John Bell was a staunch supporter of the dynamical wave function collapse approach to making a well-defined quantum theory. Through letters from him, I reminisce on my handful of interactions with him, all of which were memorable tome. Then I discuss nonlocality, violation of Bell's inequality and some further implications within the framework of the CSL (continuous spontaneous localization) model of dynamical collapse. Interactions I was an instructor at Harvard with a newly minted Ph.D. from MIT, earned with an indifferent thesis on particle theory. It took me two years to come to terms with, dare I say it, the fact that I did not care about the S-matrix. I was going to be out of a job anyway in 1966 so, in the fall of 1965, I put my full energy into writing my very first paper, about what I did care: that, to my eyes there was something deeply wrong with the quantum theory I had been taught; that the rules of how to use it were inadequate. The title of the paper [1] was “Elimination of the reduction postulate from quantum theory and a framework for hidden variable theories.” It was a long title, because it was really two rather separate papers. The first was based upon the perceived inadequacy that the collapse (reduction) postulate of the theory is ill-defined. The second stated some postulates I thought a good hidden variable theory ought to obey, and gave a model for their satisfaction in a two-dimensional (i.e., spin-1/2) Hilbert space. Try as I might, I was not able to generalize my model to a higher-dimensional (i.e., spin-1) Hilbert space, but I put it out there for someone more clever than I to achieve. I sent the paper to a very few people who I thought might be interested. One was John Bell, and he replied (see Figure 23.1)! So someone more clever than I pointed out that generalizing my model could not be achieved. I therefore excised the model and, after rewriting and retitling, published my very first paper [2]! After a three-year stint at Case Institute of Technology, which graduated to become Case Western Reserve University while I was there, in 1969 I became ensconced at Hamilton College.
John Bell was a staunch supporter of the dynamical wave function collapse approach to making a well-defined quantum theory. Through letters from him, I reminisce on my handful of interactions with him, all of which were memorable tome. Then I discuss nonlocality, violation of Bell's inequality and some further implications within the framework of the CSL (continuous spontaneous localization) model of dynamical collapse. Interactions I was an instructor at Harvard with a newly minted Ph.D. from MIT, earned with an indifferent thesis on particle theory. It took me two years to come to terms with, dare I say it, the fact that I did not care about the S-matrix. I was going to be out of a job anyway in 1966 so, in the fall of 1965, I put my full energy into writing my very first paper, about what I did care: that, to my eyes there was something deeply wrong with the quantum theory I had been taught; that the rules of how to use it were inadequate. The title of the paper [1] was “Elimination of the reduction postulate from quantum theory and a framework for hidden variable theories.” It was a long title, because it was really two rather separate papers. The first was based upon the perceived inadequacy that the collapse (reduction) postulate of the theory is ill-defined. The second stated some postulates I thought a good hidden variable theory ought to obey, and gave a model for their satisfaction in a two-dimensional (i.e., spin-1/2) Hilbert space. Try as I might, I was not able to generalize my model to a higher-dimensional (i.e., spin-1) Hilbert space, but I put it out there for someone more clever than I to achieve. I sent the paper to a very few people who I thought might be interested. One was John Bell, and he replied (see Figure 23.1)! So someone more clever than I pointed out that generalizing my model could not be achieved. I therefore excised the model and, after rewriting and retitling, published my very first paper [2]! After a three-year stint at Case Institute of Technology, which graduated to become Case Western Reserve University while I was there, in 1969 I became ensconced at Hamilton College.
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”.
Abstract This book describes one approach to resolving the ‘measurement problem’ of standard quantum theory (SQT), by changing the Schrodinger equation’s evolution of the wave function. The wave function of SQT does not describe reality. For example, the wave function corresponding to a completed experiment is the sum of terms describing the different experimental outcomes whereas one of these outcomes is what appears in Nature, The rules of SQT respond to this deficiency by imposing an ill-defined ‘collapse postulate.’ The prior smooth evolution of the wave function according to Schrodinger’s equation is replaced by an abrupt ‘jump’ to one of the outcomes. When, why, how are unanswered questions. I have added a term to Schrodinger’s equation, obtaining a theory (which I named the ‘Continuous Spontaneous Localization’ theory, or CSL) that answers these questions. The term has a random field in it: each field makes the sum of terms evolve to one of the terms. The collection of all possible fields produces the (Born rule) probabilistic predictions of SQT. Thus, CSL does something SQT does not: it describes the occurrence of events. But, it is a different theory than SQT, so it predicts different results for some carefully crafted experiments. CSL has now existed for over three decades. While no experiment as yet has proven CSL true, no experiment has conflicted with it either. In this book I have aimed to give a clear exposition of CSL and its consequences, accessible to anyone who has studied SQT.
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.
Different attempts to solve the measurement problem of the quantum me-chanics (QM) by denying the collapse principle, and replacing it with changes in the quantum formalism, failed because the changes in the formalism lead to contradictions with QM predictions. To the difference, Ghirardi, Rimini and Weber took the collapse as a real phenomenon, and proposed a calculus by which the wave-function should undergo a sudden localization. Later on, Ghirardi, Pearle and Rimini came with a change of this calculus into the CSL (continuous spontaneous localization) model of collapse. Both these proposals rely on the experimental fact that the reduction of the wave-function occurs when the microscopic system encounters a macroscopic object and involves a big amount of its particles. Both these proposals also change the quantum formalism by introducing in the Schr?dinger equation additional terms with noisy behavior. However, these terms have practically no influence as long as the studied system contains only one or a few components. Only when the amount of components is very big, these terms become significant and lead to the reduction of the wave-function to one of its components. The present work has two purposes: 1) proving that the collapse postulate is unavoidable; 2) ap-plying the CSL model to the process in a detector and showing step by step the modification of the wave-function, until reduction. As a side detail, it is argued here that the noise cannot originate in some classical field, contrary to the thought/hope of some physicists, because no classical field is tailored by the wave-functions of entanglements.
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.’