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?
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?
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.’
Various interpretations of quantum mechanics, favored (or neglected) by John Bell in the context of his nonlocality theorem, are compared and discussed. Varenna 1970 I met John Bell for the first time at the Varenna conference of 1970 [1]. I had been invited on the suggestion of Eugene P. Wigner, who had already helped me to publish my first paper on the concept that was later called decoherence – to appear in the first issue of Foundations of Physics a few months after the conference [2]. This concept arose from my conviction, based on many applications of quantum mechanics to composite systems under various conditions, that Schrödinger's wave function in configuration space, or more generally the superposition principle, is universally valid and applicable. In particular, stable narrow wavepackets can represent classical configurations, while their superpositions define novel individual properties – such as “momentum,” defined as a plane wave superposition of different positions. Superpositions of macroscopically different properties, on the other hand, are regularly irreversibly “dislocalized” (distributed over many degrees of freedom) by means of interactions described by the Schrödinger equation. The corresponding disappearance of certain local superpositions (“decoherence”) seems to explain the phenomenon of a classical world as well as the apparent occurrence of quantum jumps or stochastic “events” – see Sect. 20.4 or [3] for a historical overview of the conceptual development of quantum theory. So I had never felt any motivation to think of “hidden variables” or any other physics behind the successful wave function. Therefore, I was very surprised on my arrival in Varenna to hear everybody discuss Bell's inequality. It had been published a few years before the conference, but I had either not noticed it or not regarded it as particularly remarkable until then. As this inequality demonstrates that the predictions of quantum theory would require any conceivable reality possibly underlying the nonlocal wave function to be nonlocal itself, I simply found my conviction that the latter describes individual reality confirmed. For example, I had often discussed the conservation of total spin or angular momentum in an individual decay process, which requires nonlocal entanglement between the fragments at any distance in a form that was later called a “Bell state”.
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
Introduction Annus mirabilis 1964 1964 was a wonderful year for physics. In this annus mirabilis, summarising and simplifying a little, the quark model was proposed by Gell-Mann and Zweig and charm and colour properties were introduced, Higgs published his work on the scalar boson, the _ boson and CP violation were discovered, cosmic background radiation was identified and, finally, Bell inequalities were suggested. Most of these works were later subjects of a Nobel prize. Unluckily John Bell left us too early for this achievement, but, at least in my opinion, his work [1] is probably the most fruitful among all these huge advances, since now we can recognise that it was the root of a fundamental change in our vision of the physical world, providing, on one hand, the possibility of a test of quantum mechanics against a whole class of theories (substantially all the theories that we could define as “classical”) and, on the other hand, introducing a clear notion of quantum nonlocality that represents not only a challenge in understanding quantum mechanics, but also one of the most important resources paving the way to quantum technologies that were developed in the last decades based on the quantum correlations discussed in the Bell paper. In the following we will present the experimental progress in testing Bell inequalities. Rather amazingly even 50 years after Bell's paper, a conclusive test of his proposal is still missing [2, 3]. Nevertheless, huge progress has been achieved with respect to the first experiments.We will discuss these developments and the remaining problems for a conclusive test of Bell inequalities in detail. The Bell Inequalities, Their Hypotheses and the Experimental Loopholes In order to understand the experimental difficulties in achieving a final test of Bell inequalities, let us analyse a little how these inequalities are derived and the explicit and implicit hypotheses they contain. The proof of Bell inequalities usually starts by considering two separated subsystems of an entangled state, which are addressed to two independent measurement apparatuses measuring the expectation values of two dichotomic observables, Aa and B b . a, b are two parameters describing the settings of the measuring apparatus A and B , respectively.
I begin with some reminiscences of my delayed appreciation of the significance of John Bell'swork. Preparatory remarks on my general perspective concerning the interpretation of quantum mechanics are presented. I argue against the conflation of hyperplane dependence with frame dependence, which occurs occasionally; and that the ‘elements of reality’ of Hardy's famous gedankenexperiment can retain their Lorentz invariance, i.e., their frame independence, if one recognizes the hyperplane dependence of their localization, which follows. Finally, I criticize a view of the nature of Lorentz transformations presented by Asher Peres and co-workers which conflicts with the view employed here. Initial Reactions to Bell's Work Like many others in the physics community, I was late to come to an appreciation of the significance of John Bell's papers on the foundations of quantum mechanics (QM). But unlike many of those, my indifference to Bell was not due to a dismissive attitude to foundational studies per se or to an intransigent commitment to some version of Copenhagenism. In 1971, for example, I was very much involved in the international conference on QM foundations at my home institution, where Bell presented the paper “On the hypothesis that the Schrödinger equation is exact,” published later as [1], but I paid minimal attention to his presentation. The cause of this poor judgment (as I eventually came to realize it was) was that I was already convinced that the Schrödinger equation was not exact in the sense Bell meant, but must be augmented with primordial state reductions. I was among those who, in the words of Bob Wald, as reported by Roger Penrose [2], were inclined to “take it seriously,” the QM state that is, and, consequently, could not “really believe in it,” i.e., really believe that purely unitary QM is a complete theory. I was delighted when the experimental tests of Bell's inequalities upheld the QM predictions. I was, furthermore, uninterested in hidden variable reconstructions of QM, such as Bohmian mechanics [3] and Many Worlds interpretations [4, 5], that were, in principle, not susceptible to empirical tests of their novel details.