Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- Preface
- Part I John Stewart Bell: The Physicist
- Part II Bell's Theorem
- 4 What Did Bell Really Prove?
- 5 The Assumptions of Bell's Proof
- 6 Bell on Bell's Theorem: The Changing Face of Nonlocality
- 7 Experimental Tests of Bell Inequalities
- 8 Bell's Theorem without Inequalities: On the Inception and Scope of the GHZ Theorem
- Part III Nonlocality: Illusion or Reality?
- Part IV Nonlocal Realistic Theories
- Index
- References
6 - Bell on Bell's Theorem: The Changing Face of Nonlocality
from Part II - Bell's Theorem
Published online by Cambridge University Press: 05 September 2016
Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- Preface
- Part I John Stewart Bell: The Physicist
- Part II Bell's Theorem
- 4 What Did Bell Really Prove?
- 5 The Assumptions of Bell's Proof
- 6 Bell on Bell's Theorem: The Changing Face of Nonlocality
- 7 Experimental Tests of Bell Inequalities
- 8 Bell's Theorem without Inequalities: On the Inception and Scope of the GHZ Theorem
- Part III Nonlocality: Illusion or Reality?
- Part IV Nonlocal Realistic Theories
- Index
- References
Summary
Abstract
Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal (more precisely, that it violates ‘local causality’) became divorced from the Bell theorem per se from 1976 on, although this important point is widely overlooked in the literature. In 1990, the year of his death, Bell would express serious misgivings about themathematical form of the local causality condition and leave ill-defined the issue of the consistency between special relativity and violation of the Bell-type inequality. In our view, the significance of the Bell theorem, in both its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz covariant version of quantum theory, free of action at a distance, can be articulated in the Everett interpretation.
Introduction
John S. Bell's last word on his celebrated nonlocality theorem and its interpretation appeared in his 1990 paper ‘La nouvelle cuisine’, first published in the year of his untimely death. Bell was careful here to distinguish between the issue of ‘no superluminal signalling’ in quantum theory (both quantum field theory and quantum mechanics) and a principle he first introduced explicitly in 1976 and called ‘local causality’ [1]. In relation to the former, Bell expressed concerns that amplify doubts he had already expressed in 1976. These concerns touch on what is now widely known as the no-signalling theorem in quantum mechanics, and ultimately have to do with Bell's distaste for what he saw as an anthropocentric element in orthodox quantum thinking. In relation to local causality, Bell emphasised that his famous factorizability (no-correlations) condition is not to be seen ‘as the formulation of local causality, but as a consequence thereof’ and stressed how difficult he found it to articulate this consequence. He left the question of any strict inconsistency between violation of factorizability and special relativity theory unresolved, a not insignificant shift from his thinking up to the early 1980s.
- Type
- Chapter
- Information
- Quantum Nonlocality and Reality50 Years of Bell's Theorem, pp. 91 - 123Publisher: Cambridge University PressPrint publication year: 2016
References
[1]
1976, The theory of local beables, Epistemological Letters, March. Repr. in [33, Chap. 7].
[2]
2014, The two Bell's theorems of John Bell, Journal of Physics A 47, 063028.
[3] , and
2002, Entanglement and relativity, in and (eds.), Understanding Physical Knowledge (University of Bologna, of), arXiv:quant-ph/0212140.
[4]
2010, What Bell proved: A reply to Blaylock,
American Journal of Physics
78(1), 121–5.Google Scholar
[5]
2011, 's concept of local causality, American Journal of Physics
79, 1261.
[6]
2013, There are no particles, there are only fields,
American Journal of Physics
81, 211.Google Scholar
[7]
2013, Response toM.S. de Bianchi and , American Journal of Physics
81, 709.
[9]
1966, On the problem of hidden variables in quantum mechanics,
Reviews of Modern Physics
38, 447–52. Repr. in Bell [33, Chap. 1].Google Scholar
[10] and
1967, The problem of hidden variables in quantum mechanics,
Journal of Mathematics and Mechanics
17, 59–87.Google Scholar
[11]
1957, Measures on the closed subspaces of Hilbert space,
Journal of Mathematics and Mechanics
6(6).Google Scholar
[12]
1992, Bell's other theorem and its connection with nonlocality. Part I, in , and (eds.), Bell's Theorem and the Foundations of Modern Physics (World Scientific), pp. 104–16.
