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Quantum theory within the probability calculus: a there-you-go theorem and partially exchangeable models

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  • Porta Mana, PierGianLuca

    (Norwegian University of Science and Technology)

Abstract

"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is to show that the thesis in question is entirely without validity and is the product of a confused view of the laws of probability" (Koopman, 1957). The secondary objects are: to show that quantum inferences are cases of partially exchangeable statistical models with particular prior constraints; to wonder about such constraints; and to plead for a dialogue between quantum theory and the theory of exchangeable models.

Suggested Citation

  • Porta Mana, PierGianLuca, 2018. "Quantum theory within the probability calculus: a there-you-go theorem and partially exchangeable models," OSF Preprints m38x6, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:m38x6
    DOI: 10.31219/osf.io/m38x6
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    References listed on IDEAS

    as
    1. Kallenberg, Olav, 1989. "On the representation theorem for exchangeable arrays," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 137-154, July.
    2. Porta Mana, PierGianLuca, 2003. "Why can states and measurement outcomes be represented as vectors?," OSF Preprints q9frx, Center for Open Science.
    3. Ramsey, Frank P., 1926. "Truth and Probability," Histoy of Economic Thought Chapters, in: Braithwaite, R. B. (ed.),The Foundations of Mathematics and other Logical Essays, chapter 7, pages 156-198, McMaster University Archive for the History of Economic Thought.
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