Deep Beauty: Understanding the Quantum World through Mathematical Innovation

doi:10.1017/CBO9780511976971

No scientific theory has caused more puzzlement and confusion than quantum theory. Physics is supposed to help us to understand the world, but quantum theory makes it seem a very strange place. This book is about how mathematical innovation can help us gain deeper insight into the structure of the physical world. Chapters by top researchers in the mathematical foundations of physics explore new ideas, especially novel mathematical concepts at the cutting edge of future physics. These creative developments in mathematics may catalyze the advances that enable us to understand our current physical theories, especially quantum theory. The authors bring diverse perspectives, unified only by the attempt to introduce fresh concepts that will open up new vistas in our understanding of future physics.

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Contents

Frontmatter
pp i-vi
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Contents
pp vii-viii
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Contributors
pp ix-x
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Preface
pp xi-xii
- By Hans Halvorson, Princeton University
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Acknowledgments
pp xiii-xiv
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Introduction
pp 1-10
- By Hans Halvorson, Princeton University
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I - Beyond the Hilbert Space Formalism: Category Theory
pp 11-12
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1 - A Prehistory of n-Categorical Physics
pp 13-128
- By John C. Baez, University of California, Riverside, California, United States, Aaron D. Lauda, Columbia University, New York, New York, United States
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2 - A Universe of Processes and Some of Its Guises
pp 129-186
- By Bob Coecke, University of Oxford, United Kingdom
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3 - Topos Methods in the Foundations of Physics
pp 187-206
- By Chris J. Isham, Imperial College, London, United Kingdom
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4 - The Physical Interpretation of Daseinisation
pp 207-238
- By Andreas Döring, University of Oxford, United Kingdom
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5 - Classical and Quantum Observables
pp 239-270
- By Hans F. de Groote, Goethe-Universität Frankfurt a.M., Germany
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6 - Bohrification
pp 271-314
- By Chris Heunen, University of Oxford, United Kingdom, Nicolaas P. Landsman, Radboud University Nijmegen, Nijmegen, The Netherlands, Bas Spitters, Radboud University Nijmegen, Nijmegen, The Netherlands
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II - Beyond the Hilbert Space Formalism: Operator Algebras
pp 315-316
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7 - Yet More Ado about Nothing: The Remarkable Relativistic Vacuum State
pp 317-342
- By Stephen J. Summers, University of Florida, Gainesville, Florida, United States
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8 - Einstein Meets von Neumann: Locality and Operational Independence in Algebraic Quantum Field Theory
pp 343-362
- By Miklós Rédei, London School of Economics and Political Science, London, United Kingdom
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III - Behind the Hilbert Space Formalism
pp 363-364
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9 - Quantum Theory and Beyond: Is Entanglement Special?
pp 365-392
- By Borivoje Dakić, University of Vienna, Austria, Časlav Brukner, University of Vienna, Vienna, Austria
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10 - Is Von Neumann's “No Hidden Variables” Proof Silly?
pp 393-408
- By Jeffrey Bub, University of Maryland, College Park, Maryland, United States
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11 - Foliable Operational Structures for General Probabilistic Theories
pp 409-442
- By Lucien Hardy, Perimeter Institute, Waterloo, Ontario, Canada
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12 - The Strong Free Will Theorem
pp 443-454
- By John H. Conway, Princeton University, Princeton, New Jersey, United States, Simon Kochen, Princeton University, Princeton, New Jersey, United States
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Index
pp 455-472
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Deep Beauty

Understanding the Quantum World through Mathematical Innovation

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Contributors
pp ix-x

Preface
pp xi-xii

Acknowledgments
pp xiii-xiv

Introduction
pp 1-10

I - Beyond the Hilbert Space Formalism: Category Theory
pp 11-12

1 - A Prehistory of n-Categorical Physics
pp 13-128

2 - A Universe of Processes and Some of Its Guises
pp 129-186

3 - Topos Methods in the Foundations of Physics
pp 187-206

4 - The Physical Interpretation of Daseinisation
pp 207-238

5 - Classical and Quantum Observables
pp 239-270

6 - Bohrification
pp 271-314

II - Beyond the Hilbert Space Formalism: Operator Algebras
pp 315-316

7 - Yet More Ado about Nothing: The Remarkable Relativistic Vacuum State
pp 317-342

8 - Einstein Meets von Neumann: Locality and Operational Independence in Algebraic Quantum Field Theory
pp 343-362

III - Behind the Hilbert Space Formalism
pp 363-364

9 - Quantum Theory and Beyond: Is Entanglement Special?
pp 365-392

10 - Is Von Neumann's “No Hidden Variables” Proof Silly?
pp 393-408

11 - Foliable Operational Structures for General Probabilistic Theories
pp 409-442

12 - The Strong Free Will Theorem
pp 443-454

Index
pp 455-472

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Understanding the Quantum World through Mathematical Innovation

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