[13]
1993, Hidden variables and the two theorems of John Bell,
Reviews of Modern Physics
65, 803–15.Google Scholar
[14]
1952, A suggested interpretation of the quantum theory in terms of hidden variables, I and II,
Physical Review
85, 166–79, 180–93.Google Scholar
[15] and
1983, Nonlocality and the Kochen–Specker paradox,
Foundations of Physics
13(5), 481–99.Google Scholar
[16]
1983, Quantum logic, realism, and value definiteness,
Philosophy of Science
50(4), 578–602.Google Scholar
[17] and
1990, Nonlocality and Gleason's lemma: Part I. Deterministic theories,
Foundations of Physics
20(11), 1379–87.Google Scholar
[18]
1990, Nonlocality and Gleason's lemma. Part 2. Stochastic theories,
Foundations of Physics
20(11), 1389–97.Google Scholar
[19] , and
1989, Going beyond Bell's theorem, in (ed.), Bell's Theorem, Quantum Theory, and Conceptions of the Universe (Kluwer), pp. 73–6.
[20]
2010, The EPR paradox, Bell's inequality, and the question of locality,
American Journal of Physics
78(1), 111–20.Google Scholar
[21]
1991, Nonlocality in quantum mechanics,
Aristotelian Society Supplementary Volume
65, 141–59.Google Scholar
[22] and
1984, Bell's inequality and non-contextual dispersion-free states,
Physics Letters A
102(4), 159–62.Google Scholar
[23] and
1987, A reformulation and generalisation of a recent Bell-type theorem for a valence electron, unpublished manuscript.
[24]
1973, A Survey of Hidden-Variable Theories (Pergamon Press).
[26] , , , and
2014, No ψ-epistemic model can fully explain the indistinguishability of quantum states,
Physical Review Letters
112, 250403.Google Scholar
[27] and
2014, Quantum non-locality – It ain't necessarily so
…, Journal of Physics A
47(42), 424009.Google Scholar
[28]
1981, Bertlmann's socks and the nature of reality,
Journal de Physique
42(3C2), C241–61. Repr. in [33, Chap. 16].Google Scholar
[29]
1964, On the Einstein–Podolsky–Rosen Paradox,
Physics
1, 195–200. Repr. in Bell [33, Chap. 2].Google Scholar
[30]
1951, Quantum Mechanics (Prentice-Hall).
[31]
1981, O debate Einstein–Bohr na mecanica quantica,
Cadernos de História e Filosofia da Ciência (Brazil)
2, 59–81.Google Scholar
[33]
1987, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press). Second edition 2004.
[34]
1989, Absolute or Relative Motion: Volume 1. The Discovery of Dynamics (Oxford University Press).
[35]
1986, The Shaky Game (Chicago University Press).
[36]
1964, The Current Interpretation of Wave Mechanics: A Critical Study (Elsevier).
[37]
1956, The Direction of Time (University of California Press). Repr. Dover 1999. 120 Bell on Bell's Theorem: The Changing Face of Nonlocality
[38] , and
1993, What makes a theory physically ‘complete’?
Foundations of Physics
23(7), 971–85.Google Scholar
[39] , , and
1969, Proposed experiment to test local hidden-variable theories,
Physical Review Letters
20, 880.Google Scholar
[40]
1971, Introduction to the hidden variable question, in Foundations of Quantum Mechanics (Academic Press, New York). Repr. in [33, Chap. 4].
[41] and
1974, Experimental consequences of objective local theories,
Physical Review D
10, 526–35.Google Scholar
[42] and
1976, On the determinism of hidden variables theories with strict correlation and conditional statistical independence, in (ed.), Logic and Probability in Quantum Mechanics (Springer), pp. 445–55.
