Open main menu

John Stewart Bell FRS[2] (28 June 1928 – 1 October 1990) was a physicist from Northern Ireland, and the originator of Bell's theorem, an important theorem in quantum physics regarding hidden variable theories.[3][4][5]

John S. Bell
John Stewart Bell, CERN, 1973
John Stewart Bell

28 June 1928
Died1 October 1990 (aged 62)
Alma materQueen's University of Belfast (B.Sc.)
University of Birmingham (Ph.D.)
Known forBell's theorem
Bell state
Chiral anomaly
Bell's spaceship paradox
Quantum entanglement
AwardsHeineman Prize (1989)
Hughes Medal (1989)
Paul Dirac Medal and Prize (1988)
Scientific career
InstitutionsAtomic Energy Research Establishment
CERN, Stanford University
Thesisi. Time reversal in field theory, ii. Some functional methods in field theory. (1956)
Doctoral advisorRudolph E. Peierls
Other academic advisorsPaul Taunton Matthews[1]



Early life and workEdit

John Bell was born in Belfast, Northern Ireland. When he was 11 years old, he decided to be a scientist, and at 16 graduated from Belfast Technical High School. Bell then attended the Queen's University of Belfast, and obtained a bachelor's degree in experimental physics in 1948, and one in mathematical physics a year later. He went on to complete a Ph.D. in physics at the University of Birmingham in 1956, specialising in nuclear physics and quantum field theory. In 1954, he married Mary Ross, also a physicist, whom he had met while working on accelerator physics at Malvern, UK.[6] Bell became a vegetarian in his teen years.[7] According to his wife, Bell was an atheist.[8]

Bell's career began with the UK Atomic Energy Research Establishment, near Harwell, Oxfordshire, known as AERE or Harwell Laboratory. After several years he moved to work for the European Organization for Nuclear Research (CERN, Conseil Européen pour la Recherche Nucléaire), in Geneva, Switzerland. There he worked almost exclusively on theoretical particle physics and on accelerator design, but found time to pursue a major avocation, investigating the foundations of quantum theory. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1987.[9] Also of significance during his career, Bell, together with John Bradbury Sykes, M. J. Kearsley, and W. H. Reid, translated several volumes of the ten-volume Course of Theoretical Physics of Lev Landau and Evgeny Lifshitz, making these works available to an English-speaking audience in translation, all of which remain in print.

Bell was a proponent of pilot wave theory.[10]

Bell's theoremEdit

In 1964, after a year's leave from CERN that he spent at Stanford University, the University of Wisconsin–Madison and Brandeis University, he wrote a paper entitled "On the Einstein-Podolsky-Rosen Paradox".[11]:14 In this work, he showed that carrying forward EPR's analysis[12] permits one to derive the famous Bell's theorem.[13][14] The resultant inequality, derived from certain assumptions, is violated by quantum theory.

There is some disagreement regarding what Bell's inequality—in conjunction with the EPR analysis—can be said to imply. Bell held that not only local hidden variables, but any and all local theoretical explanations must conflict with the predictions of quantum theory: "It is known that with Bohm's example of EPR correlations, involving particles with spin, there is an irreducible nonlocality."[11]:196 According to an alternative interpretation, not all local theories in general, but only local hidden variables theories (or "local realist" theories) have shown to be incompatible with the predictions of quantum theory.

Bell's critique of von Neumann's proofEdit

Bell's interest in hidden variables was motivated by the existence in the formalism of quantum mechanics of a "movable boundary" between the quantum system and the classical apparatus:

A possibility is that we find exactly where the boundary lies. More plausible to me is that we will find that there is no boundary. ... The wave functions would prove to be a provisional or incomplete description of the quantum-mechanical part, of which an objective account would become possible. It is this possibility, of a homogeneous account of the world, which is for me the chief motivation of the study of the so-called 'hidden variable' possibility.[11]:30

Bell was impressed that in the formulation of David Bohm's nonlocal hidden variable theory, no such boundary is needed, and it was this which sparked his interest in the field of research. Bell also criticized the standard formalism of quantum mechanics on the grounds of lack of physical precision:

