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John Bell and Bell's Theorem

Sheldon Goldstein, Roderich Tumulka, Nino Zangh�

Published Jan 1, 2004• 1 citation
OpenAlex

Abstract

John Stewart Bell (1928-1990), a truly deep and serious thinker, was one of the leading physi-cists of the 20th century. He became famous for his discovery that quantum mechanics impliesthat nature is nonlocal, i.e., that there are physical inuences between events that propagatefaster than light.From 1960 until his death Bell worked at CERN in Geneva on the physics of particle accel-erators, making a number of important contributions to high-energy physics and quantum eldtheory. Noteworthy was his discovery in 1969, together with Roman Jackiw, of the so-called\Bell-Jackiw-Adler anomaly (discovered independently by Stephen Adler), a mechanism ex-plaining physical e ects such as neutral pion decay (which are unexplainable on the basis of thesymmetries of the classical eld Lagrangian), in terms of an \anomalous term arising from therenormalization of quantum eld theory. Since then this mechanism has become an importantcornerstone of quantum eld theory. Another important contribution was the argument he gavein 1967 for why weak interactions should be described using a gauge theory.John Bell was one of the leading experts|perhaps the leading expert|on the foundations ofquantum mechanics. The book collecting his articles on this subject, Speakable and unspeakablein quantum mechanics, is unsurpassed for clarity and depth and it is still the best reference forwhoever wishes to learn about the eld [4].Bell strongly opposed the \Copenhagen interpretation of quantum physics, according towhich macroscopic objects, such as chairs and planets, do exist out there, but electrons andother microscopic particles do not. According to the Copenhagen view, the world is divided intotwo realms, macro and micro, \classical and \quantum, logical and contradictory|or, as Bellput it in one of his essays, into \speakable and \unspeakable. Along with Albert Einstein,Erwin Schrodinger, Louis de Broglie and !David Bohm, Bell was one of the few physicistscompelled by his conscience to reject the Copenhagen interpretation.Bell emphasized that the empirical facts of quantum physics do not at all force us to renouncerealism. There is, in fact, a realist theory (!Bohmian mechanics, also known as the de Broglie-Bohm theory) that accounts|insofar as the nonrelativistic theory is concerned|for all of thesefacts in a most elegant way. This theory describes a world in which electrons, quarks andthe like are point particles, always having positions that move in a manner dictated by thewave function. It should be taught to students, Bell insisted, as a legitimate alternative tothe prevailing orthodoxy. After GianCarlo Ghirardi, Alberto Rimini, and Tullio Weber in 1986succeeded in formulating a second kind of realist theory, Bell encouraged the further developmentof this theory as well [4, p. 201]. He thought that such a theory contained the seeds of a1

Related papers

John Stewart Bell and Twentieth-Century Physics

Andrew Charles Whitaker

Abstract John Stewart Bell was one of the most significant physicists of the twentieth century; his work has led to a much enhanced understanding of quantum theory and what it says about the physical universe, particularly about realism, determinism, and locality. This book describes Bell's relatively humble origins and his struggles to obtain secondary and university education. It then describes his work at Harwell, where he made important theoretical contributions to the development of particle accelerators, in particular with his pioneering work on strong focussing. Later, he proved the extremely important CPT theorem. At CERN, Bell made a range of important theoretical contributions to elementary particle physics; these contributions include the physics of neutrinos, the existence of different types of neutrinos, the suitability of gauge theory for all physical interactions, and the Adler–Bell–Jackiw anomaly, which shows how classical symmetries are lost under quantum theory. In his work on quantum theory, he criticized the orthodox 'Copenhagen' interpretation of quantum theory, which did not allow the actual state of the physical world to be analysed. He showed that the famous von Neumann theorem, which claimed to show that 'hidden variables' were not allowed in quantum theory, was incorrect; his famous Bell's theorem, or Bell's inequality, showed that any such variables much be non-local. Bell's work led to greatly increased freedom in the discussion of quantum theory, and the development of quantum information theory.