[43]
1984, On the physical significance of the locality conditions in the Bell arguments,
Noûs
18(4), 569–89.Google Scholar
[44]
1989, Against ‘measurement’, in 62 Years of Uncertainty (Plenum). Repr. in [33, Chap. 23].
[45]
1986, EPR correlations and EPW distributions, in New Techniques and Ideas in Quantum Measurement Theory (New York Academy of Sciences). Repr. in [33, Chap. 20].
[46]
1984, Speakable and unspeakable in quantum mechanics. Repr. in [33, Chap. 18].
[47]
1976, How to teach special relativity,
Progress in Scientific Culture
1(2). Repr. in [33, Chap. 9].Google Scholar
[48]
1986, Chapter 3 in and (eds.), The Ghost in the Atom (Cambridge University Press).
[49]
1990, La nouvelle cuisine, in and (eds.), Between Science and Technology, Amsterdam: Elsevier, Chap. 6, p. 97. Repr. in [33, Chap. 24].
[50]
2014, Quantum nonlocality does not exist,
Proceedings of the National Academy of Sciences
111(31), 11281–6.Google Scholar
[51] , and Shack|Rudiger 2007, Subjective probability and quantum certainty,
Studies in History and Philosophy of Modern Physics
38, 255–74.Google Scholar
[53]
2013, How to use quantum theory locally to explain EPR–Bell correlations, in and (eds.), EPSA11: Perspectives and Foundational Problems in Philosophy of Science, The European Philosophy of Science Association Proceedings, Vol. 2 (Springer), pp. 195–205.
[52] , Mermin|N. David and Schack|Rudiger 2014, An introduction to QBism with an application to the locality of quantum mechanics,
American Journal of Physics
82(8), 749–54.Google Scholar
[54] and
2011, Not throwing out the baby with the bathwater: Bell's condition of local causality mathematically ‘sharp and clean’, in , , , and (eds.), Explanation, Prediction and Confirmation (Springer).
[55]
1984, Controllable and uncontrollable non-locality, in (ed.), Proceedings of the International Symposium: Foundations of Quantum Mechanics in the Light of New Technology (Physical Society of Japan), pp. 225–30.
[56]
1982, The Charybdis of realism: Epistemological implications of Bell's inequality, in [102, pp. 97–113].
[57]
1989, A space-time approach to the Bell inequality, in [102, pp. 114–44].
[58]
1992, Bell's theorem: What it takes.
British Journal for the Philosophy of Science
43(1), 41–83.Google Scholar
[59]
2007, Stochastic Einstein locality revisited,
The British Journal for the Philosophy of Science
58(4), 805–67.Google Scholar
[60]
2010, Causality, Bell's theorem, and ontic definiteness. arXiv:quantph/ 1102.2855.
[61]
1998, Quantum Chance and Non-locality (Cambridge University Press).
[62]
2014, Many-Worlds Interpretation of Quantum Mechanics, in Edward N. Zalta (ed.), the Stanford Encyclopedia of Philosophy (Spring 2014 ed.) URL=http://plato.stanford.edu/archives/spr2014/entries/qm-manyworlds.
[63]
1957, “Relative state” formulation of quantum mechanics
Reviews of Modern Physics
29, 454–62.Google Scholar
[64]
1982, The Einstein–Podolsky–Rosen physical reality is completely described by quantum mechanics,
Physics Letters A
91, 57–60.Google Scholar
[65]
1994, On the paradoxical aspects of new quantum experiments, in , and (eds.), PSA 1994 (Philosophy of Science Association), Vol. 1, pp. 211–7.
[66]
2000, Does quantum nonlocality exist? Bell's theorem and the manyworlds interpretation, arXiv:quant-ph/0003146.
[67]
2002, Remarks on space–time and locality in Everett's interpretation, in , and (eds.), Nonlocality and Modality, NATO Science Series II (Kluwer Academic), Pitt-Phil-Sci 00000504.
[68]
2012, The Emergent Multiverse: Quantum Mechanics according to the Everett Interpretation (Oxford University Press).
