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Re-Thinking Time at the Interface of Physics and Philosophy pp 193–210Cite as

Classical and Quantum Probability: The Two Logics of Science

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Part of the book series: On Thinking ((ONTHINKING,volume 4))

Abstract

We review and discuss first briefly the algebraic framework of classical and quantum physics and commutative and noncommutative probability theory. After that we propose a mathematical definition of decoherence sufficiently general to accommodate quantum systems with infinitely many degrees of freedom and give an exhaustive list of possible scenarios that can emerge due to decoherence. We conclude with some messages of quantum science.

The true logic of this world is probability theory

J.C. Maxwell

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Notes

  1. 1.

    Dedicated with admiration and affection to Rudolf Haag on his ninetieth birthday

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Acknowledgements

In this paper I reported on results obtained together with Mario Hellmich and Robert Olkiewicz. It is a pleasure to express my gratitude to both of them for the joy of a long and friendly collaboration. I also benefited from numerous discussions with my colleague and friend Jürg Fröhlich during the ZIF-Research Group “The message of Quantum Science—Attempts towards a synthesis” (February–May 2012) at the Center for Interdisciplinary Research (ZiF) of Bielefeld University. I am grateful to Mario Hellmich for precious remarks and Hanne Litschewsky for help in preparing the manuscript.

Author information

Authors and Affiliations

  1. Mathematical Physics and BiBoS, University of Bielefeld, Universitätsstr. 25, D-33615, Bielefeld, Germany

    Philippe Blanchard

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  1. Philippe Blanchard
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Correspondence to Philippe Blanchard .

Editor information

Editors and Affiliations

  1. Parmenides Stiftung, Pullach, Bayern, Germany

    Albrecht von Müller

  2. Institute of Physics, University of Freiburg, Freiburg, Germany

    Thomas Filk

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Blanchard, P. (2015). Classical and Quantum Probability: The Two Logics of Science. In: von Müller, A., Filk, T. (eds) Re-Thinking Time at the Interface of Physics and Philosophy. On Thinking, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-10446-1_9

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