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The Structural Foundations of Quantum Gravity
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Contents Notes on Contributors xi 1. Quantum Gravity Meets Structuralism: Interweaving Relations in the Foundations of Physics 1 Dean Rickles and Steven French 1.1 Quantum Gravity: Background, Concepts, and Methods 1 1.1.1 The Hole Argument and Spacetime Ontology 2 1.1.2 Gauging the Hole Argument 4 1.1.3 Enter Quantum Gravity 7 1.1.4 Categorizing the Manifold Methods 14 1.1.5 What’s Wrong with Background-Dependent Methods? 16 1.1.6 What’s Right about Background-Independent Methods? 18 1.1.7 Background Independence and Structuralism 20 1.2 Structuralism and Structural Realism 25 1.2.1 Motivating Structuralism 25 1.2.2 What is Structuralism? 25 1.2.3 …and Where Does it Come from? 26 1.2.4 Structural Realism 30 2. Structural Realism and Quantum Gravity 40 Tian Yu Cao 2.1 Structural Realism 41 2.2 Physical Reality of Spacetime and Quantum Fields 43 2.3 Quantum Gravity 47 3. Structure, Individuality, and Quantum Gravity 53 John Stachel 3.1 What is Structural Realism? 53 3.2 Structure and Individuality 55 3.3 Effective Field Theory and Asymptotic Quantization 60 3.4 String Theory 63 3.5 Quantum General Relativity: Some Preliminary Problems 65 3.5.1 States or Processes: Which is Primary? 65 3.5.2 Formalism and Measurability 68 3.6 Canonical Quantization (Loop Quantum Gravity) 71 3.7 The Causal Set (Causet) Approach 75 3.8 What Structures to Quantize? 77 viii Contents 4. Points, Particles, and Structural Realism 83 Oliver Pooley 4.1 What is Structural Realism? 84 4.2 Underdetermination 86 4.3 What is Ontic Structural Realism? 91 4.4 Objects 94 4.5 Sophisticated Substantivalism 99 4.6 Stachel’s Generalized Hole Argument for Sets 104 4.7 Stachel on Identical Particles 109 4.8 Identical Particles and Identity over Time 114 4.9 Two Morals for Quantum Gravity 116 5. Holism and Structuralism in Classical and Quantum General Relativity 121 Mauro Dorato and Massimo Pauri 5.1 Introduction: Two Strands of Philosophy of Physics that Ought to be Brought together 121 5.2 Many ‘Realisms’ or One? 123 5.2.1 What, Exactly, is a Physical Structure? 124 5.3 A Case Study: The Holistic and Structural Nature of General-Relativistic Spacetime in a Class of Models of GR 126 5.3.1 The Hole Argument and its Consequences 126 5.3.2 The Dynamical Individuation of Point-Events 130 5.4 Developing Hints for the Quantum Gravity Programme 140 5.5 Structural Spacetime Realism 144 5.5.1 The Nature of Point-Events and Overcoming the Substantivalism/Relationism Debate 145 6. Time and Structure in Canonical Gravity 152 Dean Rickles 6.1 Introduction 152 6.2 Constraints, Gauge, and Holes 153 6.2.1 Hamiltonian Systems: Constraints and Gauge 154 6.2.2 Constraints and Gauge in General Relativity 157 6.2.3 Interpreting Gauge Theories 159 6.3 What is the Problem of Time? 163 6.4 A Snapshot of the Philosophical Debate 166 6.4.1 Time Series from A to D 167 6.4.2 Maudlin versus Earman 171 6.5 Catalogue of Responses 175 6.5.1 Timefull Stratagems 176 6.5.2 Timeless Stratagems 179 6.6 Enter Structuralism 188 6.7 Conclusion 191 Contents ix 7. The Case for Background Independence 196 Lee Smolin 7.1 Introduction 196 7.2 A Brief History of Relational Time 200 7.3 What Physicists Mean When We Talk about Relational Space and Time 203 7.4 General Relativity as a Partly Relational Theory 204 7.4.1 The Problem of Time and Related Issues 207 7.5 Relationalism and the Search for the Quantum Theory of Gravity 209 7.5.1 The Causal Set Theory 210 7.5.2 Loop Quantum Gravity 212 7.5.3 Causal Dynamical Triangulation Models 216 7.5.4 Background-Independent Approaches to String and M Theory 217 7.6 Relationalism and Reductionism 219 7.6.1 The Challenge of the String Theory Landscape 223 7.7 A Relational Approach to the Problems of Unification and Determination of the Standard Model Parameters 226 7.8 Relationalism and Natural Selection 227 7.9 What about the Cosmological Constant Problem? 229 7.10 The Issue of Extending Quantum Theory to Cosmology 230 7.10.1 Relational Approaches to Quantum Cosmology 230 7.10.2 Relational Approaches to Going beyond Quantum Theory 232 7.11 Conclusions 233 8. Quantum Quandaries: A Category-Theoretic Perspective 240 John Baez 8.1 Introduction 240 8.2 Lessons from Topological Quantum Field Theory 244 8.3 The ∗-Category of Hilbert Spaces 249 8.4 The Monoidal Category of Hilbert Spaces 254 8.5 Conclusions 261 Index 267 |
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