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A First Course in Topos Quantum Theory

  • Cecilia Flori

Part of the Lecture Notes in Physics book series (LNP, volume 868)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Cecilia Flori
    Pages 1-5
  3. Cecilia Flori
    Pages 7-12
  4. Cecilia Flori
    Pages 13-24
  5. Cecilia Flori
    Pages 25-61
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    Pages 63-74
  7. Cecilia Flori
    Pages 75-84
  8. Cecilia Flori
    Pages 85-115
  9. Cecilia Flori
    Pages 117-129
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    Pages 131-146
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  13. Cecilia Flori
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    Pages 191-217
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  19. Cecilia Flori
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  20. Cecilia Flori
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  21. Cecilia Flori
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  22. Back Matter
    Pages 397-449

About this book

Introduction

In the last five decades various attempts to formulate theories of quantum gravity have been made, but none has fully succeeded in becoming the quantum theory of gravity. One possible explanation for this failure might be the unresolved fundamental issues in quantum theory as it stands now. Indeed, most approaches to quantum gravity adopt standard quantum theory as their starting point, with the hope that the theory’s unresolved issues will get solved along the way. However, these fundamental issues may need to be solved before attempting to define a quantum theory of gravity.

The present text adopts this point of view, addressing the following basic questions:  What are the main conceptual issues in quantum theory? How can these issues be solved within a new theoretical framework of quantum theory?

A possible way to overcome critical issues in present-day quantum physics – such as a priori assumptions about space and time that are not compatible with a theory of quantum gravity, and the impossibility of talking about systems without reference to an external observer – is through a reformulation of quantum theory in terms of a different mathematical framework called topos theory.

This course-tested primer sets out to explain to graduate students and newcomers to the field alike, the reasons for choosing topos theory to resolve the above-mentioned issues and how it brings quantum physics back to looking more like a “neo-realist” classical physics theory again.

Keywords

Category Theory Foundations of Quantum Mechanics Kochen-Specker Theorem Quantum Logic Topos Quantum Theory Textbook Topos Theory

Authors and affiliations

  • Cecilia Flori
    • 1
  1. 1.Perimeter Inst. for Theor. StudiesWaterlooCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-35713-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-642-35712-1
  • Online ISBN 978-3-642-35713-8
  • Series Print ISSN 0075-8450
  • Series Online ISSN 1616-6361
  • Buy this book on publisher's site
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