Oxford University Press eBooks•Jun 16, 2016•15 citations

Bell on Bohm

Sheldon Goldstein

Prologue A memorial conference for John Bell, open to the public, was held at Rutgers University around 20 years ago. I gave a short talk there on Bell's views about David Bohm's “hidden variables” formulation of quantum mechanics, a version of quantum mechanics often called the de Broglie–Bohm theory or Bohmian mechanics. This theory was in fact discovered by Louis de Broglie in 1927. In 1952, it was rediscovered and developed by Bohm, who was the first to appreciate its connection to the predictions of standard quantum mechanics. I did not publish the talk. I have decided that it would be appropriate to publish a very lightly edited version of it here, in this volume devoted to the work of Bell on the foundation of quantum mechanics. One reason for doing so is that the connection between Bell and Bohm continues to be somewhat underplayed, with the strength of his advocacy of Bohmian mechanics not properly appreciated. For example, about half of the papers in Bell's collected works on the foundations of quantum mechanics deal with Bohmian mechanics. But in his fine introduction to the revised edition of this great book [1], Alain Aspect mentions this theory in only a single sentence, and parenthetically at that. For several decades after Bell proved his nonlocality theorem, based in part on Bell's inequality, it was widely claimed that Bell had shown that hidden variables – and Bohmian mechanics in particular – were impossible, that they were incompatible with the predictions of quantum mechanics. For example, the great physicist Eugene Wigner, who, unlike most of his contemporaries, was profoundly concerned with the conceptual foundations of quantum mechanics and usually wrote on the subject with great clarity and insight, has written that This [hidden variables] is an interesting idea and even though few of us were ready to accept it, it must be admitted that the truly telling argument against it was produced as late as 1965, by J. S. Bell … This appears to give a convincing argument against the hidden variables theory.

Cambridge University Press eBooks•Aug 31, 2016•0 citations

John Stewart Bell and Twentieth-Century Physics: Vision and Integrity

Andrew Whitaker

John Stewart Bell (1928-1990) was one of the most important figures in twentieth-century physics, famous for his work on the fundamental aspects of the century's most important theory, quantum mechanics. While the debate over quantum theory between the supremely famous physicists, Albert Einstein and Niels Bohr, appeared to have become sterile in the 1930s, Bell was able to revive it and to make crucial advances - Bell's Theorem or Bell's Inequalities. He was able to demonstrate a contradiction between quantum theory and essential elements of pre-quantum theory - locality and causality. The book gives a non-mathematical account of Bell's relatively impoverished upbringing in Belfast and his education. It describes his major contributions to quantum theory, but also his important work in the physics of accelerators, and nuclear and elementary particle physics.

•Jul 7, 2016•4 citations

Some Personal Reflections on Quantum Nonlocality and the Contributions of John Bell

Basil J. Hiley

I present the background of the Bohm approach that led John Bell to a study of quantum nonlocality, from which his famous inequalities emerged. I recall the early experiments done at Birkbeck with the aim of exploring the possibility of ‘spontaneous collapse’, a way suggested by Schrödinger to avoid the conclusion that quantum mechanics is grossly nonlocal. I also review some of the work that John did which directly impinged on my own investigations into the foundations of quantum mechanics and report some new investigations towards a more fundamental theory. Introduction My first encounter with quantum nonlocality was in discussions with David Bohm when I joined him as an assistant lecturer at Birkbeck in the sixties. Although my PhD thesis had been in condensed matter physics under the supervision of Cyril Domb, I had always been fascinated and puzzled by quantum phenomena, and when the opportunity to study the subject with Bohm came up, I took it. I would listen to the discussions between Bohm and Roger Penrose, who was at Birkbeck at the time, and it soon became clear that the prescribed interpretation of quantum mechanics that I was taught as an undergraduate left too many questions unanswered. At that time there was a very strange atmosphere in the physics community. I was often informed that there were no problems with the interpretation of the quantum formalism. If I did not follow the well-prescribed rules of the quantum algorithm, I would be ‘wasting my time’. There was no alternative, just do it! But Louis de Broglie and David Bohm had shown there was another way. However, their views were strongly opposed by many, and as far as I could judge their reasons did not seem to be based on mathematics or on logic, but on a preconceived notion that the formalism was, in principle, the best we could do. The experimental data were bizarre when looked upon from the standpoint of classical physics, but the uncertainty principle somehow prevented us from examining the actual process in detail. Reality was somehow veiled (see [1]).Were we condemned to use a mere algorithm or was there an underlying ontology?

