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.
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.
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”.
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.
It may well be that a relativistic version of the theory, while Lorentz invariant and local at the observational level, may be necessarily non-local and with a preferred frame (or aether) at the fundamental level. – John Bell [1] Introduction Bell's theorem establishes a contradiction between locality (and a few other assumptions) and certain predictions of quantum mechanics [2]. There have been two main issues surrounding the deep implications of this celebrated theorem. The first issue is basic, and it concerns whether the theorem really establishes that nonlocality is a necessary feature of any empirically viable theory and hence a feature of nature itself. One aspect of the issue concerns exactly what the underlying assumptions of Bell's theorem are. For example, some argue that these assumptions include the assumption of counterfactual definiteness [3–5], while others disagree [6–8]. The other aspect of the issue concerns which assumption should be dropped due to the resulting contradiction. Some believe that standard quantum mechanics may avoid nonlocality by denying counterfactual definiteness [3–5]. The second issue is much deeper, and it concerns how to make sense of the strange nonlocality when assuming that Bell's theorem establishes that our world is nonlocal. In particular, it has yet to be determined whether such quantum nonlocality is compatible with the theory of relativity, e.g., whether the nonlocality requires the existence of a preferred Lorentz frame [7, 9, 10]. It seems that “there is a preferred frame of reference, and in this preferred frame of reference things do go faster than light … Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant” [11]. But it also seems possible that the existence of a preferred Lorentz frame is an illusion, since it cannot be detected according to standard quantum mechanics. A more subtle issue is whether quantum nonlocality permits superluminal signaling. It is widely thought that the answers to these questions will lead to a deeper understanding of Bell's theorem and quantum nonlocality. In this paper, we will present a new analysis of quantum nonlocality and its apparent incompatibility with relativity.
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?
Quantum nonlocality is shown to be an artifact of the Copenhagen interpretation, in which each observed quantity has exactly one value at any instant. In reality, all physical systems obey quantum mechanics, which obeys no such rule. Locality is restored if observed and observer are both assumed to obey quantum mechanics, as in the many-worlds interpretation (MWI). Using the MWI, I show that the quantum side of Bell's inequality, generally believed nonlocal, is really due to a series of three measurements (not two as in the standard, oversimplified analysis), all three of which have only local effects. Thus, experiments confirming "nonlocality" are actually confirming the MWI. The mistaken interpretation of nonlocality experiments depends crucially on a question-begging version of the Born interpretation, which makes sense only in "collapse" versions of quantum theory, about the meaning of the modulus of the wave function, so I use the interpretation based on the MWI, namely that the wave function is a world density amplitude, not a probability amplitude. This view allows the Born interpretation to be derived directly from the Schrödinger equation, by applying the Schrödinger equation to both the observed and the observer.
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.