Introduction John S. Bell, of course, is best known for the result now referred to simply as “Bell's theorem,” which removed from consideration the class of so-called local hidden-variable theories that at the time of its publishing appeared to be the most natural class of theories among those that would render quantum mechanics a form of statistical mechanics. If, as this and other results suggest, quantum theory is to serve as a truly fundamental theory, conceptual precision in its interpretation is not only desirable but paramount. John Bell was accordingly concerned about what he viewed as conceptual imprecision, from the physical point of view, within the standard approaches to the theory. He saw this as most acute in the case of their treatment of measurement at the level of principle . His concerns were strongly expressed in the article “Against measurement” [1]. This was published in 1990 in a volume of proceedings of the 1989 Erice meeting “Sixty-Two Years of Uncertainty,” during which it was my pleasure to meet and eat with Bell, and to listen to him present this paper. He pointed out that this conceptual imprecision is reflected in the terminology of the foundations of quantum theory, a great deal of which he explicitly deemed worthy of banishment from discussions of principle, because it corresponds to a set of what he saw as vague and, in some instances, outright destructive concepts. His concern was thus not one regarding mathematics so much as regarding basic concepts used in contemporary quantum physics, which he viewed as failing the needs of natural philosophy and so of fundamental physics, despite their practical adequacy. Here, I consider John Bell's critique of standard quantum measurement theory and some alternative treatments wherein he saw greater conceptual precision, and make further suggestions as to how to improve conceptual precision, as he advocated. That the source of difficulties is to be understood specifically as a problem of imprecision of physical concepts that stands in the way of the achievement of an exact fundamental mechanical theory is pointed out at the outset of “Against measurement”: Bell wished to make it clear “at once that it is not mathematical precision, but physical” that caused him such great concern.
Introduction John S. Bell, of course, is best known for the result now referred to simply as “Bell's theorem,” which removed from consideration the class of so-called local hidden-variable theories that at the time of its publishing appeared to be the most natural class of theories among those that would render quantum mechanics a form of statistical mechanics. If, as this and other results suggest, quantum theory is to serve as a truly fundamental theory, conceptual precision in its interpretation is not only desirable but paramount. John Bell was accordingly concerned about what he viewed as conceptual imprecision, from the physical point of view, within the standard approaches to the theory. He saw this as most acute in the case of their treatment of measurement at the level of principle . His concerns were strongly expressed in the article “Against measurement” [1]. This was published in 1990 in a volume of proceedings of the 1989 Erice meeting “Sixty-Two Years of Uncertainty,” during which it was my pleasure to meet and eat with Bell, and to listen to him present this paper. He pointed out that this conceptual imprecision is reflected in the terminology of the foundations of quantum theory, a great deal of which he explicitly deemed worthy of banishment from discussions of principle, because it corresponds to a set of what he saw as vague and, in some instances, outright destructive concepts. His concern was thus not one regarding mathematics so much as regarding basic concepts used in contemporary quantum physics, which he viewed as failing the needs of natural philosophy and so of fundamental physics, despite their practical adequacy. Here, I consider John Bell's critique of standard quantum measurement theory and some alternative treatments wherein he saw greater conceptual precision, and make further suggestions as to how to improve conceptual precision, as he advocated. That the source of difficulties is to be understood specifically as a problem of imprecision of physical concepts that stands in the way of the achievement of an exact fundamental mechanical theory is pointed out at the outset of “Against measurement”: Bell wished to make it clear “at once that it is not mathematical precision, but physical” that caused him such great concern.
Lying at the heart of quantum mechanics, the notion of quantum superposition causes enormous difficulty in understanding the problem of quantum measurement, which concerns the Einstein-Bohr debate on the conceptual foundations of the quantum theory. According to Bell’s theorem, Einstein’s viewpoint in his debate with Bohr seems to be wrong. In the present paper, a new principle (referred to as the general principle of measurements) is introduced and proved as a mathematical theorem. Based on this principle, various forms of quantum superposition (including quantum entanglement) and the corresponding experiments are scrutinized. The main findings are as follows. (a) Einstein’s viewpoint is correct and Bell’s theorem is problematic. (b) Measurement outcomes of any actual experiment with individual microscopic objects described in a form of quantum superposition, in particular, the experimental results of testing Bell inequalities, are all erroneously explained. (c) Bell inequalities failed to capture the essence of the Einstein-Bohr debate, i.e., whether quantum superposition is legitimate for describing individual microscopic objects. (d) All kinds of quantum superposition violate the general principle of measurements and hence are illegitimate. (e) Quantum mechanics can be completed by using disjunction (“or”) as the logical relation between the orthonormal vectors that span an arbitrarily given Hilbert space for describing a single microscopic object, and the mathematical setting will remain essentially unchanged; hidden-variable theories are irrelevant to the real world. (f) After completing quantum mechanics as above, the difficulty in understanding the problem of quantum measurement disappears naturally. Implications of the findings are also discussed.
