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Dynamics and Statistics in the Operator Algebra of Quantum Mechanics

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Reality and Measurement in Algebraic Quantum Theory (NWW 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 261))

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Abstract

Physics explains the laws of motion that govern the time evolution of observable properties and the dynamical response of systems to various interactions. However, quantum theory separates the observable part of physics from the unobservable time evolution by introducing mathematical objects that are only loosely connected to the actual physics by statistical concepts and cannot be explained by any conventional sets of events. Here, I examine the relation between statistics and dynamics in quantum theory and point out that the Hilbert space formalism can be understood as a theory of ergodic randomization, where the deterministic laws of motion define probabilities according to a randomization of the dynamics that occurs in the processes of state preparation and measurement.

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Authors and Affiliations

  1. Graduate School of Advanced Sciences of Matter, Hiroshima University, Kagamiyama 1-3-1, Higashi Hiroshima, 739-8530, Japan

    Holger F. Hofmann

Authors
  1. Holger F. Hofmann
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Correspondence to Holger F. Hofmann .

Editor information

Editors and Affiliations

  1. Graduate School of Informatics, Nagoya University, Nagoya, Japan

    Masanao Ozawa

  2. Trinity College, Cambridge University, Cambridge, UK

    Jeremy Butterfield

  3. Department of Philosophy, Princeton University, Princeton, NJ, USA

    Hans Halvorson

  4. Department of Philosophy, Logic and Scientific Method, London School of Economics and Political Science, London, UK

    Miklós Rédei

  5. College of Industrial Technology, Nihon University, Narashino, Japan

    Yuichiro Kitajima

  6. Graduate School of Informatics, Nagoya University, Nagoya, Japan

    Francesco Buscemi

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Hofmann, H.F. (2018). Dynamics and Statistics in the Operator Algebra of Quantum Mechanics. In: Ozawa, M., Butterfield, J., Halvorson, H., Rédei, M., Kitajima, Y., Buscemi, F. (eds) Reality and Measurement in Algebraic Quantum Theory. NWW 2015. Springer Proceedings in Mathematics & Statistics, vol 261. Springer, Singapore. https://doi.org/10.1007/978-981-13-2487-1_8

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