Hidden variables and the two theorems of John Bell

@article{Mermin1993HiddenVA,
  title={Hidden variables and the two theorems of John Bell},
  author={N. Mermin},
  journal={Reviews of Modern Physics},
  year={1993},
  volume={65},
  pages={803-815}
}
  • N. Mermin
  • Published 1993
  • Physics
  • Reviews of Modern Physics
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 two (familiar to experts as the "Kochen-Specker theorem") which have transparently simple proofs. One of the new versions can be converted without additional analysis into a powerful form of the very much better known "Bell's Theorem," thereby clarifying the conceptual link between these two… Expand
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References

SHOWING 1-10 OF 34 REFERENCES
Going Beyond Bell’s Theorem
Bell’s Theorem proved that one cannot in general reproduce the results of quantum theory with a classical, deterministic local model. However, Einstein originally considered the case where one couldExpand
The Problem of Hidden Variables in Quantum Mechanics
Forty years after the advent of quantum mechanics the problem of hidden variables, that is, the possibility of imbedding quantum theory into a classical theory, remains a controversial and obscureExpand
On the Einstein-Podolsky-Rosen paradox
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 additionalExpand
Bell’s theorem without inequalities
It is demonstrated that the premisses of the Einstein–Podolsky–Rosen paper are inconsistent when applied to quantum systems consisting of at least three particles. The demonstration reveals that theExpand
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
Bell's theorem, quantum theory and conceptions of the universe
On a Theory of the Collapse of the Wave Function.- On the Measurement Problem of Quantum Mechanics.- A New Characteristic of a Quantum System Between Two Measurements - A "Weak Value".- Can theExpand
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
What's Wrong with these Elements of Reality?
The subject of Einstein-PodolskyRosen correlations—those strong quantum correlations that seem to imply "spooky actions at a distance"—has just been given a new and beautiful twist. DanielExpand
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
TLDR
Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that one is led to conclude that the description of reality as given by a wave function is not complete. Expand
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
...
1
2
3
4
...