For the good books known to me are not much concerned with physical precision. This is clear already from their vocabulary. Here are some words which, however legitimate and necessary in application, have no place in a formulation with any pretension to physical precision: system, apparatus, environment, microscopic, macroscopic, reversible, irreversible, observable, information, measurement. . ... On this list of bad words from good books, the worst of all is 'measurement'.[11]:215

But if he were to thoroughly explore the viability of Bohm's theory, Bell needed to answer the challenge of the so-called impossibility proofs against hidden variables. Bell addressed these in a paper entitled "On the Problem of Hidden Variables in Quantum Mechanics".[11]:1 (Bell had actually written this paper before his paper on the EPR paradox, but it did not appear until two years later, in 1966, due to publishing delays.[15]) Here he showed that John von Neumann's argument[16] does not prove the impossibility of hidden variables, as it was widely claimed, due to its reliance on a physical assumption that is not valid for quantum mechanics—namely, that the probability-weighted average of the sum of observable quantities equals the sum of the average values of each of the separate observable quantities.[17] Bell subsequently claimed, "The proof of von Neumann is not merely false but foolish!".[18] In this same work, Bell showed that a stronger effort at such a proof (based upon Gleason's theorem) also fails to eliminate the hidden variables program. The supposed flaw in von Neumann's proof had been previously discovered by Grete Hermann in 1935, but did not become common knowledge until after it was rediscovered by Bell.[19]

However, in 2010, Jeffrey Bub published an argument that Bell (and, implicitly, Hermann) had misconstrued von Neumann's proof, claiming that it does not attempt to prove the absolute impossibility of hidden variables, and is actually not flawed, after all. (Thus, it was the physics community as a whole that had misinterpreted von Neumann's proof as applying universally.) Bub provides evidence that von Neumann understood the limits of his proof, but there is no record of von Neumann attempting to correct the near universal misinterpretation which lingered for over 30 years and exists to some extent to this day. Von Neumann's proof does not in fact apply to contextual hidden variables, as in Bohm's theory.[citation needed]

Conclusions from experimental testsEdit

In 1972 an experiment was conducted that, when extrapolated to ideal detector efficiencies, showed a violation of Bell's inequality. It was the first of many such experiments. Bell himself concludes from these experiments that "It now seems that the non-locality is deeply rooted in quantum mechanics itself and will persist in any completion."[11]:132 This, according to Bell, also implied that quantum theory is not locally causal and cannot be embedded into any locally causal theory. Bell regretted that results of the tests did not agree with the concept of local hidden variables:

For me, it is so reasonable to assume that the photons in those experiments carry with them programs, which have been correlated in advance, telling them how to behave. This is so rational that I think that when Einstein saw that, and the others refused to see it, he was the rational man. The other people, although history has justified them, were burying their heads in the sand. ... So for me, it is a pity that Einstein's idea doesn't work. The reasonable thing just doesn't work."[20]

Bell seemed to have become resigned to the notion that future experiments would continue to agree with quantum mechanics and violate his inequality. Referring to the Bell test experiments, he remarked:

It is difficult for me to believe that quantum mechanics, working very well for currently practical set-ups, will nevertheless fail badly with improvements in counter efficiency ..."[11]:109

Some people continue to believe that agreement with Bell's inequalities might yet be saved. They argue that in the future much more precise experiments could reveal that one of the known loopholes, for example the so-called "fair sampling loophole", had been biasing the interpretations. Most mainstream physicists are highly skeptical about all these "loopholes", admitting their existence but continuing to believe that Bell's inequalities must fail.

Bell remained interested in objective 'observer-free' quantum mechanics. He felt that at the most fundamental level, physical theories ought not to be concerned with observables, but with 'be-ables': "The beables of the theory are those elements which might correspond to elements of reality, to things which exist. Their existence does not depend on 'observation'."[11]:174 He remained impressed with Bohm's hidden variables as an example of such a scheme and he attacked the more subjective alternatives such as the Copenhagen interpretation.[11]:92,133,181

