John Stewart Bell | |
---|---|

Born | John Stewart Bell 28 July 1928 |

Died | 1 October 1990 (aged 62) |

Alma mater | Queen's University of Belfast (B.Sc.) University of Birmingham (Ph.D.) |

Known for | Bell's theorem Bell state Bell's spaceship paradox Bell–Kochen–Specker theorem Adler–Bell–Jackiw anomaly Chiral anomaly CPT symmetry Superdeterminism Quantum entanglement |

Awards | Heineman Prize (1989) Hughes Medal (1989) Paul Dirac Medal and Prize (1988) |

Scientific career | |

Institutions | Atomic Energy Research Establishment CERN, Stanford University |

Thesis | i. Time reversal in field theory, ii. Some functional methods in field theory. (1956) |

Doctoral advisor | Rudolph E. Peierls |

Other academic advisors | Paul Taunton Matthews ^{ [1] }^{:137} |

**John Stewart Bell** FRS ^{ [2] } (28 July 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] }^{ [6] }

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, where, in 1948, he obtained a bachelor's degree in experimental physics and, a year later, a bachelor's degree in mathematical physics. 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.^{ [7] }^{:139} Bell became a vegetarian in his teen years.^{ [8] } According to his wife, Bell was an atheist.^{ [9] }

Bell's career began with the UK Atomic Energy Research Establishment, near Harwell, Oxfordshire, known as AERE or Harwell Laboratory. In 1960, he moved to work for the European Organization for Nuclear Research (CERN, *Conseil Européen pour la Recherche Nucléaire*), in Geneva, Switzerland.^{ [10] } 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.^{ [11] } 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.^{ [12] }

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".^{ [13] } In this work, he showed that carrying forward EPR's analysis^{ [14] } permits one to derive the famous Bell's theorem.^{ [15] } 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."^{ [16] }^{: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 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.

^{ [16] }^{: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

formulationwith 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'.^{ [16] }^{: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".^{ [17] } (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.^{ [7] }^{:144}) Here he showed that John von Neumann's argument^{ [18] } does not prove the impossibility of hidden variables, as 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.^{ [7] }^{:141} Bell subsequently claimed, "The proof of von Neumann is not merely false but *foolish*!".^{ [19] }^{:88} 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.^{ [20] }

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.^{ [21] } (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.^{ [22] }

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 concluded from these experiments that "It now seems that the non-locality is deeply rooted in quantum mechanics itself and will persist in any completion."^{ [16] }^{: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,

hewas 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."^{ [23] }^{:84}

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 ..."

^{ [16] }^{: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.^{ [24] } 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'."^{ [16] }^{: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.^{ [16] }^{:92,133,181}

Bell and his wife, Mary Ross Bell, also a physicist, 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.^{ [25] } 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"),^{ [16] }^{:67–80} 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".^{ [26] }^{:ix} 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".^{ [25] } 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).^{ [26] } 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.

Bell died unexpectedly of a cerebral hemorrhage in Geneva in 1990.^{ [27] }^{ [28] }^{ [29] } It is widely claimed that, unknown to Bell, that year he had been nominated for a Nobel Prize.^{ [30] }^{:3}^{ [31] }^{:155}^{ [1] }^{:374} 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.

- In 2008, the John Stewart Bell Prize was created by the Centre for Quantum Information and Quantum Control at the University of Toronto.
^{ [32] }The prize is awarded every other year for significant contributions first published during the six preceding years. The award recognizes major advances relating to the foundations of quantum mechanics and to the applications of these principles. In 2009, the first award was presented by Alain Aspect to Nicolas Gisin for his theoretical and experimental work on foundations and applications of quantum physics — notably quantum nonlocality, quantum cryptography, and quantum teleportation.^{ [33] }

- 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] }

- Since 2015, a street has been named Bell's Theorem Crescent in his city of birth, Belfast.
^{ [36] } - The John Bell House, named in his honour, finished construction in 2016 and houses over 400 students in Belfast city centre.
^{ [37] } - 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.
^{ [38] } - In the Queen's University of Belfast one of the Physics lecture theatres is named in honour of John Stewart Bell.
^{ [39] } - There is a blue plaque commemorating John Stewart Bell in Queen's university main campus
- There is a blue plaque commemorating John Stewart Bell at his childhood home in Tates Avenue in Belfast
- In 2017 the Institue of Physics commisioned classical composer Matthew Whiteside's Quartet No 4 (Entangled) to be performed at the 2018 NI Science Festival inspired by Bell's work,
^{ [40] }the piece went on to become the title track on Whiteside's second album and was the inspiration for a short film by Marisa Zanotti.^{ [41] }

- Bell, John Stewart (2004).
*Speakable and Unspeakable in Quantum Mechanics*(2nd ed.). Cambridge: Cambridge University Press. ISBN 978-0-521-52338-7. 2004 edition with introduction by Alain Aspect and two additional papers: ISBN 0-521-52338-9.

