Time, quantum mechanics, and probability

Synthese 114 (3):373-404 (1997)

Authors
Simon Saunders
Oxford University
Abstract
A variety of ideas arising in decoherence theory, and in the ongoing debate over Everett's relative-state theory, can be linked to issues in relativity theory and the philosophy of time, specifically the relational theory of tense and of identity over time. These have been systematically presented in companion papers (Saunders 1995; 1996a); in what follows we shall consider the same circle of ideas, but specifically in relation to the interpretation of probability, and its identification with relations in the Hilbert Space norm. The familiar objection that Everett's approach yields probabilities different from quantum mechanics is easily dealt with. The more fundamental question is how to interpret these probabilities consistent with the relational theory of change, and the relational theory of identity over time. I shall show that the relational theory needs nothing more than the physical, minimal criterion of identity as defined by Everett's theory, and that this can be transparently interpreted in terms of the ordinary notion of the chance occurrence of an event, as witnessed in the present. It is in this sense that the theory has empirical content.
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
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Reprint years 1998
DOI 10.1023/A:1005079904008
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References found in this work BETA

Reasons and Persons.Derek Parfit - 1984 - Philosophy and Phenomenological Research 47 (2):311-327.
Physics and Chance.Lawrence Sklar - 1995 - British Journal for the Philosophy of Science 46 (1):145-149.
Quantum Non-Locality and Relativity: Aristotelian Society Series.Tim Maudlin & Lawrence Sklar - 1994 - British Journal for the Philosophy of Science 45 (3):933-934.

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Citations of this work BETA

Everett and Structure.David Wallace - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (1):87-105.
Understanding Deutsch's Probability in a Deterministic Universe.Hilary Greaves - 2004 - Studies in History and Philosophy of Modern Physics 35 (3):423-456.
Quantum Probability From Subjective Likelihood: Improving on Deutsch's Proof of the Probability Rule.David Wallace - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):311-332.

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