Classical and Quantum Probability: The Two Logics of Science
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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.
KeywordsClassical Probability Quantum Probability Superselection Rule Algebraic Framework Classical Probability Theory
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.
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