*Epistemological Letters*- EPR paradox, a thought experiment by Einstein, Podolsky, and Rosen published in 1935 as an attack on quantum theory
- Local hidden variable theory
- Quantum entanglement
- Bell's theorem, published in 1964
- Bell state
- Bell test experiments
- CHSH Bell test, an application of Bell's theorem
- GHZ experiment
- Superdeterminism

Other work by Bell:

The **Einstein–Podolsky–Rosen paradox** is a thought experiment proposed by physicists Albert Einstein, Boris Podolsky and Nathan Rosen (EPR), with which they argued that the description of physical reality provided by quantum mechanics was incomplete. In a 1935 paper titled "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?", they argued for the existence of "elements of reality" that were not part of quantum theory, and speculated that it should be possible to construct a theory containing them. Resolutions of the paradox have important implications for the interpretation of quantum mechanics.

**Quantum mechanics** is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.

**Quantum entanglement** is a physical phenomenon that occurs when a group of particles is generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics lacking in classical mechanics.

In quantum mechanics, **counterfactual definiteness** (**CFD**) is the ability to speak "meaningfully" of the definiteness of the results of measurements that have not been performed. The term "counterfactual definiteness" is used in discussions of physics calculations, especially those related to the phenomenon called quantum entanglement and those related to the Bell inequalities. In such discussions "meaningfully" means the ability to treat these unmeasured results on an equal footing with measured results in statistical calculations. It is this aspect of counterfactual definiteness that is of direct relevance to physics and mathematical models of physical systems and not philosophical concerns regarding the meaning of unmeasured results.

**Bell's theorem** proves that quantum physics is incompatible with local hidden-variable theories. It was introduced by physicist John Stewart Bell in a 1964 paper titled "On the Einstein Podolsky Rosen Paradox", referring to a 1935 thought experiment that Albert Einstein, Boris Podolsky and Nathan Rosen used to argue that quantum physics is an "incomplete" theory. By 1935, it was already recognized that the predictions of quantum physics are probabilistic. Einstein, Podolsky and Rosen presented a scenario that, in their view, indicated that quantum particles, like electrons and photons, must carry physical properties or attributes not included in quantum theory, and the uncertainties in quantum theory's predictions were due to ignorance of these properties, later termed "hidden variables". Their scenario involves a pair of widely separated physical objects, prepared in such a way that the quantum state of the pair is entangled.

**Quantum indeterminacy** is the apparent *necessary* incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics. Prior to quantum physics, it was thought that

In physics, **hidden-variable theories** are proposals to provide explanations of quantum mechanical phenomena through the introduction of unobservable hypothetical entities. The existence of fundamental indeterminacy for some measurements is assumed as part of the mathematical formulation of quantum mechanics; moreover, bounds for indeterminacy can be expressed in a quantitative form by the Heisenberg uncertainty principle. Most hidden-variable theories are attempts at a deterministic description of quantum mechanics, to avoid quantum indeterminacy, but at the expense of requiring the existence of nonlocal interactions.

In physics, the **principle of locality** states that an object is directly influenced only by its immediate surroundings. A theory that includes the principle of locality is said to be a "local theory". This is an alternative to the older concept of instantaneous "action at a distance". Locality evolved out of the field theories of classical physics. The concept is that for an action at one point to have an influence at another point, something in the space between those points such as a field must mediate the action. To exert an influence, something, such as a wave or particle, must travel through the space between the two points, carrying the influence.

In physics, **action at a distance** is the concept that an object can be moved, changed, or otherwise affected without being physically touched by another object. That is, it is the non-local interaction of objects that are separated in space.

In quantum physics, a **measurement** is the testing or manipulation of a physical system in order to yield a numerical result. The predictions that quantum physics makes are in general probabilistic. The mathematical tools for making predictions about what measurement outcomes may occur were developed during the 20th century and make use of linear algebra and functional analysis.

