The Structural Foundations of Quantum Gravity

Quantum gravity is the name given to a theory that unites general relativity - Einstein's theory of gravitation and spacetime - with quantum field theory, our framework for describing non-gravitational forces. The Structural Foundations of Quantum Gravity brings together philosophers andphysicists to discuss a range of conceptual issues that surface in the effort to unite these theories, focusing in particular on the ontological nature of the spacetime that results. Although there has been a great deal written about quantum gravity from the perspective of physicists andmathematicians, very little attention has been paid to the philosophical aspects. This volume closes that gap, with essays written by some of the leading researchers in the field. Individual papers defend or attack a structuralist perspective on the fundamental ontologies of our physical theories,which offers the possibility of shedding new light on a number of foundational problems. It is a book that will be of interest not only to physicists and philosophers of physics but to anyone concerned with foundational issues and curious to explore new directions in our understanding of spacetimeand quantum physics.

Notes on Contributors	p. xi
Quantum Gravity Meets Structuralism; Interweaving Relations in the Foundations of Physics	p. 1
Quantum Gravity: Background, Concepts, and Methods	p. 1
The Hole Argument and Spacetime Ontology	p. 2
Gauging the Hole Argument	p. 4
Enter Quantum Gravity	p. 7
Categorizing the Manifold Methods	p. 14
What's Wrong with Background-Dependent Methods?	p. 16
What's Right about Background-Independent Methods?	p. 18
Background Independence and Structuralism	p. 20
Structuralism and Structural Realism	p. 25
Motivating Structuralism	p. 25
What is Structuralism?	p. 25
...And Where Does it Come from?	p. 26
Structural Realism	p. 30
Structural Realism and Quantum Gravity	p. 40
Structural Realism	p. 41
Physical Reality of Spacetime and Quantum Fields	p. 43
Quantum Gravity	p. 47
Structure, Individuality, and Quantum Gravity	p. 53
What is Structural Realism?	p. 53
Structure and Individuality	p. 55
Effective Field Theory and Asymptotic Quantization	p. 60
String Theory	p. 63
Quantum General Relativity: Some Preliminary Problems	p. 65
States or Processes: Which is Primary?	p. 65
Formalism and Measurability	p. 68
Canonical Quantization (Loop Quantum Gravity)	p. 71
The Causal Set (Causet) Approach	p. 75
What Structures to Quantize?	p. 77
Points, Particles, and Structural Realism	p. 83
What is Structural Realism?	p. 84
Underdetermination	p. 86
What is Ontic Structural Realism?	p. 91
Objects	p. 94
Sophisticated Substantivalism	p. 99
Stachel's Generalized Hole Argument for Sets	p. 104
Stachel on Identical Particles	p. 109
Identical Particles and Identity over Time	p. 114
Two Morals for Quantum Gravity	p. 116
Holism and Structuralism in Classical and Quantum General Relativity	p. 121
Introduction: Two Strands of Philosophy of Physics that Ought to be Brought together	p. 121
Many 'Realisms' or One?	p. 123
What, Exactly, is a Physical Structure?	p. 124
A Case Study: The Holistic and Structural Nature of General-Relativistic Spacetime in a Class of Models of GR	p. 126
The Hole Argument and its Consequences	p. 126
The Dynamical Individuation of Point-Events	p. 130
Developing Hints for the Quantum Gravity Programme	p. 140
Structural Spacetime Realism	p. 144
The Nature of Point-Events and Overcoming the Substantivalism/Relationism Debate	p. 145
Time and Structure in Canonical Gravity	p. 152
Introduction	p. 152
Constraints, Gauge, and Holes	p. 153
Hamiltonian Systems: Constraints and Gauge	p. 154
Constraints and Gauge In General Relativity	p. 157
Interpreting Gauge Theories	p. 159
What is the Problem of Time?	p. 163
A Snapshot of the Philosophical Debate	p. 166
Time Series from A to D	p. 167
Maudlin versus Earman	p. 171
Catalogue of Responses	p. 175
Timefull Stratagems	p. 176
Timeless Stratagems	p. 179
Enter Structuralism	p. 188
Conclusion	p. 191
The Case for Background Independence	p. 196
Introduction	p. 196
A Brief History of Relational Time	p. 200
What Physicists Mean When We Talk about Relational Space and Time	p. 203
General Relativity as a Partly Relational Theory	p. 204
The Problem of Time and Related Issues	p. 207
Relationalism and the Search for the Quantum Theory of Gravity	p. 209
The Causal Set Theory	p. 210
Loop Quantum Gravity	p. 212
Causal Dynamical Triangulation Models	p. 216
Background-Independent Approaches to String and M Theory	p. 217
Relationalism and Reductionism	p. 219
The Challenge of the String Theory Landscape	p. 223
A Relational Approach to the Problems of Unification and Determination of the Standard Model Parameters	p. 226
Relationalism and Natural Selection	p. 227
What about the Cosmological Constant Problem?	p. 229
The Issue of Extending Quantum Theory to Cosmology	p. 230
Relational Approaches to Quantum Cosmology	p. 230
Relational Approaches to Going beyond Quantum Theory	p. 232
Conclusions	p. 233
Quantum Quandaries: A Category-Theoretic Perspective	p. 240
Introduction	p. 240
Lessons from Topological Quantum Field Theory	p. 244
The *-Category of Hilbert Spaces	p. 249
The Monoidal Category of Hilbert Spaces	p. 254
Conclusions	p. 261
Index	p. 267
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The Structural Foundations of Quantum Gravity

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