[69] and
2000, Information flow in entangled quantum systems,
Proceedings of the Royal Society of London A
456, 1759–74.Google Scholar
[71]
2001, Locality in the Everett interpretation of Heisenberg-picture quantum mechanics,
Foundations of Physics Letters
14, 301–22.Google Scholar
[72]
2002, Locality in the Everett interpretation of quantum field theory,
Foundations of Physics
32, 1495–523.Google Scholar
[73]
2011, Observers and locality in Everett quantum field theory,
Foundations of Physics
41, 1236–62.Google Scholar
[74]
2012, Space, Time and Stuff (Oxford University Press), Chap. 4.
[75]
2005, Nonlocality and information flow: The approach of Deutsch and Hayden,
Foundations of Physics
35(2), 313–43.Google Scholar
[76] and
2007, Non-locality and gauge freedom in Deutsch and Hayden's formulation of quantum mechanics,
Foundations of Physics
37(6), 951–5.Google Scholar
[77] and
2014, Quantum Mechanics on Space– Time II. [Forthcoming].
[78] and
2013, Can free will emerge from determinism in quantum theory, in Is Science Compatible with Free Will?: 122 Bell on Bell's Theorem: The Changing Face of Nonlocality Exploring Free Will and Consciousness in the Light of Quantum Physics and Neuroscience (Springer), pp. 41–61.
[80]
1996, Relativism, in (ed.), Perspectives on Quantum Reality (Kluwer Academic Publishers), pp. 125–42.
[83]
, and (eds.) 2010, Many Worlds? Everett, Realism and Quantum Mechanics (Oxford University Press).
[84]
1985, Einstein on locality and separability,
Studies in History and Philosophy of Science Part A
16(3), 171–201.Google Scholar
[85]
1989, Holism, separability, and the metaphysical implications of the Bell experiments, in [102, pp. 224–53].
[86]
1986, Relational holism and quantum mechanics,
The British Journal for the Philosophy of Science
37(1), 71–81.Google Scholar
[87]
1989, Relativity, relational holism, and the Bell inequalities, in [102, pp. 208–23].
[88]
1989, Individuality, supervenience and Bell's theorem,
Philosophical Studies
55(1), 1–22.Google Scholar
[90]
1994, Nonseparable processes and causal explanation,
Studies in History and Philosophy of Science
25, 337–74.Google Scholar
[92]
1998, What is quantum mechanics trying to tell us?
American Journal of Physics
66, 753.Google Scholar
[93]
1999, What do these correlations know about reality? Nonlocality and the absurd,
Foundations of Physics
29, 571–87.Google Scholar
[94]
2013, Non-separability does not relieve the problem of Bell's theorem,
Foundations of Physics
43(8), 1008–38.Google Scholar
[95] and
2014, On modifications of Reichenbach's principle of common cause in light of Bell's theorem,
Journal of Physics A
47, 424018.Google Scholar
[96]
1999, Quantum theory of probability and decisions,
Proceedings of the Royal Society of London A
455(1988), 3129–37.Google Scholar
[97]
2004, Understanding Deutsch's probability in a deterministic multiverse,
Studies in History and Philosophy of Modern Physics
35(3), 423–56.Google Scholar
[98]
2003, Everettian rationality: Defending Deutsch's approach to probability in the Everett interpretation,
Studies in History and Philosophy of Modern Physics
34(3), 415–39.Google Scholar
[99]
2007, Quantum probability from subjective likelihood: Improving on Deutsch's proof of the probability rule,
Studies in History and Philosophy of Modern Physics
38(2), 311–32.Google Scholar
[100]
2010, How to prove the Born rule, in [83, Chap. 8].
[101]
1986, Six possible worlds of quantum mechanics, in (ed.), Proceedings of the Nobel Symposium 65: Possible Worlds in Arts and Sciences (The Nobel Foundation). Repr. in [33, Chap. 20].
[102] and
1989, Philosophical Consequences of Quantum Theory: Reflections on Bell's Theorem (University of Notre Dame Press).
- 4
- Cited by