It is a pleasure to contribute to this anthology some of my recollections of John Bell. I first met him at SLAC, where we were visitors during 1964–5 when he was on leave from CERN, and I was on leave from the Columbia University Physics Department. Soon I found that we had a common interest in the foundations of quantum mechanics, and we had lively discussions on this subject. We were concerned with the “reduction of the wave packet” after an experiment in quantum mechanics was completed, and wrote a tongue-incheek article on this subject for a festschrift in honor of Viki Weisskopf [1], stating that We emphasize not only that our view is that of a minority but also that current interest in such questions is small. The typical physicist feels that they have long been answered, and that he will fully understand just how, if ever he can spare twenty minutes to think about it. Now, 50 years later, this topic, known as the measurement problem , has become the source of numerous articles representing many different viewpoints. At the time, however, I confess that I did not realize that the main flaw in John von Neumann's presentation of this problem was his assumption that a measuring device can be represented by a pointer with only two quantum states. Actually, a measuring device must be able to record the outcome of an experiment, and for this purpose it has to have an enormous number of quantum states, leading to an irreversible macroscopic transition in the device. A correct discussion of the measurement problemwas given, for example, by Nico vanKampen [2], but recently he told me that he was unable to persuade Bell, who continued to be concerned about this problem for the rest of his life. Indeed, shortly before he died, he wrote a diatribe [3] entitled “Against Measurement,” where he continued to argue that this problem constituted a fundamental flaw in quantum mechanics. Kurt Gottfried, who referred to this problem as Bell's second major theme, called his article “a fervent jeremiad summarizing a lifetime of reflection on what he saw as the fatal flaws of the orthodox theory” [4].
The newly revised edition of this well-known book categorizes prevalent views on measurement as described by quantum mechanics, discusses basics agreed to by many who on other issues disagree, and describes some of the problems. Although many paragraphs rest unchanged from the first (1991) edition, results found since 1991 are used to reorganize and sharpen the focus of the book, so that even the old paragraphs are now understood differently and more clearly. One advance in the second edition is a new and more general no-go theorem; another is separation of formal derivations from interpretation. The dozen or so definitions essential to following the book even casually are stated clearly. By this means the authors succeed pretty well in achieving their stated desire to make the book comprehensible to those who do not share their philosophic predispositions. While I differ in philosophy from the authors, attending to their discussion uncovered weaknesses in my own thinking and improved it. The mathematical language of quantum mechanics expresses a system under measurement by states (as rays in a Hilbert space) and a hamiltonian operator, distinct from the apparatus that produces outcomes, which is expressed by a positive operator-valued (POV) measure. In this way quantum language separates state preparation from state measurement. Often the Hilbert space is viewed as a tensor product of subspaces, allowing further conceptual separations. The authors take the stance that quantum mechanics calls for splitting the empirical world into parts, the most essential being (1) objective systems S (to be observed) and (2) apparatus A (preparation and registration devices that produces outcomes (or, as the authors write, definite pointer values) of the observed system). In some interpretations, one or both of an observer and an environment appear as additional parts. What is to be included in the system S versus the apparatus A is not specified by the language, but is open to the theoretician; a probe, for example, can be analysed as either part of the apparatus or as part of the system, as was discussed by von Neumann in work cited by the authors. With what should a theory of measurement be concerned? A broad division of approaches is defined by how one answers the question: should one try to do away with the cut between measuring apparatus and system? The authors phrase this as a choice of REFERENT, a term which in my mind puts them on shaky semantic ground; anyway The Quantum Theory of Measurement is concerned with implications of the `yes'. The book unfolds with the power of a tragedy, in which the logical consequences lead, step-by-step, to the statement and proof of theorem 6.2.1, which, roughly speaking, asserts the non-existence of a solution to the problem of getting definite pointer values from measuring apparatus that exhibits the superposition demanded by its description as a quantum system. Possible responses to this theorem are discussed, among them the many-worlds interpretation and a modification of quantum mechanics that elevates decoherence to a principle. Citations of the literature are thorough, and many points of view are crisply summarized. The book is indispensable to both those who work in the broad direction chosen by the authors and to those who wish to set any other direction in context.
In this paper, we shall show how the theory of measurements is to be understood from the point of view of a physical interpretation of the quantum theory in terms of "hidden" variables, developed in a previous paper. We find that in principle, these "hidden" variables determine the precise results of each individual measurement process. In practice, however, in measurements that we now know how to carry out, the observing apparatus disturbs the observed system in an unpredictable and uncontrollable way, so that the uncertainty principle is obtained as a practical limitation on the possible precision of measurements. This limitation is not, however, inherent in the conceptual structure of our interpretation. We shall see, for example, that simultaneous measurements of position and momentum having unlimited precision would in principle be possible if, as suggested in the previous paper, the mathematical formulation of the quantum theory needs to be modified at very short distances in certain ways that are consistent with our interpretation but not with the usual interpretation.We give a simple explanation of the origin of quantum-mechanical correlations of distant objects in the hypothetical experiment of Einstein, Podolsky, and Rosen, which was suggested by these authors as a criticism of the usual interpretation.Finally, we show that von Neumann's proof that quantum theory is not consistent with hidden variables does not apply to our interpretation, because the hidden variables contemplated here depend both on the state of the measuring apparatus and the observed system and therefore go beyond certain of von Neumann's assumptions.In two appendixes, we treat the problem of the electromagnetic field in our interpretation and answer certain additional objections which have arisen in the attempt to give a precise description for an individual system at the quantum level.
The notion of macroscopic realism has been used in attempts to achieve consistency between physics and everyday experience and to locate some boundary between the realms of classical mechanics and quantum meachanics. Its ostensibly underlying conceptual components, realism and macroscopicity, have most often appeared in the foundations of physics in relation to quantum measurement: reality became a prominent topic of discussion in quantum physics after the notion of element of reality was defined and used by Einstein, Podolsky and Rosen in that context, and macroscopicity is often explicitly assumed to be an essential property of any measuring apparatus. However, macroscopicity turns out to be a rather vaguer and less consistently understood notion than typically assumed by physicists who have not explicitly explored the notion themselves. For this reason, it behooves those investigating the foundations of quantum mechanics from a realist perspective to look for alternative notions for grounding quantum measurement. Here, the merits of treating the measuring instrument as a ‘natural kind’ as a means of avoiding anthropocentrism in the foundations of quantum measurement are pointed out as a means of advancing quantum measurement theory.