2011/03/30 by Christopher A. Fuchs, Rüdiger Schack, Ruediger Schack · 2 citations
Arts and Humanities · Physics and Astronomy · Psychology · #Epistemology, Ethics, and Metaphysics #Philosophy and Theoretical Science #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1007/978-3-642-21329-8_15
14 pages, written in memory of Itamar Pitowsky
arxiv created 2011/03/30 · crossref issued 2011/08/13 · crossref published 2011/08/13 · crossref published-online 2011/08/13 · openalex publication_date 2011/08/13 · crossref published-print 2012/01/01 · crossref created 2012/01/09 · arxiv updated 2015/05/27 · openalex created_date 2016/06/24 · crossref deposited 2024/04/17 · crossref indexed 2025/09/08 · openalex updated_date 2026/08/04
The probabilities a Bayesian agent assigns to a set of events typically change with time, for instance when the agent updates them in the light of new data. In this paper we address the question of how an agent's probabilities at different times are constrained by Dutch-book coherence. We review and attempt to clarify the argument that, although an agent is not forced by coherence to use the usual Bayesian conditioning rule to update his probabilities, coherence does require the agent's probabilities to satisfy van Fraassen's [1984] reflection principle (which entails a related constraint pointed out by Goldstein [1983]). We then exhibit the specialized assumption needed to recover Bayesian conditioning from an analogous reflection-style consideration. Bringing the argument to the context of quantum measurement theory, we show that "quantum decoherence" can be understood in purely personalist terms---quantum decoherence (as supposed in a von Neumann chain) is not a physical process at all, but an application of the reflection principle. From this point of view, the decoherence theory of Zeh, Zurek, and others as a story of quantum measurement has the plot turned exactly backward.