Introduction: The Theory of Local Beables John Bell's most celebrated contribution to the foundations of physics is his famous theorem. The theorem demonstrates that any physical theory capable of generating the predictions of the standard quantum-mechanical algorithm, in particular the prediction of violations of Bell's inequality for experiments done at spacelike separation, cannot be local. The sense of “locality” used here is the same sense that Einstein had in mind when he pointed out that the standard interpretation of the quantum algorithm was committed to “spooky action at a distance” To this day, the import of Bell's theorem is not universally appreciated. I have written about this elsewhere [1], and others in this volume will take up that task. It is properly the main focus during this 50th anniversary of that great achievement. But it is also important to recall and celebrate Bell's other achievements. In many of his later writings, including “The Theory of Local Beables,” “Quantum Mechanics for Cosmologists,” “On the Impossible Pilot Wave,” “Beables for Quantum Field Theory,” “Six Possible Worlds of Quantum Mechanics,” “Are There Quantum Jumps?” and “Against ‘Measurement,”’ 1 Bell turned his attention to the more general problem of physically construing the mathematical formalism used to derive these predictions. This activity is often denominated “interpreting quantum theory” as if there were some precise physical theory that might somehow be supplemented with an “interpretation” Once the issue is framed this way it is easy to ask: But if I already have a theory in hand, what can be gained by supplementing it with an “interpretation”? Many physicists, at this juncture, are happy to conclude that “interpretations” are not a matter of physics at all – maybe they are only of interest to philosophers – and that therefore the whole enterprise of “interpreting quantum theory” is not within the purview of physics per se. What then is in the purviewof physics proper?One answer to this question goes under the banner “instrumentalism”: all physics as such, is concerned about is predicting the outcomes of experiments .
Introduction: The Theory of Local Beables John Bell's most celebrated contribution to the foundations of physics is his famous theorem. The theorem demonstrates that any physical theory capable of generating the predictions of the standard quantum-mechanical algorithm, in particular the prediction of violations of Bell's inequality for experiments done at spacelike separation, cannot be local. The sense of “locality” used here is the same sense that Einstein had in mind when he pointed out that the standard interpretation of the quantum algorithm was committed to “spooky action at a distance” To this day, the import of Bell's theorem is not universally appreciated. I have written about this elsewhere [1], and others in this volume will take up that task. It is properly the main focus during this 50th anniversary of that great achievement. But it is also important to recall and celebrate Bell's other achievements. In many of his later writings, including “The Theory of Local Beables,” “Quantum Mechanics for Cosmologists,” “On the Impossible Pilot Wave,” “Beables for Quantum Field Theory,” “Six Possible Worlds of Quantum Mechanics,” “Are There Quantum Jumps?” and “Against ‘Measurement,”’ 1 Bell turned his attention to the more general problem of physically construing the mathematical formalism used to derive these predictions. This activity is often denominated “interpreting quantum theory” as if there were some precise physical theory that might somehow be supplemented with an “interpretation” Once the issue is framed this way it is easy to ask: But if I already have a theory in hand, what can be gained by supplementing it with an “interpretation”? Many physicists, at this juncture, are happy to conclude that “interpretations” are not a matter of physics at all – maybe they are only of interest to philosophers – and that therefore the whole enterprise of “interpreting quantum theory” is not within the purview of physics per se. What then is in the purviewof physics proper?One answer to this question goes under the banner “instrumentalism”: all physics as such, is concerned about is predicting the outcomes of experiments .
John Stewart Bell’s famous theorem is widely regarded as one of the most important developments in the foundations of physics. Yet even as we approach the 50th anniversary of Bell’s discovery, its meaning and implications remain controversial. Many workers assert that Bell’s theorem refutes the possibility suggested by Einstein, Podolsky, and Rosen (EPR) of supplementing ordinary quantum theory with “hidden” variables that might restore determinism and/or some notion of an observer-independent reality. But Bell himself interpreted the theorem very differently—as establishing an “essential conflict” between the well-tested empirical predictions of quantum theory and relativistic local causality. Our goal is to make Bell’s own views more widely known and to explain Bell’s little-known formulation of the concept of relativistic local causality on which his theorem rests. We also show precisely how Bell’s formulation of local causality can be used to derive an empirically testable Bell-type inequality and to recapitulate the EPR argument.
