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
2 - On the Einstein–Podolsky–Rosen paradox
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
The paradox of Einstein, Podolsky and Rosen was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics. It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty. There have been attempts to show that even without such a separability or locality requirement no ‘hidden variable’ interpretation of quantum mechanics is possible. These attempts have been examined elsewhere and found wanting. Moreover, a hidden variable interpretation of elementary quantum theory has been explicitly constructed. That particular interpretation has indeed a grossly non-local structure. This is characteristic, according to the result to be proved here, of any such theory which reproduces exactly the quantum mechanical predictions.
Formulation
With the example advocated by Bohm and Aharonov, the EPR argument is the following. Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite directions. Measurements can be made, say by Stern–Gerlach magnets, on selected components of the spins σ1 and σ2.
- Type
- Chapter
- Information
- Speakable and Unspeakable in Quantum MechanicsCollected Papers on Quantum Philosophy, pp. 14 - 21Publisher: Cambridge University PressPrint publication year: 2004
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