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A topos perspective on the KochenSpecker Theorem: I. Quantum States . . .
, 1998
"... Any attempt to construct a realist interpretation of quantum theory founders on the KochenSpecker theorem, which asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on al ..."
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Cited by 72 (13 self)
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Any attempt to construct a realist interpretation of quantum theory founders on the KochenSpecker theorem, which asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which respects an appropriate version of the functional composition principle. The truthvalues assigned to propositions are (i) contextual; and (ii) multivalued, where the space of contexts and the multivalued logic for each context come naturally from the topos theory of presheaves. The first step in our theory is to demonstrate that the KochenSpecker theorem is equivalent to the statement that a certain presheaf
Why the Quantum?
, 2004
"... This paper is a commentary on the foundational significance of the CliftonBubHalvorson theorem characterizing quantum theory in terms of three informationtheoretic constraints. I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of informa ..."
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Cited by 17 (1 self)
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This paper is a commentary on the foundational significance of the CliftonBubHalvorson theorem characterizing quantum theory in terms of three informationtheoretic constraints. I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of information transfer, as opposed to a theory about the mechanics of nonclassical waves or particles, (2) given the informationtheoretic constraints, any mechanical theory of quantum phenomena that includes an account of the measuring instruments that reveal these phenomena must be empirically equivalent to a quantum theory, and (3) assuming the informationtheoretic constraints are in fact satisfied in our world, no mechanical theory of quantum phenomena that includes an account of measurement interactions can be acceptable, and the appropriate aim of physics at the fundamental level then becomes the representation and manipulation of information.
Betting on the outcomes of measurements: a Bayesian theory of quantum probability
, 2003
"... We develop a systematic approach to quantum probability as a theory of rational bettingin quantum gambles. In these games of chance, the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One of the measurements is subsequently chosen and performed and ..."
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Cited by 13 (4 self)
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We develop a systematic approach to quantum probability as a theory of rational bettingin quantum gambles. In these games of chance, the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One of the measurements is subsequently chosen and performed and the money placed on the other measurements is returned to the agent. We show how the rules of rational betting imply all the interesting features of quantum probability, even in such finite gambles. These include the uncertainty principle and the violation of Bell’s inequality amongothers. Quantum gambles are closely related to quantum logic and provide a new semantics for it. We conclude with a philosophical discussion on the interpretation of quantum mechanics.
The Modal Interpretation of Quantum Mechanics
, 1998
"... Modal interpretations have the ambition to construe quantum mechanics as an objective, manindependent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but yields probabilities. In working out these ideas an importa ..."
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Cited by 6 (0 self)
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Modal interpretations have the ambition to construe quantum mechanics as an objective, manindependent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but yields probabilities. In working out these ideas an important motif is to stay close to the standard formalism of quantum mechanics and to refrain from introducing new structure by hand. In this paper we explain how this programme can be made concrete. In particular, we show that the Born probability rule, and sets of definitevalued observables to which the Born probabilities pertain, can be uniquely defined from the quantum state and Hilbert space structure. We discuss the status of probability in modal interpretations, and to this end we make a comparison with manyworlds alternatives. An overall point that we stress is that the modal ideas define a general framework and research programme rather than one definite and finished interpretation. Key words: interpretation of quantum mechanics; modal interpretation; probability; many worlds
Quantum information and computation
 arXiv:quantph/0512125. Forthcoming in Butterfield and Earman (eds.) Handbook of Philosophy of Physics
, 2005
"... This Chapter deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum communication, quantum cryptography, and quantum computation, ..."
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Cited by 4 (0 self)
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This Chapter deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum communication, quantum cryptography, and quantum computation, and concludes by considering whether a perspective in terms of quantum information
Reconsidering Bohr's Reply to EPR
 NonLocality and Modality
, 2002
"... Although Bohr’s reply to the EPR argument is supposed to be a watershed moment in the development of his philosophy of quantum theory, it is difficult to find a clear statement of the reply’s philosophical point. Moreover, some have claimed that the point is simply that Bohr is a radical positivist. ..."
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Cited by 3 (0 self)
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Although Bohr’s reply to the EPR argument is supposed to be a watershed moment in the development of his philosophy of quantum theory, it is difficult to find a clear statement of the reply’s philosophical point. Moreover, some have claimed that the point is simply that Bohr is a radical positivist. In this paper, we show that such claims are unfounded. In particular, we give a mathematically rigorous reconstruction of Bohr’s reply to the original EPR argument that clarifies its logical structure, and which shows that it does not rest on questionable philosophical assumptions. Rather, Bohr’s reply is dictated by his commitment to provide “classical ” and “objective ” descriptions of experimental phenomena. 1
The Quantum Measurement Problem: State of Play
, 2007
"... This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics. In it, I aim to review, in a way accessible to foundationally interested physicists as well as physicsinformed philosophers, just where we have got to in the quest for a solu ..."
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Cited by 1 (0 self)
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This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics. In it, I aim to review, in a way accessible to foundationally interested physicists as well as physicsinformed philosophers, just where we have got to in the quest for a solution to the measurement problem. I don’t advocate any particular approach to the measurement problem (not here, at any rate!) but I do focus on the importance of decoherence theory to modern attempts to solve the measurement problem, and I am fairly sharply critical of some aspects of the “traditional ” formulation of the problem.
Proposed Running Head: Maximal Beable Subalgebras Please address correspondence to:
, 1999
"... be accessible. ..."
Is logic empirical?
, 2007
"... The philosophical debate about quantum logic between the late 1960s and the early 1980s was generated mainly by Putnam’s claims that quantum mechanics empirically motivates introducing a new form of logic, that such an empirically founded quantum logic is the ‘true’ logic, and that adopting quantum ..."
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The philosophical debate about quantum logic between the late 1960s and the early 1980s was generated mainly by Putnam’s claims that quantum mechanics empirically motivates introducing a new form of logic, that such an empirically founded quantum logic is the ‘true’ logic, and that adopting quantum logic would resolve all the paradoxes of quantum mechanics. Most of that debate focussed on the latter claim, reaching the conclusion that it was mistaken. This chapter will attempt to clarify the possible misunderstandings surrounding the more radical claims about the revision of logic, assessing them in particular both in the context of more general quantumlike theories (in the framework of von Neumann algebras), and against the background of the current state of play in the philosophy and interpretation of quantum mechanics. Characteristically, the conclusions that might be drawn depend crucially on which of the currently proposed solutions to the measurement problem is adopted.