In the mid-nineteenth century George Boole formulated his ‘conditions of possible experience’. These are equations and ineqaulities that the relative frequencies of events must satisfy. Some of Boole's conditions have been rediscovered in more recent years by physicists, including Bell inequalities, Clauser Horne inequalities, and many others. In this paper, the nature of Boole's conditions and their relation to propositional logic is explained, and the puzzle associated with their violation by quantum frequencies is investigated in relation to a variety of (...) approaches to the interpretation of quantum mechanics. * While preparing this paper for publication I have learnt of the untimely death of Professor J. S. Bell, and I wish to dedicate the paper to his memory. This research was undertaken while I spent a sabbatical leave at Wolfson College, and the History and Philosophy of Science Department at the University of Cambridge. I would like to thank Michael Redhead and Jeremy Butterfield for their hospitality and for helpful discussions. A first draft of this paper has been distributed among the participants of the conference 'Einstein in Context' which was held in Israel, in April 1990.1 have benefited from the comments of many colleagues. I would like to thank in particular Arthur Fine who enlightened me on the prism models, David Albert. Maya Bar-Hillel. Yemima Ben-Menachem, Mara Beller. Simon Saunders, and Mark Steiner. This research is partially supported by the Edelstein Center for the History and Philosophy of Science at the Hebrew University. (shrink)

One way to characterize dispositions is to take them to be reducible to categorical properties plus experimental arrangements. We argue that this view applied to Bohm 's ontological interpretation of quantum theory provides a good picture of the unremarkable nature of spin in that interpretation, and so explains how a simple realism of possessed values may be retained in the face of Kochen and Specker's theorem. With this in mind we discuss Redhead's influential analysis of Kochen and Specker's theorem which (...) does nor appear to allow for the above view. (shrink)

A central problem in the interpretation of non-relativistic quantum mechanics is to relate the conceptual structure of the theory to the classical idea of the state of a physical system. This paper approaches the problem by presenting an analysis of the notion of an elementary physical proposition. The notion is shown to be realized in standard formulations of the theory and to illuminate the significance of proofs of the impossibility of hidden variable extensions. In the interpretation of quantum mechanics that (...) emerges from this analysis, the philosophically distinctive features of the theory derive from the fact that it seeks to represent a reality of which complete knowledge is essentially unattainable. (shrink)

We show that the Bub-Clifton uniqueness theorem (1996) for 'no collapse' interpretations of quantum mechanics can be proved without the 'weak separability' assumption.

We prove a uniqueness theorem showing that, subject to certain natural constraints, all 'no collapse' interpretations of quantum mechanics can be uniquely characterized and reduced to the choice of a particular preferred observable as determine (definite, sharp). We show how certain versions of the modal interpretation, Bohm's 'causal' interpretation, Bohr's complementarity interpretation, and the orthodox (Dirac-von Neumann) interpretation without the projection postulate can be recovered from the theorem. Bohr's complementarity and Einstein's realism appear as two quite different proposals for selecting (...) the preferred determinate observable--either settled pragmatically by what we choose to observe, or fixed once and for all, as the Einsteinian realist would require, in which case the preferred observable is a 'beable' in Bell's sense, as in Bohm's interpretation (where the preferred observable is position in configuration space). (shrink)

"Science is rooted in conversations," wrote Werner Heisenberg, one of the twentieth century's great physicists. In Quantum Dialogue, Mara Beller shows that science is rooted not just in conversation but in disagreement, doubt, and uncertainty. She argues that it is precisely this culture of dialogue and controversy within the scientific community that fuels creativity. Beller draws her argument from her radical new reading of the history of the quantum revolution, especially the development of the Copenhagen interpretation. One of several competing (...) approaches, this version succeeded largely due to the rhetorical skills of Niels Bohr and his colleagues. Using extensive archival research, Beller shows how Bohr and others marketed their views, misrepresenting and dismissing their opponents as "unreasonable" and championing their own not always coherent or well-supported position as "inevitable." Quantum Dialogue, winner of the 1999 Morris D. Forkosch Prize of the Journal of the History of Ideas, will fascinate everyone interested in how stories of "scientific revolutions" are constructed and "scientific consensus" achieved. "[A]n intellectually stimulating piece of work, energised by a distinct point of view."—Dipankar Home, Times Higher Education Supplement "[R]emarkable and original. . . . [Beller's] arguments are thoroughly supported and her conclusions are meticulously argued. . . . This is an important book that all who are interested in the emergence of quantum mechanics will want to read."—William Evenson, History of Physics Newsletter. (shrink)

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)

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.

We consider the set of all matrices of the form pij = tr[W (Ei ⊗ Fj)] where Ei, Fj are projections on a Hilbert space H, and W is some state on H ⊗ H. We derive the basic properties of this set, compare it with the classical range of probability, and note how its properties may be related to a geometric measures of entanglement.