A **Bell test**, also known as **Bell inequality test** or **Bell experiment**, is a real-world physics experiment designed to test the theory of quantum mechanics in relation to Albert Einstein's concept of local realism. The experiments test whether or not the real world satisfies local realism, which requires the presence of some additional local variables to explain the behavior of particles like photons and electrons. To date, all Bell tests have found that the hypothesis of local hidden variables is inconsistent with the way that physical systems behave.

A **local hidden-variable theory** in the interpretation of quantum mechanics is a hidden-variable theory that has the added requirement of being consistent with local realism. It refers to all types of the theory that attempt to account for the probabilistic features of quantum mechanics by the mechanism of underlying inaccessible variables, with the additional requirement from local realism that distant events be independent, ruling out *instantaneous* interactions between separate events.

In theoretical physics, the **pilot wave theory**, also known as **Bohmian mechanics**, was the first known example of a hidden-variable theory, presented by Louis de Broglie in 1927. Its more modern version, the de Broglie–Bohm theory, interprets quantum mechanics as a deterministic theory, avoiding troublesome notions such as wave–particle duality, instantaneous wave function collapse, and the paradox of Schrödinger's cat. To solve these problems, the theory is inherently nonlocal.

The **free will theorem** of John H. Conway and Simon B. Kochen states that if we have a free will in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in *Foundations of Physics* in 2006. In 2009, the authors published a stronger version of the theorem in the Notices of the AMS. Later, in 2017, Kochen elaborated some details.

In quantum mechanics, the **Kochen–Specker** (**KS**) **theorem**, also known as the **Bell–Kochen–Specker theorem**, is a "no-go" theorem proved by John S. Bell in 1966 and by Simon B. Kochen and Ernst Specker in 1967. It places certain constraints on the permissible types of hidden-variable theories, which try to explain the predictions of quantum mechanics in a context-independent way. The version of the theorem proved by Kochen and Specker also gave an explicit example for this constraint in terms of a finite number of state vectors.

The **Born rule** is a key postulate of quantum mechanics which gives the probability that a measurement of a quantum system will yield a given result. In its simplest form, it states that the probability density of finding a particle at a given point, when measured, is proportional to the square of the magnitude of the particle's wavefunction at that point. It was formulated by German physicist Max Born in 1926.

In mathematical physics, **Gleason's theorem** shows that the rule one uses to calculate probabilities in quantum physics, the Born rule, can be derived from the usual mathematical representation of measurements in quantum physics together with the assumption of non-contextuality. Andrew M. Gleason first proved the theorem in 1957, answering a question posed by George W. Mackey, an accomplishment that was historically significant for the role it played in showing that wide classes of hidden-variable theories are inconsistent with quantum physics. Multiple variations have been proven in the years since. Gleason's theorem is of particular importance for the field of quantum logic and its attempt to find a minimal set of mathematical axioms for quantum theory.

**Reinhold Anton Bertlmann** is an Austrian-born physicist and professor of physics at the University of Vienna. He is known for his research in particle physics, where he wrote the standard textbook *Anomalies in Quantum Field Theory*, and in the field of Bell inequalities, in particular from the quantum comparison *Bertlmann’s Socks* of John Bell.

* Quantum Reality* is a 1985 popular science book by physicist Nick Herbert, a member the Fundamental Fysiks Group which was formed to explore the philosophical implications of quantum theory. The book attempts to address the ontology of quantum objects, their attributes, and their interactions, without reliance on advanced mathematical concepts. Herbert discusses the most common interpretations of quantum mechanics and their consequences in turn, highlighting the conceptual advantages and drawbacks of each.

**Aspect's experiment** was the first quantum mechanics experiment to demonstrate the violation of Bell's inequalities. Its irrefutable result allowed for further validation of the quantum entanglement and locality principles. It also offered an experimental answer to Albert Einstein, Boris Podolsky and Nathan Rosen's paradox which had been proposed about fifty years earlier.

