Showing papers on "Consistent histories published in 1970"
TL;DR: The Statistical Interpretation of quantum theory is formulated for the purpose of providing a sound interpretation using a minimum of assumptions as discussed by the authors, and it is based on the assumption that the quantum state description applies only to an ensemble of similarly prepared systems, rather than supposing, as is often done, that it exhaustively represents an individual physical system.
Abstract: The Statistical Interpretation of quantum theory is formulated for the purpose of providing a sound interpretation using a minimum of assumptions Several arguments are advanced in favor of considering the quantum state description to apply only to an ensemble of similarily prepared systems, rather than supposing, as is often done, that it exhaustively represents an individual physical system Most of the problems associated with the quantum theory of measurement are artifacts of the attempt to maintain the latter interpretation The introduction of hidden variables to determine the outcome of individual events is fully compatible with the statistical predictions of quantum theory However, a theorem due to Bell seems to require that any such hidden-variable theory which reproduces all of quantum mechanics exactly (ie, not merely in some limiting case) must possess a rather pathological character with respect to correlated, but spacially separated, systems
933 citations
TL;DR: In this article, the authors provide a mathematical framework for the process of making repeated measurements on continuous observables in a statistical system and make a mathematical definition of an instrument, a concept which generalises the notion of an observable and that of an operation.
Abstract: In order to provide a mathmatical framework for the process of making repeated measurements on continuous observables in a statistical system we make a mathematical definition of an instrument, a concept which generalises that of an observable and that of an operation. It is then possible to develop such notions as joint and conditional probabilities without any of the commutation conditions needed in the approach via observables. One of the crucial notions is that of repeatability which we show is implicitly assumed in most of the axiomatic treatments of quantum mechanics, but whose abandonment leads to a much more flexible approach to measurement theory.
890 citations
TL;DR: In this paper, it is argued that the probability interpretation is compatible with an objective interpretation of the wave function, and it is shown that this interpretation is also compatible with the objective interpretation.
Abstract: It is demonstrated that neither the arguments leading to inconsistencies in the description of quantum-mechanical measurement nor those “explaining” the process of measurement by means of thermodynamical statistics are valid. Instead, it is argued that the probability interpretation is compatible with an objective interpretation of the wave function.
841 citations
TL;DR: An abstract definition of a general hidden-variables theory is given, and it is shown that such a theory is always possible in the present framework of quantum mechanics and is, in fact, unique in a certain sense as discussed by the authors.
Abstract: An abstract definition of a general hidden‐variables theory is given, and it is shown that such a theory is always possible in the present framework of quantum mechanics and is, in fact, unique in a certain sense. It is noted that the Bohm‐Bub hidden‐variables example is contained in this theory and an attempt is made to clarify the position of this theory with respect to hidden‐variable impossibility proofs. The general definition is used in the consideration of quantum‐mechanical ordering and the measurement process.
99 citations
TL;DR: In this paper, the authors argue that although Jauch does exhibit a consistent quantum formalism for dealing with situations of the type involved in the original paradox, that formalism, so far from doing away with the paradox, serves only to highlight the difficulties of providing an acceptable physical understanding of it.
Abstract: Professor J. Jauch, in his recent book, Foundations of Quantum Mechanics, claims to resolve the paradox of Einstein, Podolsky, and Rosen. Jauch's approach is representative of that adopted by the majority of physicists. I argue that, although Jauch does exhibit a consistent quantum formalism for dealing with situations of the type involved in the original paradox, that formalism, so far from doing away with the paradox, serves only to highlight the difficulties of providing an acceptable physical understanding of it. The paradox must remain, therefore, as a central clue in the search for a more adequate understanding of quantum theory.
13 citations
5 citations
5 citations
TL;DR: In this paper it was shown that the Segal model can be embedded in the Mackey model in a structure-preserving way, and that Segal's original model can also be extended to a Mackey-type model.
Abstract: Mackey (1963) and Segal (1947) have constructed two elegant and quite general models for quantum mechanics. These two models are not equivalent, yet both have led to fruitful results and a deeper understanding of quantum theory. Mackey's work has led to the 'quantum logic' approach which has been carried on by many investigators [for some of these the reader might refer to the bibliographies in Jauch (1968) and Varadarajan (1968)], while Segal's approach is the forerunner of the important C*algebra theory of quantum mechanics (e.g., Haag & Kastler, 1964; Segal, 1963). As important as these two models are, very little research seems to have been performed comparing the two. The only works known to the author along these lines are those of Plymen (1967, 1968) and Davies (1968), who have shown that a C*-algebra can be embedded in a Z*-algebra. The C*-algebra corresponds to the Segal model, and Plymen shows that the Z*-algebra satisfies the postulates of Mackey's model. However, a C*-algebra is much stronger than Segal's original model, and Segal, himself, admits that the distributive and associative laws required in a C*-algebra are physically very artificial. Also, the Z*-algebra cannot be physically justified and is much stronger than the general structure given by what Plymen calls 'Mackey's essential axioms'. In this paper we consider Segal's original model and a generalization of Mackey's model which we feel is physically more reasonable. We then show that the Segal model can be embedded in the Mackey model in a structure-preserving way. This generalizes Plymen's results and shows that Segal's original model can be extended to a Mackey-type model.
4 citations
TL;DR: In this paper, it is shown that the interpretation of quantum mechanics as a theory describing systems for which their propositions are always valid or not leads to a contradiction within the theory, and the proof does not depend on any specific property of measurements, but only the usual description of ensembles of quantum objects by statistical operators is used.
Abstract: It is shown that the interpretation of quantum mechanics as a theory describing systems for which their propositions are always valid or not leads to a contradiction within the theory. The proof does not depend on any specific property of measurements, but only the usual description of ensembles of quantum objects by statistical operators is used.
1 citations