arXiv:1412.0594•Cambridge University Press eBooks•Aug 31, 2016•0 citations

The 1960s

Andrew Charles Whitaker

During the 1960s, Bell produced his seminal work on the foundations of quantum theory, first showing that, contrary to von Neumann’s argument, hidden variable theories were allowed but then that they had to be non-local. Thus, he showed that quantum theory did not respect local causality, and he outlined experiments that could be used to test whether the assumption of local realism was true in quantum theory: Bell’s theorem, or Bell’s inequality, or Bell’s inequalities. His work was followed up by John Clauser, Abner Shimony, Michael Horne, and Richard Holt, who produced the CHSH inequality. Bell had moved to CERN, where he worked on the theory of neutrino experiments, and on nuclear and elementary particle physics, making crucial suggestions concerning the use of gauge theory for each type of physical force and also producing the Adler–Bell–Jackiw anomaly, or the ABJ anomaly.

Oxford University Press eBooks•Jun 16, 2016•0 citations

Speakable and Unspeakable in Quantum Mechanics

James S. Bell, Alain Aspect

John Bell, FRS was one of the leading expositors and interpreters of modern quantum theory. He is particularly famous for his discovery of the crucial difference between the predictions of conventional quantum mechanics and the implications of local causality, a concept insisted on by Einstein. John Bell's work played a major role in the development of our current understanding of the profound nature of quantum concepts and of the fundamental limitations they impose on the applicability of the classical ideas of space, time and locality. This book includes all of John Bell's published and unpublished papers on the conceptual and philosophical problems of quantum mechanics, including two papers that appeared after the first edition was published. The book includes a short Preface written by the author for the first edition, and also an introduction by Alain Aspect that puts into context John Bell's enormous contribution to the quantum philosophy debate.

