This book compares various approaches to the interpretation of quantum mechanics, in particular those which are related to the key words "the Copenhagen interpretation", "the antirealist view", "quantum logic" and "hidden variable theory". Using the concept of "correlation" carefully analyzed in the context of classical probability and in quantum theory, the author provides a framework to compare these approaches. He also develops an extension of probability theory to construct a local hidden variable theory. The book should be of interest for (...) physicists and philosophers of science interested in the foundations of quantum theory. (shrink)

Bell inequalities play a central role in the study of quantum nonlocality and entanglement, with many applications in quantum information. Despite the huge literature on Bell inequalities, it is not easy to find a clear conceptual answer to what a Bell inequality is, or a clear guiding principle as to how they may be derived. In this paper, we introduce a notion of logical Bell inequality which can be used to systematically derive testable inequalities for a very wide variety of (...) situations. There is a single clear conceptual principle, based on purely logical consistency conditions, which underlies our notion of logical Bell inequalities. We show that in a precise sense, all Bell inequalities can be taken to be of this form. Our approach is very general. It applies directly to any family of sets of commuting observables. Thus it covers not only the n-partite scenarios to which Bell inequalities are standardly applied, but also Kochen-Specker configurations, and many other examples. There is much current work on experimental tests for contextuality. Our approach directly yields, in a systematic fashion, testable inequalities for a very general notion of contextuality. There has been much work on obtaining proofs of Bell's theorem “without inequalities” or “without probabilities.” These proofs are seen as being in a sense more definitive and logically robust than the inequality-based proofs. On the hand, they lack the fault-tolerant aspect of inequalities. Our approach reconciles these aspects, and in fact shows how the logical robustness can be converted into systematic, general derivations of inequalities with provable violations. Moreover, the kind of strong non-locality or contextuality exhibited by the GHZ argument or by Kochen-Specker configurations can be shown to lead to maximal violations of the corresponding logical Bell inequalities. Thus the qualitative and the quantitative aspects are combined harmoniously. (shrink)

The aim of this paper is to state the single most powerful argument for use of a non-classical logic in quantum mechanics. In outline the argument is the following. The working logic of a science is the logic of the events and propositions to which probabilities are assigned. A probability should be assigned to every element of the algebra of events. In the case of quantum mechanics probabilities may be assigned to events but not, without restriction, to the conjunction of (...) two events. The conclusion is that the working logic of quantum mechanics is not classical. The nature of the logic that is appropriate for quantum mechanics is examined. (shrink)

A new proof of the impossibility of reconciling realism and locality in quantum mechanics is given. Unlike proofs based on Bell's inequality, the present work makes minimal and transparent use of probability theory and proceeds by demonstrating a Kochen-Specker type of paradox based on the value assignments to the spin components of two spatially separated spin-1 systems in the singlet state of their total spin. An essential part of the argument is to distinguish carefully two commonly confused types of contextuality; (...) we call them ontological and environmental contextuality. These in turn are associated with two quite distinct senses of nonlocality. We indicate the relevance of our treatment to other related discussions in recent literature on the philosophy of quantum mechanics. (shrink)