Book contents
- Frontmatter
- Contents
- List of papers on quantum philosophy by J. S. Bell
- Preface to the first edition
- Acknowledgements
- Introduction: John Bell and the second quantum revolution
- 1 On the problem of hidden variables in quantum mechanics
- 2 On the Einstein–Podolsky–Rosen paradox
- 3 The moral aspect of quantum mechanics
- 4 Introduction to the hidden-variable question
- 5 Subject and object
- 6 On wave packet reduction in the Coleman–Hepp model
- 7 The theory of local beables
- 8 Locality in quantum mechanics: reply to critics
- 9 How to teach special relativity
- 10 Einstein–Podolsky–Rosen experiments
- 11 The measurement theory of Everett and de Broglie's pilot wave
- 12 Free variables and local causality
- 13 Atomic-cascade photons and quantum-mechanical nonlocality
- 14 de Broglie–Bohm, delayed-choice double-slit experiment, and density matrix
- 15 Quantum mechanics for cosmologists
- 16 Bertlmann's socks and the nature of reality
- 17 On the impossible pilot wave
- 18 Speakable and unspeakable in quantum mechanics
- 19 Beables for quantum field theory
- 20 Six possible worlds of quantum mechanics
- 21 EPR correlations and EPW distributions
- 22 Are there quantum jumps?
- 23 Against ‘measurement’
- 24 La nouvelle cuisine
1 - On the problem of hidden variables in quantum mechanics
Published online by Cambridge University Press: 11 April 2011
- Frontmatter
- Contents
- List of papers on quantum philosophy by J. S. Bell
- Preface to the first edition
- Acknowledgements
- Introduction: John Bell and the second quantum revolution
- 1 On the problem of hidden variables in quantum mechanics
- 2 On the Einstein–Podolsky–Rosen paradox
- 3 The moral aspect of quantum mechanics
- 4 Introduction to the hidden-variable question
- 5 Subject and object
- 6 On wave packet reduction in the Coleman–Hepp model
- 7 The theory of local beables
- 8 Locality in quantum mechanics: reply to critics
- 9 How to teach special relativity
- 10 Einstein–Podolsky–Rosen experiments
- 11 The measurement theory of Everett and de Broglie's pilot wave
- 12 Free variables and local causality
- 13 Atomic-cascade photons and quantum-mechanical nonlocality
- 14 de Broglie–Bohm, delayed-choice double-slit experiment, and density matrix
- 15 Quantum mechanics for cosmologists
- 16 Bertlmann's socks and the nature of reality
- 17 On the impossible pilot wave
- 18 Speakable and unspeakable in quantum mechanics
- 19 Beables for quantum field theory
- 20 Six possible worlds of quantum mechanics
- 21 EPR correlations and EPW distributions
- 22 Are there quantum jumps?
- 23 Against ‘measurement’
- 24 La nouvelle cuisine
Summary
Introduction
To know the quantum mechanical state of a system implies, in general, only statistical restrictions on the results of measurements. It seems interesting to ask if this statistical element be thought of as arising, as in classical statistical mechanics, because the states in question are averages over better defined states for which individually the results would be quite determined. These hypothetical ‘dispersion free’ states would be specified not only by the quantum mechanical state vector but also by additional ‘hidden variables’ – ‘hidden’ because if states with prescribed values of these variables could actually be prepared, quantum mechanics would be observably inadequate.
Whether this question is indeed interesting has been the subject of debate. The present paper does not contribute to that debate. It is addressed to those who do find the question interesting, and more particularly to those among them who believe that ‘the question concerning the existence of such hidden variables received an early and rather decisive answer in the form of von Neumann's proof on the mathematical impossibility of such variables in quantum theory.’ An attempt will be made to clarify what von Neumann and his successors actually demonstrated. This will cover, as well as von Neumann's treatment, the recent version of the argument by Jauch and Piron, and the stronger result consequent on the work of Gleason. It will be urged that these analyses leave the real question untouched.
- Type
- Chapter
- Information
- Speakable and Unspeakable in Quantum MechanicsCollected Papers on Quantum Philosophy, pp. 1 - 13Publisher: Cambridge University PressPrint publication year: 2004
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