Hidden variables and the two theorems of John Bell

  title={Hidden variables and the two theorems of John Bell},
  author={N. David Mermin},
  journal={Reviews of Modern Physics},
  • N. Mermin
  • Published 1 July 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… 
The Two Bell's Theorems of John Bell
Many of the heated arguments about the meaning of ‘Bellʼs theorem’ arise because this phrase can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His
The Kochen-Specker theorem and Bell's theorem: An algebraic approach
In this paper we present a systematic formulation of some recent results concerning the algebraic demonstration of the two major no-hidden-variables theorems for N spin-1/2 particles. We derive
On Hidden Variables: Value and Expectation No-Go Theorems
No-go theorems assert that hidden-variable theories, subject to appropriate hypotheses, cannot reproduce the predictions of quantum theory. We examine two species of such theorems, value no-go
Oversights in the Respective Theorems of von Neumann and Bell are Homologous
We show that the respective oversights in the von Neumann's general theorem against all hidden variable theories and Bell's theorem against their local-realistic counterparts are homologous. Both
Hidden variable theories and quantum nonlocality
We clarify the meaning of Bell's theorem and its implications for the construction of hidden variable theories by considering an example system consisting of two entangled spin-1/2 particles. Using
A Criticism of the article "An experimental test of non-local realism"
There is hardly a result that is more widely misunderstood in the scien-tific community than Bell’s theorem. In a nutshell, there is a widespreadbelief that in his celebrated article [1], Bell has
Optimal no-go theorem on hidden-variable predictions of effect expectations
No-go theorems assert that hidden-variable theories, subject to appropriate hypotheses, cannot reproduce the predictions of quantum theory. We examine two species of such theorems, value no-go
Context Independence as a Statistical Property of Hidden Variable Theories
The compatibility of the context dependence of individual measurement results with the context independence of the statistic results is shown to warrant the consistency of the Bell framework with respect to the Gleason no-hidden-variables theorem.
A simple proof of Bell's inequality
Bell’s theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of


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 could
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 obscure
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 additional
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 the
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
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 the
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
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. Daniel
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
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.
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