Bell and Special Theory of RelativityEdit

Bell and his wife, physicist Mary Ross Bell, contributed substantially to the physics of particle accelerators, and with numerous young theorists at CERN, Bell developed particle physics itself. An overview of this work is available in the volume of collected works edited by Mary Bell, Kurt Gottfried, and Martinus Veltman.[21] Apart from his particle physics research, Bell often raised an issue of special relativity comprehension, and although there is only one written report on this topic available ("How to teach special relativity"),[22] reprinted in,[23] this was a critical subject to him. Bell admired Einstein's contribution to special relativity, but warned in 1985 "Einstein's approach is ... pedagogically dangerous, in my opinion".[24] In 1989 on the occasion of the centenary of the Lorentz-FitzGerald body contraction Bell writes "A great deal of nonsense has been written about the FitzGerald contraction".[21] Bell preferred to think of Lorentz-FitzGerald contraction as a phenomenon that is real and observable as a property of a material body, which was also Einstein's opinion, but in Bell's view Einstein's approach leaves a lot of room for misinterpretation. This situation and the background of Bell's position is described in detail by his collaborator Johann Rafelski in the textbook "Relativity Matters" (2017).[25] In order to combat misconceptions surrounding Lorentz-FitzGerald body contraction Bell adopted and promoted a relativistic thought experiment which became widely known as Bell's spaceship paradox.


Blue plaque honouring John Bell at the Queen's University of Belfast

Bell died unexpectedly of a cerebral hemorrhage in Geneva in 1990.[26][27][28] It is widely claimed that unknown to Bell, that year he had been nominated for a Nobel Prize.[29][30][31] His contribution to the issues raised by EPR was significant. Some regard him as having demonstrated the failure of local realism (local hidden variables). Bell's own interpretation is that locality itself met its demise.


  • At the CERN site in Meyrin, close to Geneva, there is a street called Route Bell in honour of John Stewart Bell.
  • In 2016, his colleague from CERN, Reinhold Bertlmann, wrote a lengthy piece "Bell's Universe: A Personal Recollection",[34] explaining in some detail his amazement at finding out about Bell's paper on Bertlmann's socks, in which Bell compared the EPR paradox with socks.
  • A day was named after him, referring to the date he released Bell's Theorem, 4 November.[35]

Northern IrelandEdit

  • Since 2015, there is also a street named Bell's Theorem Crescent in his city of birth, Belfast.[35]
  • The John Bell House, named in his honour, finished construction in 2016 and houses over 400 students in Belfast city centre.[36]
  • The pedestrian entrance to the Olympia leisure centre in Belfast located 200 meters from Bell's childhood home is named the "John Stewart Bell Entrance" in honour of the local man.[37]
  • In the Queen's University of Belfast one of the Physics lecture theatres is named in honour of John Stewart Bell[38]

See alsoEdit

Other work by Bell:


