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

@article{Bub2010VonN,
  title={Von Neumann’s ‘No Hidden Variables’ Proof: A Re-Appraisal},
  author={Jeffrey Bub},
  journal={Foundations of Physics},
  year={2010},
  volume={40},
  pages={1333-1340}
}
  • J. Bub
  • Published 2010
  • Mathematics, Physics
  • Foundations of Physics
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 question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense ‘like Bohm’s theory.’ His seminal result provides a positive answer to the question. I argue that Bell’s analysis misconstrues von Neumann’s argument. What von Neumann proved was the… Expand
On the Unconditional Validity of J. von Neumann's Proof of the Impossibility of Hidden Variables in Quantum Mechanics
The impossibility of theories with hidden variables as an alternative and replacement for quantum mechanics was discussed by J. von Neumann in 1932. His proof was criticized as being logicallyExpand
von Neumann’s Theorem Revisited
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, BellExpand
Von Neumann's Impossibility Proof: Mathematics in the Service of Rhetorics
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 whichExpand
Must hidden variables theories be contextual? Kochen & Specker meet von Neumann and Gleason
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’sExpand
(Never) Mind your p’s and q’s: Von Neumann versus Jordan on the foundations of quantum theory
In 1927, in two papers entitled “On a new foundation [Neue Begründung] of quantum mechanics,” Pascual Jordan presented his version of what came to be known as the Dirac-Jordan statisticalExpand
Homer Nodded: Von Neumann’s Surprising Oversight
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,Expand
Quantum entanglement
Expository paper providing a historical survey of the gradual transformation of the “philosophical discussions” between Bohr, Einstein and Schrödinger on foundational issues in quantum mechanics intoExpand
Why a Relativistic Quantum Mechanical World Must Be Indeterministic
We present the framework of Empirical Models and Hidden Variables Models in the foundations of Quantum Mechanics and its relation to Special Relativity. In this framework we discuss the definitionsExpand
On a deterministic disguise of orthodox quantum mechanics
According to quantum theory, pure physical states correspond to equivalence classes of state vectors, where any two members of one class differ by a complex factor. The point is that such a factorExpand
Unifying Hidden-Variable Problems from Quantum Mechanics by Logics of Dependence and Independence
TLDR
It is shown that common desirable properties of hidden-variable models can be defined in an elegant and concise way in dependence and independence logic, and the relationship between different properties, and their simultaneous realisability can be formulated and proved on a purely logical level. Expand
...
1
2
3
...

References

SHOWING 1-10 OF 10 REFERENCES
A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES. II
In this paper, we shall show how the theory of measurements is to be understood from the point of view of a physical interpretation of the quantum theory in terms of hidden variables developed in aExpand
CAN HIDDEN VARIABLES BE EXCLUDED IN QUANTUM MECHANICS
The question of the possible existence of hidden variables is re- examined. It is shown that hidden variables can exist only if every proposition (yes-no experiment) is compatible with every otherExpand
Hidden variables and the two theorems of John Bell
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 ofExpand
On the Problem of Hidden Variables in Quantum Mechanics
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. ItExpand
Mathematical Foundations of Quantum Mechanics
Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentiethExpand
Measures on the Closed Subspaces of a Hilbert Space
In his investigations of the mathematical foundations of quantum mechanics, Mackey1 has proposed the following problem: Determine all measures on the closed subspaces of a Hilbert space. A measure onExpand
Beables for quantum field theory
  • In Speakable and Unspeakable in Quantum Mechanics ,
  • 1987
Measures on the closed sub-spaces of Hilbe rt spaces.Journal of Mathematics and Mechanics
  • 1957