- 1 2 Whitaker, Andrew (2016).
*John Stewart Bell and Twentieth-Century Physics: Vision and Integrity*. Oxford: Oxford University Press. doi:10.1093/acprof:oso/9780198742999.001.0001. ISBN 978-0198742999. OCLC 960219296. - ↑ Burke, Philip G.; Percival, Ian 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**: 1–17. doi:10.1098/rsbm.1999.0001. JSTOR 770260. S2CID 72616247. - ↑ Shimony, Abner; Telegdi, Valentine; Veltman, Martinus (1991). "John S. Bell".
*Physics Today*.**44**(8): 82–86. Bibcode:1991PhT....44h..82S. doi: 10.1063/1.2810223 . - ↑ O'Connor, John J.; Robertson, Edmund F., "John Stewart Bell",
*MacTutor History of Mathematics archive*, University of St Andrews . - ↑ Whitaker, Andrew (1998). "John Bell and the most profound discovery of science".
*Physics World*.**11**(12): 29–34. doi:10.1088/2058-7058/11/12/24. - ↑ Stapp, Henry P. (1975). "Bell's Theorem and World Process".
*Il Nuovo Cimento B*.**29**(2): 270–276. Bibcode:1975NCimB..29..270S. doi:10.1007/BF02728310. S2CID 117358907. - 1 2 3 Aczel, Amir D. (2002).
*Entanglement: The Greatest Mystery in Physics*. New York: Basic Books. ISBN 978-1-56858-232-0. OCLC 49649300. - ↑ Bell, Mary (2016). "Bell the vegetarian".
*Physics Today*.**69**(8): 12. Bibcode:2016PhT....69h..12B. doi: 10.1063/pt.3.3252 . - ↑ Bell, Mary (2002). "Some Reminiscences". In Bertlmann, Reinhold A.; Zeilinger, Anton (eds.).
*Quantum [Un]speakables: From Bell to Quantum Information*. The Frontiers Collection. Berlin: Springer. pp. 3–5. doi:10.1007/978-3-662-05032-3_1. ISBN 978-3-642-07664-0.Although an atheist for most of his life, while at Queen's University [John Bell] had many discussions with a Catholic friend, Denis McConalogue, about the devil, and even attended some meetings of the Student Christian Movement for the sake of argument.

- ↑
*People and things*. 1990. - ↑ "Bell, John Stewart".
*Members of the Academy of Arts & Sciences, 1780–2010*(PDF). American Academy of Arts and Sciences. p. 41. Retrieved 8 October 2019. - ↑ Hardesty, Larry (12 September 2014). "Fluid mechanics suggests alternative to quantum orthodoxy".
*Phys.org*. Science X. Retrieved 8 October 2019. - ↑ Bell, John Stewart (1964). "On the Einstein Podolsky Rosen paradox".
*Physics Physique Физика*.**1**(3): 195–200. doi: 10.1103/PhysicsPhysiqueFizika.1.195 . - ↑ Einstein, Albert; Podolsky, Boris; Rosen, Nathan (1935). "Can quantum-mechanical description of physical reality be considered complete?".
*Physical Review*.**47**(10): 777–780. Bibcode:1935PhRv...47..777E. doi: 10.1103/PhysRev.47.777 . - ↑ Sutton, Christine (4 November 2014). "Fifty years of Bell's theorem".
*CERN official website*. CERN . Retrieved 8 October 2019.A paper by John Bell published on 4 November 1964 laid the foundations for the modern field of quantum-information science

- 1 2 3 4 5 6 7 8 Bell, John Stewart (1987).
*Speakable and Unspeakable in Quantum Mechanics*. Cambridge: Cambridge University Press. ISBN 978-0-521-36869-8. - ↑ Bell, John Stewart (1966). "On the problem of hidden variables in quantum mechanics".
*Reviews of Modern Physics*.**38**(3): 447–452. Bibcode:1966RvMP...38..447B. doi:10.1103/RevModPhys.38.447. OSTI 1444158. - ↑ von Neumann, John (1955).
*Mathematical Foundations of Quantum Mechanics*. Princeton: Princeton University Press. ISBN 978-0-691-02893-4. - ↑ Mann, Charles; Crease, Robert (1988). "Interview: John Bell".
*Omni*.**10**(8): 84–86, 88, 90, 92, 121. - ↑ Herzenberg, C. L. (2008). "Grete Hermann: An early contributor to quantum theory". arXiv: 0812.3986 [physics.gen-ph].
- ↑ Bub, Jeffrey (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. S2CID 118595119. - ↑ Bacciagaluppi, Guido; Crull, Elise (2009). "Heisenberg (and Schrödinger, and Pauli) on hidden variables".
*Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics*.**40**(4): 374–382. Bibcode:2009SHPMP..40..374B. CiteSeerX 10.1.1.484.3421 . doi:10.1016/j.shpsb.2009.08.004.Non-contextual hidden variables are those that fix values or probabilities or expectation values for all quantum mechanical observables, independent of any experimental context. The impossibility proofs of von Neumann (1932), Gleason (1957), and Kochen and Specker (1967) refer to this kind of hidden variables.