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.
On the 50th anniversary of Bell's monumental 1964 paper, there is still widespread misunderstanding about exactly what Bell proved. This misunderstanding derives in turn from a failure to appreciate the earlier argument of Einstein, Podolsky and Rosen. I retrace the history and logical structure of these arguments in order to clarify the proper conclusion, namely that any world that displays violations of Bell's inequality for experiments done far from one another must be non-local. Since the world we happen to live in displays such violations, actual physics is non-local. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.
J.S. Bell's remarkable 1964 theorem showed that any theory sharing the empirical predictions of orthodox quantum mechanics would have to exhibit a surprising – and, from the point of view of relativity theory, very troubling – kind of nonlocality. Unfortunately, even still on this 50th anniversary, many commentators and textbook authors continue to misrepresent Bell's theorem. In particular, one continues to hear the claim that Bell's result leaves open the option of concluding either nonlocality or the failure of some unorthodox “hidden variable” (or “determinism” or “realism”) premise. This mistaken claim is often based on a failure to appreciate the role of the earlier 1935 argument of Einstein, Podolsky, and Rosen in Bell's reasoning. After briefly reviewing this situation, I turn to two alternative versions of quantum theory – the “many worlds” theory of Everett and the quantum Bayesian interpretation of Fuchs, Schack, Caves, and Mermin – that purport to provide actual counterexamples to Bell's claim that nonlocality is required to account for the empirically verified quantum predictions. After analyzing each theory's grounds for claiming to explain the EPR–Bell correlations locally, however, one can see that (despite a number of fundamental differences) the two theories share a common for-all-practical-purposes (FAPP) solipsistic character. This dramatically undermines such theories’ claims to provide a local explanation of the correlations and thus, by concretizing the ridiculous philosophical lengths to which one must go to elude Bell's own conclusion, reinforces the assertion that nonlocality really is required to coherently explain the empirical data. Introduction Fifty years ago, in 1964 [1], John Stewart Bell first proved the theorem that has become widely known as “Bell's Theorem” but that Bell himself instead referred to as the “locality inequality theorem” [2]. In Bell's own view, the theorem showed that the empirical predictions of local theories will be constrained by Bell's inequality (or as Bell himself preferred to call it, the “locality inequality”). Hence, nonlocality is a necessary feature of any theory that shares the empirical predictions of standard quantum mechanics.
Introduction This contribution to the book in honour of J. S. Bell will probably differ from the remaining ones, in particular since only a part of it will be devoted to specific technical arguments. In fact I have considered it appropriate to share with the community of physicists interested in the foundational problems of our best theory the repeated interactions I had with him in the last four years of his life, the deep discussions in which we have been involved in particular in connection with the elaboration of collapse theories and their interpretation, and the contributions he gave to the development of this approach at a formal level, as well as championing it on repeated occasions. In brief, I intend to play here the role of one of those lucky persons who became acquainted with him personally, who has exchanged important views with him, who has learned a lot from his deep insight and conceptual lucidity, and, last but not least, whose scientific work has been appreciated by him. Moreover, due to the fact that this book intends to celebrate the 50th anniversary of the derivation of the fundamental inequality which bears his name, I will also devote a small part of the text to recalling his clearcut views about the locality issue, views that I believe have not been grasped correctly by a remarkable part of the scientific community. I will analyze this problem in quite general terms at the end of the paper. Some of Bell's Scientific Achievements Bell received bachelor's degrees in experimental physics and in mathematical physics at Queen'sUniversity of Belfast in the years 1948 and 1949, respectively, and a PhD in physics at the University of Birmingham. We all know very well that already at that time he was absolutely unsatisfied with the conceptual structure of quantum mechanics and with the way in which it was taught. This is significantly expressed by the statement he made during an interview to Jeremy Bernstein: I remember arguing with one of my professors, a Doctor Sloane, about that. I was getting very heated and accusing him, more or less, of dishonesty. He was getting very heated too and said, ‘You're going too far.’
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?