Steeger, Jer (2017) Betting on Quantum Objects. [Preprint]

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Abstract

Dutch book arguments have been applied to beliefs about the outcomes of measurements of quantum systems, but not to beliefs about quantum objects prior to measurement. In this paper, we prove a quantum version of the probabilists' Dutch book theorem that applies to both sorts of beliefs: roughly, if ideal beliefs are given by vector states, all and only Born-rule probabilities avoid Dutch books. This theorem and associated results have implications for operational and realist interpretations of the logic of a Hilbert lattice. In the latter case, we show that the defenders of the eigenstate-value orthodoxy face a trilemma. Those who favor vague properties avoid the trilemma, admitting all and only those beliefs about quantum objects that avoid Dutch books.

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Item Type:	Preprint
Creators:	Creators Email ORCID Steeger, Jer jsteeger@nd.edu 0000-0003-2771-4145
Additional Information:	This version contains improved operational semantics. The results are unchanged.
Keywords:	Dutch book arguments; Hilbert lattice; quantum logic; eigenstate-value link; vague properties
Subjects:	Specific Sciences > Mathematics > Logic Specific Sciences > Probability/Statistics Specific Sciences > Physics > Quantum Mechanics
Depositing User:	Jer Steeger
Date Deposited:	03 Aug 2017 12:38
Last Modified:	17 Sep 2022 00:53
Item ID:	13266
Subjects:	Specific Sciences > Mathematics > Logic Specific Sciences > Probability/Statistics Specific Sciences > Physics > Quantum Mechanics
Date:	18 July 2017
URI:	https://philsci-archive.pitt.edu/id/eprint/13266

Available Versions of this Item

• Betting on Quantum Objects. (deposited 20 Jul 2017 15:21)
  • Betting on Quantum Objects. (deposited 24 Jul 2017 13:09)
    • Betting on Quantum Objects. (deposited 03 Aug 2017 12:38) [Currently Displayed]

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