Cambridge University Press eBooks•Jun 3, 2004•1,258 citations
John Stewart Bell (1928-1990), a truly deep and serious thinker, was one of the leading physi-cists of the 20th century. He became famous for his discovery that quantum mechanics impliesthat nature is nonlocal, i.e., that there are physical inuences between events that propagatefaster than light.From 1960 until his death Bell worked at CERN in Geneva on the physics of particle accel-erators, making a number of important contributions to high-energy physics and quantum eldtheory. Noteworthy was his discovery in 1969, together with Roman Jackiw, of the so-called\Bell-Jackiw-Adler anomaly (discovered independently by Stephen Adler), a mechanism ex-plaining physical e ects such as neutral pion decay (which are unexplainable on the basis of thesymmetries of the classical eld Lagrangian), in terms of an \anomalous term arising from therenormalization of quantum eld theory. Since then this mechanism has become an importantcornerstone of quantum eld theory. Another important contribution was the argument he gavein 1967 for why weak interactions should be described using a gauge theory.John Bell was one of the leading experts|perhaps the leading expert|on the foundations ofquantum mechanics. The book collecting his articles on this subject, Speakable and unspeakablein quantum mechanics, is unsurpassed for clarity and depth and it is still the best reference forwhoever wishes to learn about the eld [4].Bell strongly opposed the \Copenhagen interpretation of quantum physics, according towhich macroscopic objects, such as chairs and planets, do exist out there, but electrons andother microscopic particles do not. According to the Copenhagen view, the world is divided intotwo realms, macro and micro, \classical and \quantum, logical and contradictory|or, as Bellput it in one of his essays, into \speakable and \unspeakable. Along with Albert Einstein,Erwin Schrodinger, Louis de Broglie and !David Bohm, Bell was one of the few physicistscompelled by his conscience to reject the Copenhagen interpretation.Bell emphasized that the empirical facts of quantum physics do not at all force us to renouncerealism. There is, in fact, a realist theory (!Bohmian mechanics, also known as the de Broglie-Bohm theory) that accounts|insofar as the nonrelativistic theory is concerned|for all of thesefacts in a most elegant way. This theory describes a world in which electrons, quarks andthe like are point particles, always having positions that move in a manner dictated by thewave function. It should be taught to students, Bell insisted, as a legitimate alternative tothe prevailing orthodoxy. After GianCarlo Ghirardi, Alberto Rimini, and Tullio Weber in 1986succeeded in formulating a second kind of realist theory, Bell encouraged the further developmentof this theory as well [4, p. 201]. He thought that such a theory contained the seeds of a1
Abstract John Stewart Bell was one of the most significant physicists of the twentieth century; his work has led to a much enhanced understanding of quantum theory and what it says about the physical universe, particularly about realism, determinism, and locality. This book describes Bell's relatively humble origins and his struggles to obtain secondary and university education. It then describes his work at Harwell, where he made important theoretical contributions to the development of particle accelerators, in particular with his pioneering work on strong focussing. Later, he proved the extremely important CPT theorem. At CERN, Bell made a range of important theoretical contributions to elementary particle physics; these contributions include the physics of neutrinos, the existence of different types of neutrinos, the suitability of gauge theory for all physical interactions, and the Adler–Bell–Jackiw anomaly, which shows how classical symmetries are lost under quantum theory. In his work on quantum theory, he criticized the orthodox 'Copenhagen' interpretation of quantum theory, which did not allow the actual state of the physical world to be analysed. He showed that the famous von Neumann theorem, which claimed to show that 'hidden variables' were not allowed in quantum theory, was incorrect; his famous Bell's theorem, or Bell's inequality, showed that any such variables much be non-local. Bell's work led to greatly increased freedom in the discussion of quantum theory, and the development of quantum information theory.
Prologue A memorial conference for John Bell, open to the public, was held at Rutgers University around 20 years ago. I gave a short talk there on Bell's views about David Bohm's “hidden variables” formulation of quantum mechanics, a version of quantum mechanics often called the de Broglie–Bohm theory or Bohmian mechanics. This theory was in fact discovered by Louis de Broglie in 1927. In 1952, it was rediscovered and developed by Bohm, who was the first to appreciate its connection to the predictions of standard quantum mechanics. I did not publish the talk. I have decided that it would be appropriate to publish a very lightly edited version of it here, in this volume devoted to the work of Bell on the foundation of quantum mechanics. One reason for doing so is that the connection between Bell and Bohm continues to be somewhat underplayed, with the strength of his advocacy of Bohmian mechanics not properly appreciated. For example, about half of the papers in Bell's collected works on the foundations of quantum mechanics deal with Bohmian mechanics. But in his fine introduction to the revised edition of this great book [1], Alain Aspect mentions this theory in only a single sentence, and parenthetically at that. For several decades after Bell proved his nonlocality theorem, based in part on Bell's inequality, it was widely claimed that Bell had shown that hidden variables – and Bohmian mechanics in particular – were impossible, that they were incompatible with the predictions of quantum mechanics. For example, the great physicist Eugene Wigner, who, unlike most of his contemporaries, was profoundly concerned with the conceptual foundations of quantum mechanics and usually wrote on the subject with great clarity and insight, has written that This [hidden variables] is an interesting idea and even though few of us were ready to accept it, it must be admitted that the truly telling argument against it was produced as late as 1965, by J. S. Bell … This appears to give a convincing argument against the hidden variables theory.
