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 2 June 2010
  • Philosophy
  • 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… 

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References

SHOWING 1-8 OF 8 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 a

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 other

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 of

The mathematical foundations of quantum mechanics

Classical mechanics was first envisaged by Newton, formed into a powerful tool by Euler, and brought to perfection by Lagrange and Laplace. It has served as the paradigm of science ever since. Even

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. It

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 on