three sporadic SICs reveals an illuminating relation between different ways of quantifying the extent to which quantum theory deviates from classical expectations. In brief, the SIC… Expand

#### References

SHOWING 1-10 OF 11 REFERENCES

Deep Beauty: Is Von Neumann's “No Hidden Variables” Proof Silly?

- Mathematics
- 2011

Introduction In his Mathematical Foundations of Quantum Mechanics , John von Neumann presented a proof that the quantum statistics cannot be recovered from probability distributions over “hidden”… Expand

Von Neumann's Impossibility Proof: Mathematics in the Service of Rhetorics

- Mathematics, Physics
- 2017

According to what has become a standard history of quantum mechanics, in 1932 von Neumann persuaded the physics community that hidden variables are impossible as a matter of principle, after which… Expand

Von Neumann’s ‘No Hidden Variables’ Proof: A Re-Appraisal

- Mathematics, Physics
- 2010

Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann’s ‘no hidden variables’ proof fails to exclude any significant class of hidden variables. Bell raised the… Expand

On the Einstein-Podolsky-Rosen paradox

- Physics
- 1964

THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional… Expand

On the Problem of Hidden Variables in Quantum Mechanics

- Physics
- 1966

The demonstrations of von Neumann and others, that quantum mechanics does not permit a hidden variable interpretation, are reconsidered. It is shown that their essential axioms are unreasonable. It… Expand

Simultaneous measurability in quantum theory

- Mathematics
- 1968

This paper presents a study of what is sometimes regarded as the conceptual heart of quantum theory, namely, the orthodox ‘physical’ interpretation of non-commuting operators as representatives of… Expand

Hidden variables and the two theorems of John Bell

- Physics
- 1993

Although skeptical of the prohibitive power of no-hidden-variables theorems, John Bell was himself responsible for the two most important ones. I describe some recent versions of the lesser known of… Expand

Die naturphilosophischen Grundlagen der Quantenmechanik

- Naturwissenschaften
- 2005

//718// Das physikalische Ergebnis der Quantenmechanik, von dem die Erschutterung altgewohnter naturphilosophischer Auffassungen, insbesondere der Kausalvorstellungen ausgeht, besagt, das der… Expand