- ↑ Bernstein, Jeremy (1991).
*Quantum Profiles*. Princeton: Princeton University Press. ISBN 978-0691087252. OCLC 21971886. - ↑ Sudbery, Anthony (2018). "John Bell and the Great Enterprise".
*Quanta*.**7**(1): 68–73. arXiv: 1808.06845 . doi:10.12743/quanta.v7i1.79. MR 3894852. S2CID 53705805. - 1 2 Bell, Mary; Gottfried, Kurt; Veltman, Martinus, eds. (1995).
*Quantum Mechanics, High Energy Physics and Accelerators: Selected Papers of John S. Bell (With Commentary)*. World Scientific Series in 20th Century Physics.**9**. Singapore: World Scientific. doi:10.1142/2611. ISBN 9810221150. - 1 2 Rafelski, Johann (2017).
*Relativity Matters: From Einstein's EMC2 to Laser Particle Acceleration and Quark-Gluon Plasma*. Cham, Switzerland: Springer. doi:10.1007/978-3-319-51231-0. ISBN 978-3-319-51230-3. - ↑ Jackiw, R.; Shimony, A. (2008). "Bell, John Stewart".
*Complete Dictionary of Scientific Biography*. Retrieved 8 October 2019. - ↑ Sullivan, W. (10 October 1990). "John Stewart Bell Is Dead at 62; Physicist Tested Particle Actions".
*New York Times*. Retrieved 8 October 2019. - ↑ Fraser, Gordon (1990). "John Stewart Bell 1928-1990".
*CERN Courier*.**30**(8): 25. - ↑ Gilder, Louisa (2008).
*The Age of Entanglement: When Quantum Physics Was Reborn*. New York: Alfred A. Knopf. ISBN 978-1-4000-4417-7. OCLC 608258970. - ↑ Bernstein, Jeremy (2009).
*Quantum Leaps*. Cambridge, Massachusetts: Belknap Press: An Imprint of Harvard University Press. ISBN 978-0674035416. OCLC 648759731. - ↑ "John Stewart Bell Prize".
*Centre for Quantum Information and Quantum Control*. University of Toronto. Retrieved 8 October 2019. - ↑ "Prof. Nicolas Gisin awarded the First Bell Prize".
*Centre for Quantum Information and Quantum Control*. University of Toronto. Retrieved 8 October 2019. - ↑ Bertlmann, Reinhold A. (2017). "Bell's Universe: A Personal Recollection". In Bertlmann, Reinhold A.; Zeilinger, Anton (eds.).
*Quantum [Un]Speakables II: Half a Century of Bell's Theorem*. The Frontiers Collection. Cham, Switzerland: Springer. pp. 17–80. arXiv: 1605.08081 . doi:10.1007/978-3-319-38987-5_3. ISBN 978-3-319-38985-1. S2CID 119259828. - ↑ "John Bell Day".
*RIA*. The Royal Irish Academy. 2019. Retrieved 8 October 2019. - ↑ "John Bell: Belfast street named after physicist who proved Einstein wrong".
*BBC News*. BBC. 19 February 2015. Retrieved 8 October 2019. - ↑ "John Bell House, Belfast".
*Accommodation for Students*. 2019. Retrieved 8 October 2019. - ↑ "Sculpture celebrates football and physics links". Belfast City Council. 13 April 2018. Retrieved 8 October 2019.
- ↑ "Location".
*School of Maths and Physics*. Queen's University Belfast. 2019. Archived from the original on 9 January 2019. Retrieved 8 October 2019. - ↑ "Classical CDs Weekly: Haydn, Mahler, Matthew Whiteside | reviews, news & interviews | The Arts Desk".
*theartsdesk.com*. Retrieved 26 April 2021. - ↑
*Quartet No. 4 (Entangled) composed by Matthew Whiteside and film by Marisa Zanotti*, retrieved 26 April 2021

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