John Stewart Bell (1928-1990) was one of the most important figures in twentieth-century physics, famous for his work on the fundamental aspects of the century's most important theory, quantum mechanics. While the debate over quantum theory between the supremely famous physicists, Albert Einstein and Niels Bohr, appeared to have become sterile in the 1930s, Bell was able to revive it and to make crucial advances - Bell's Theorem or Bell's Inequalities. He was able to demonstrate a contradiction between quantum theory and essential elements of pre-quantum theory - locality and causality. The book gives a non-mathematical account of Bell's relatively impoverished upbringing in Belfast and his education. It describes his major contributions to quantum theory, but also his important work in the physics of accelerators, and nuclear and elementary particle physics.
I present the background of the Bohm approach that led John Bell to a study of quantum nonlocality, from which his famous inequalities emerged. I recall the early experiments done at Birkbeck with the aim of exploring the possibility of ‘spontaneous collapse’, a way suggested by Schrödinger to avoid the conclusion that quantum mechanics is grossly nonlocal. I also review some of the work that John did which directly impinged on my own investigations into the foundations of quantum mechanics and report some new investigations towards a more fundamental theory. Introduction My first encounter with quantum nonlocality was in discussions with David Bohm when I joined him as an assistant lecturer at Birkbeck in the sixties. Although my PhD thesis had been in condensed matter physics under the supervision of Cyril Domb, I had always been fascinated and puzzled by quantum phenomena, and when the opportunity to study the subject with Bohm came up, I took it. I would listen to the discussions between Bohm and Roger Penrose, who was at Birkbeck at the time, and it soon became clear that the prescribed interpretation of quantum mechanics that I was taught as an undergraduate left too many questions unanswered. At that time there was a very strange atmosphere in the physics community. I was often informed that there were no problems with the interpretation of the quantum formalism. If I did not follow the well-prescribed rules of the quantum algorithm, I would be ‘wasting my time’. There was no alternative, just do it! But Louis de Broglie and David Bohm had shown there was another way. However, their views were strongly opposed by many, and as far as I could judge their reasons did not seem to be based on mathematics or on logic, but on a preconceived notion that the formalism was, in principle, the best we could do. The experimental data were bizarre when looked upon from the standpoint of classical physics, but the uncertainty principle somehow prevented us from examining the actual process in detail. Reality was somehow veiled (see [1]).Were we condemned to use a mere algorithm or was there an underlying ontology?
During the 1960s, Bell produced his seminal work on the foundations of quantum theory, first showing that, contrary to von Neumann’s argument, hidden variable theories were allowed but then that they had to be non-local. Thus, he showed that quantum theory did not respect local causality, and he outlined experiments that could be used to test whether the assumption of local realism was true in quantum theory: Bell’s theorem, or Bell’s inequality, or Bell’s inequalities. His work was followed up by John Clauser, Abner Shimony, Michael Horne, and Richard Holt, who produced the CHSH inequality. Bell had moved to CERN, where he worked on the theory of neutrino experiments, and on nuclear and elementary particle physics, making crucial suggestions concerning the use of gauge theory for each type of physical force and also producing the Adler–Bell–Jackiw anomaly, or the ABJ anomaly.
John Bell, FRS was one of the leading expositors and interpreters of modern quantum theory. He is particularly famous for his discovery of the crucial difference between the predictions of conventional quantum mechanics and the implications of local causality, a concept insisted on by Einstein. John Bell's work played a major role in the development of our current understanding of the profound nature of quantum concepts and of the fundamental limitations they impose on the applicability of the classical ideas of space, time and locality. This book includes all of John Bell's published and unpublished papers on the conceptual and philosophical problems of quantum mechanics, including two papers that appeared after the first edition was published. The book includes a short Preface written by the author for the first edition, and also an introduction by Alain Aspect that puts into context John Bell's enormous contribution to the quantum philosophy debate.