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Foundations of Quantum Theory: From Classical Concepts to Operator Algebras

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Book Series: Fundamental Theories of Physics ISSN: 0168-1222 ISBN: 9783319517773 Volume: 188 Pages: 861 DOI: http://dx.doi.org/10.1007/978-3-319-51777-3 Language: English
Publisher: Springer
Subject: Physics (General)
Added to DOAB on : 2017-07-19 16:33:13
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This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.

The Challenge of Chance: A Multidisciplinary Approach from Science and the Humanities

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Book Series: The Frontiers Collection ISSN: 1612-3018 ISBN: 9783319262987 9783319263007 Year: Pages: 276 DOI: 10.1007/978-3-319-26300-7 Language: English
Publisher: Springer
Subject: Statistics
Added to DOAB on : 2017-01-24 17:28:09
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This book presents a multidisciplinary perspective on chance, with contributions from distinguished researchers in the areas of biology, cognitive neuroscience, economics, genetics, general history, law, linguistics, logic, mathematical physics, statistics, theology and philosophy. The individual chapters are bound together by a general introduction followed by an opening chapter that surveys 2500 years of linguistic, philosophical, and scientific reflections on chance, coincidence, fortune, randomness, luck and related concepts.A main conclusion that can be drawn is that, even after all this time, we still cannot be sure whether chance is a truly fundamental and irreducible phenomenon, in that certain events are simply uncaused and could have been otherwise, or whether it is always simply a reflection of our ignorance. Other challenges that emerge from this book include a better understanding of the contextuality and perspectival character of chance (including its scale-dependence), and the curious fact that, throughout history (including contemporary science), chance has been used both as an explanation and as a hallmark of the absence of explanation. As such, this book challenges the reader to think about chance in a new way and to come to grips with this endlessly fascinating phenomenon.

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