One of the most interesting programs in the foundations of quantum mechanics is the realist quantum logic approach associated with Putnam, Bub, Demopoulos and Friedman (and which is the focus of my own research.) I believe that realist quantum logic is our best hope for making sense of quantum mechanics, but I have come to suspect that the usual version may not be the correct one. In this paper, I would like to say why and to propose an alternative.

In a recent paper, Michael Friedman and Hilary Putnam argued that the Luders rule is ad hoc from the point of view of the Copenhagen interpretation but that it receives a natural explanation within realist quantum logic as a probability conditionalization rule. Geoffrey Hellman maintains that quantum logic cannot give a non-circular explanation of the rule, while Jeffrey Bub argues that the rule is not ad hoc within the Copenhagen interpretation. As I see it, all four are wrong. Given that (...) there is to be a projection postulate, there are at least two natural arguments which the Copenhagen advocate can offer on behalf of the Luders rule, contrary to Friedman and Putnam. However, the argument which Bub offers is not a good one. At the same time, contrary to Hellman, quantum logic really does provide an explanation of the Luders rule, and one which is superior to that of the Copenhagen account, since it provides an understanding of why there should be a projection postulate at all. (shrink)

We define a family of ‘no signaling’ bipartite boxes with arbitrary inputs and binary outputs, and with a range of marginal probabilities. The defining correlations are motivated by the Klyachko version of the Kochen-Specker theorem, so we call these boxes Kochen-Specker-Klyachko boxes or, briefly, KS-boxes. The marginals cover a variety of cases, from those that can be simulated classically to the superquantum correlations that saturate the Clauser-Horne-Shimony-Holt inequality, when the KS-box is a generalized PR-box (hence a vertex of the ‘no (...) signaling’ polytope). We show that for certain marginal probabilities a KS-box is classical with respect to nonlocality as measured by the Clauser-Horne-Shimony-Holt correlation, i.e., no better than shared randomness as a resource in simulating a PR-box, even though such KS-boxes cannot be perfectly simulated by classical or quantum resources for all inputs. We comment on the significance of these results for contextuality and nonlocality in ‘no signaling’ theories. (shrink)

This book concentrates on research done during the last twenty years on the philosophy of quantum mechanics. In particular, the author focuses on three major issues: whether quantum mechanics is an incomplete theory, whether it is non-local, and whether it can be interpreted realistically. Much of the book is concerned with distinguishing various senses in which these questions can be taken, and assessing the bewildering variety of answers philosophers and physicists have given up to now. The book is self-contained in (...) that it presents the necessary parts of the mathematical formalism of quantum mechanics and also covers other interpretative topics, such as the problem of measurement and the uncertainty relations. A considerable portion of the book is based on original arguments presented by the author in lectures and research papers over the past ten years. However, this material is integrated with a broad coverage of most of the recent research in the field, so as to provide a balanced introduction to the whole subject. (shrink)

Quantum theory is a probabilistic theory that embodies notoriously striking correlations, stronger than any that classical theories allow but not as strong as those of hypothetical ‘super-quantum’ theories. This raises the question ‘Why the quantum?’—whether there is a handful of principles that account for the character of quantum probability. We ask what quantum-logical notions correspond to this investigation. This project isn’t meant to compete with the many beautiful results that information-theoretic approaches have yielded but rather aims to complement that work.

Emilio Santos has argued (Santos, Studies in History and Philosophy of Physics http: //arxiv-org/abs/quant-ph/0410193) that to date, no experiment has provided a loophole-free refutation of Bell’s inequalities. He believes that this provides strong evidence for the principle of local realism, and argues that we should reject this principle only if we have extremely strong evidence. However, recent work by Malley and Fine (Non-commuting observables and local realism, http: //arxiv-org/abs/quant-ph/0505016) appears to suggest that experiments refuting Bell’s inequalities could at most confirm (...) that quantum mechanical quantities do not commute. They also suggest that experiments performed on a single system could refute local realism. In this paper, we develop a connection between the work of Malley and Fine and an argument by Bub from some years ago [Bub, The Interpretation of Quantum Mechanics, Chapter VI(Reidel, Dodrecht,1974)]. We also argue that the appearance of conflict between Santos on the one hand and Malley and Fine on the other is a result of differences in the way they understand local realism. (shrink)

Quantum logic understood as a reconstruction program had real successes and genuine limitations. This paper offers a synopsis of both and suggests a way of seeing quantum logic in a larger, still thriving context.

Jarrett (1984) and Ballentine and Jarrett (1987) have argued that violations of Jarrett's locality condition are strictly forbidden by the theory of relativity. In Ballentine and Jarrett, this claim is supported by an appeal to the fact that superluminal signalling gives rise to causal paradoxes. In this paper, it is argued that if violations of locality are permitted, certain puzzles indeed arise. The result takes the form of a set of apparent "no go" theorems. However, it is argued that the (...) results may not really show what they seem to, and that contrary to Ballentine and Jarrett, it is by no means clear that relativity forbids violations of Jarrett's locality condition. (shrink)

In this paper, I want to present a family of results that may seem to add up to a new proof of the impossibility of hidden variables. In fact, I very much doubt that that’s really what really emerges, but I think the results are nonetheless interesting because they help to sharpen the discussion of Jon Jarrett’s very useful decompostion theorem, in particular, of the condition he calls locality. Jarrett (1984) and Ballentine and Jarrett (1987) have suggested that the so-called (...) condition of locality is the one that provides the conceptual link between hidden variable theories and relativity: if locality is violated, so is relativity. On the other hand, a theory may violate the condition Jarrett calls completeness without running afoul of relativity. Now I agree with Jarrett and Ballentine about completeness, but I strongly suspect that we have quite a way to go before we really understand what would be involved in a violation of locality. (shrink)

I begin with an appeal to the GHZ/Mermin state to illustrate the allure of contextualism and value-definiteness. I then point out that standard contextualism, with its special status for non-degenerate operators, faces some embarrassing questions. Further, there is an alternative that apparently does not have the same problems. A modest re-pasting of Hilbert space makes the honors almost even between these two varieties. The paper closes with some reflections on the peculiarities of contextualism.