David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studies in History and Philosophy of Science Part B 34 (3):395-414 (2003)
We develop a systematic approach to quantum probability as a theory of rational betting in 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 among others. 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.
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References found in this work BETA
J. S. Bell (2004 ). On the Einstein-Podolsky-Rosen Paradox. In Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press 14--21.
Garrett Birkhoff & John von Neumann (1937). The Logic of Quantum Mechanics. Journal of Symbolic Logic 2 (1):44-45.
J. Bub & R. Clifton (1996). A Uniqueness Theorem for 'No Collapse' Interpretations of Quantum Mechanics. Studies in History and Philosophy of Science Part B 27 (2):181-219.
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Citations of this work BETA
Meir Hemmo (2007). Quantum Probability and Many Worlds. Studies in History and Philosophy of Science Part B 38 (2):333-350.
Simon Friederich (2011). How to Spell Out the Epistemic Conception of Quantum States. Studies in History and Philosophy of Science Part B 42 (3):149-157.
Carlton M. Caves, Christopher A. Fuchs & Rüdiger Schack (2007). Subjective Probability and Quantum Certainty. Studies in History and Philosophy of Science Part B 38 (2):255-274.
Jeffrey Bub (2007). Quantum Probabilities as Degrees of Belief. Studies in History and Philosophy of Science Part B 38 (2):232-254.
Ehud Hrushovski & Itamar Pitowsky (2004). Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem. Studies in History and Philosophy of Science Part B 35 (2):177-194.
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