  1. ^ Andrew Whitaker, John Stewart Bell and Twentieth-Century Physics: Vision and Integrity, Oxford University Press, 2016, ch. 2.
  2. ^ Burke, P. G.; Percival, I. C. (1999). "John Stewart Bell. 28 July 1928 – 1 October 1990: Elected F.R.S. 1972". Biographical Memoirs of Fellows of the Royal Society. 45: 1. doi:10.1098/rsbm.1999.0001.
  3. ^ Shimony, A.; Telegdi, V.; Veltman, M. (1991). "John S. Bell". Physics Today. 44 (8): 82. Bibcode:1991PhT....44h..82S. doi:10.1063/1.2810223.
  4. ^ O'Connor, John J.; Robertson, Edmund F., "John Stewart Bell", MacTutor History of Mathematics archive, University of St Andrews.
  5. ^ John Stewart Bell's publications indexed by the Scopus bibliographic database. (subscription required)
  6. ^ Aczel, A. D. (2002). Entanglement: The Greatest Mystery in Physics. Basic Books. p. 139. ISBN 978-1-56858-232-0.
  7. ^ Bell, Mary (2016). "Bell the vegetarian". Bibcode:2016PhT....69h..12B. doi:10.1063/PT.3.3252.
  8. ^ Andrew Whitaker; Mary Bell; Shan Gao (19 September 2016). "1 - John Bell - The Irish Connection". Quantum Nonlocality and Reality: 50 Years of Bell's Theorem. Cambridge University Press. p. 8. ISBN 9781107104341. John Bell was certainly not interested in Protestantism as such – his wife Mary [33] has reported that he was an atheist most of his life.
  9. ^ "Bell, John Stewart". Members of the Academy of Arts & Sciences, 1780–2010 (PDF). American Academy of Arts and Sciences. p. 38. Retrieved 30 May 2011.
  10. ^ - Fluid mechanics suggests alternative to quantum orthodoxy
  11. ^ a b c d e f g h i Bell 1988
  12. ^ Einstein, A.; Podolsky, B.; Rosen, N. (1935). "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" (PDF). Physical Review. 47 (10): 777. Bibcode:1935PhRv...47..777E. doi:10.1103/PhysRev.47.777.
  13. ^ "Faces and places: John Stewart Bell". CERN Courier. August 2014.
  14. ^ Sutton, Christine. "Fifty years of Bell's theorem". CERN official website. CERN.
  15. ^ Aczel 2002, p. 144
  16. ^ von Neumann, J. (1996). Mathematical Foundations of Quantum Mechanics. Princeton University Press. ISBN 978-0-691-02893-4.
  17. ^ Aczel 2002, p. 141
  18. ^ Bub, J. (2010). "Von Neumann's 'No Hidden Variables' Proof: A Re-Appraisal". Foundations of Physics. 40 (9–10): 1333–1340. arXiv:1006.0499. Bibcode:2010FoPh...40.1333B. doi:10.1007/s10701-010-9480-9.
  19. ^ C. L. Herzenberg: "Grete Hermann, An early contributor to quantum theory" arXiv:0812.3986
  20. ^ Bernstein, J. (1991). Quantum Profiles. Princeton University Press. p. 84.
  21. ^ a b Mary Bell; Kurt Gottfried; Martinus Veltman, eds. (1995). Quantum Mechanics, High Energy Physics and Accelerators (selected paper of John S Bell with commentary). World Scientific. ISBN 9810221150.
  22. ^ Bell, John Stewart (1976). Zichichi Antonino (ed.). Progress in Scientific Culture. 1, No. 2. pp. 135–148.
  23. ^ Bell, John (1987). Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press. pp. 67–80.
  24. ^ Johann Rafelski (2017). Relativity Matters: From Einstein's EMC2 to Laser Particle Acceleration and Quark-Gluon Plasma. Springer. pp. ix. ISBN 978-3-319-51230-3.
  25. ^ Johann Rafelski (2017). Relativity Matters: From Einstein's EMC2 to Laser Particle Acceleration and Quark-Gluon Plasma. Springer. ISBN 978-3-319-51230-3.
  26. ^ Jackiw, R.; Shimony, A. (2008). "Bell, John Stewart". Complete Dictionary of Scientific Biography. Retrieved 24 November 2013.
  27. ^ Sullivan, W. (10 October 1990). "John Stewart Bell Is Dead at 62; Physicist Tested Particle Actions". New York Times. Retrieved 24 November 2013.
  28. ^ "Faces and things: John Stewart Bell 1928-1990". CERN Courier. 30 (8): 25. November 1990.
  29. ^ Louisa Gilder, The Age of Entanglement, Vintage Books, 2008, p. 3.
  30. ^ Jeremy Bernstein, Quantum Leaps, The Belknap Press of Harvard University Press, 2009, p. 155.
  31. ^ Andrew Whitaker, John Stewart Bell and Twentieth-Century Physics: Vision and Integrity, Oxford University Press, 2016, p. 374. ("[Bell] was not only nominated but shortlisted in 1989 (and perhaps previous years) ...")
  32. ^ "John Stewart Bell Prize". Centre for Quantum Information and Quantum Control.
  33. ^ "Prof. Nicolas Gisin awarded the First Bell Prize". Centre for Quantum Information and Quantum Control. 3 August 2009. Retrieved 24 November 2013.
  34. ^ Bell's Universe: A Personal Recollection (My collaboration and friendship with John Bell is recollected.), Reinhold Bertlmann, 25 May 2016, accessed 27 May 2016
  35. ^ a b "Street named after NI physicist". 19 February 2015. Retrieved 10 April 2018 – via
  36. ^ "John Bell House - Fresh Student Living - Student Privatehall in Belfast". afs. Retrieved 31 March 2017.
  37. ^ "Sculpture celebrates football and physics links". afs. Retrieved 3 June 2018.
  38. ^ "Location". afs. Retrieved 3 June 2018.


External linksEdit