Cover -- Half-title -- Title -- Copyright -- Didication -- Contents -- Preface -- 1 Introduction -- 1.1 Why quantum gravity? -- 1.2 Must the gravitational field be quantized? -- 1.2.1 No-go theorems? -- 1.2.2 The semiclassical theory -- 1.3 Approaches to quantum gravity -- 1.3.1 Superstrings -- 1.3.2 Canonical quantum gravity -- 1.4 What quantum gravity and philosophy have to say to each other -- 1.4.1 The demise of classical spacetime -- 1.4.2 The nature of time -- 1.4.3 The interpretation of general relativity -- 1.4.4 The interpretation of quantum mechanics -- 1.4.5 The status of the wave function -- Notes -- Part I Theories of Quantum Gravity and their Philosophical Dimensions -- 2 Spacetime and the philosophical challenge of quantum gravity -- 2.1 Introduction -- 2.1.1 Prologue -- 2.1.2 No data, no theory, no philosophy? -- 2.1.3 Realism? -- 2.1.3.1 Beware scientific realism -- 2.1.3.2 The fragility of ontology in physics -- 2.1.3.3 The question of transcendental idealism -- 2.2 Conceptual problems of quantum theory and general relativity -- 2.2.1 Interpreting quantum theory -- 2.2.1.1 Instrumentalism -- 2.2.1.2 Literalism -- 2.2.1.3 Extra values -- 2.2.1.4 New dynamics -- 2.2.2 Interpreting general relativity -- 2.3 Introducing quantum gravity -- 2.3.1 Approaches to quantum gravity -- 2.3.1.1 Motivations for studying quantum gravity -- 2.3.1.2 Can quantum gravity be avoided? -- 2.3.1.3 Four types of approach to quantum gravity -- 2.3.2 The role of diffeomorphisms -- 2.3.2.1 Spacetime diffeomorphisms in classical general relativity -- 2.3.3 The problem of time -- 2.3.3.1 Time in quantum theory -- 2.3.3.2 Time in general relativity -- and the problem of time -- 2.4 Research programmes in quantum gravity -- 2.4.1 Focussing the question: how is spacetime treated? -- 2.4.2 Some historical background to the three programmes.

2.4.3 The particle-physics programme -- 2.4.3.1 The basic ideas -- 2.4.4 The superstrings programme -- 2.4.4.1 The introduction of supersymmetry -- 2.4.4.2 Perturbative superstrings -- 2.4.4.3 Spacetime according to the perturbative superstrings programme -- 2.4.4.4 The second phase of superstrings -- 2.4.5 The canonical quantum gravity programme -- 2.4.5.1 Quantum geometrodynamics -- 2.4.5.2 The Ashtekar programme and loop variables -- 2.4.5.3 Spacetime according to the canonical quantum gravity programme -- 2.5 Towards quantum spacetime? -- 2.5.1 Introduction: quantization and emergence -- 2.5.1 Introduction: quantization and emergence -- 2.5.1.1 Some suggestions from the three programmes -- 2.5.1.2 Emergence and quantization -- 2.5.2 Quantization 'below' the metric -- 2.5.3 Spacetime from a non-quantization -- 2.5.4 Spacetime emergent from a non-quantum theory -- 2.5.5 Envoi -- Notes -- 3 Naive quantum gravity -- 3.1 Introduction -- 3.2 What is a field? -- 3.3 The uncertainty of quantization -- 3.4 Quantifying the effects of gravity: local field strength -- 3.4.1 Absolute acceleration -- 3.4.2 Relative acceleration and the Riemann tensor -- 3.5 Causal structure -- 3.6 What's the point? -- 3.7 Conclusion -- Notes -- 4 Quantum spacetime: What do we know? -- 4.1 The incomplete revolution -- 4.2 The problem -- 4.2.1 First step. A new actor on the stage: the field -- 4.2.2 Second step. Dynamical entities have quantum properties -- 4.2.3 Third step. The stage becomes an actor -- 4.2.4 Bringing the three steps together -- 4.3 Quantum spacetime -- 4.3.1 Space -- 4.3.2 Time -- 4.3.3 Glimpses -- 4.4 Considerations on method and content -- 4.4.1 Method -- 4.4.2 On content and truth in physical theories -- Part II Strings -- 5 Reflections on the fate of spacetime -- 5.1 Introduction -- 5.2 String theory -- 5.3 Some of the symptoms.

5.4 Duality and the minimum length -- 5.5 Strings and quantum mechanics -- Notes -- 6 A philosopher looks at string theory -- Notes -- 7 Black holes, dumb holes, and entropy -- 7.1 Thermodynamics of black holes -- 7.2 A problem in the derivation of black hole evaporation -- 7.3 Dumb holes -- 7.4 Entropy and the 'information paradox' -- 7.5 Conclusion -- Notes -- Part III Topological Quantum Field Theory -- 8 Higher-dimensional algebra and Planck scale physics -- 8.1 Introduction -- 8.2 The Planck length -- 8.3 Topological quantum field theory -- 8.4 Three-dimensional quantum gravity -- 8.5 Higher-dimensional algebra -- 8.6 Four-dimensional quantum gravity -- Notes -- Part IV Quantum Gravity and the Interpretation of General Relativity -- 9 On general covariance and best matching -- 9.1 Introduction -- 9.2 Einstein's understanding of general covariance -- 9.2.1 The historical background -- 9.2.2 Einstein and the determination of inertial frames -- 9.2.3 Einstein, Kretschmann, and the relativity principle -- 9.3 General covariance is not a physical principle -- 9.3.1 Newtonian mechanics in generally covariant form -- 9.3.2 Poincar ́e and the initial-value problem -- 9.3.3 Mechanics without background structures -- 9.3.4 Amodification of Einstein's simplicity argument -- 9.3.5 Cartan's reformulation misses the point -- 9.4 Penrose's argument -- 9.5 The significant issue -- 9.6 Conclusions -- Notes -- 10 Pre-Socratic quantum gravity -- 10.1 Introduction -- 10.2 Hamiltonian and gauge systems -- 10.2.1 Hamiltonian systems -- 10.2.1.1 The free particle -- 10.2.1.2 The Klein-Gordon Field -- 10.2.2 Gauge systems -- 10.2.2.1 Trivial gauge-invariant function -- 10.2.2.2 Vacuum electromagnetism -- 10.2.3 Interpreting gauge theories -- 10.2.4 Quantizing gauge theories -- 10.3 General relativity as a gauge theory -- 10.3.1 Formalism -- 10.3.2 Interpretation.

10.4 Gauge invariance and change -- 10.5 Life without change -- 10.5.1 The classical theory -- 10.5.2 Quantum gravity -- 10.6 Vive le change! -- 10.7 The status of spacetime -- 10.7.1 Rovelli's evolving constants -- 10.7.2 Constant mean curvature as time -- 10.7.3 Internal time -- 10.8 Appendix -- 10.8.1 Hamiltonian systems -- 10.8.2 Gauge systems -- 10.8.3 Reduced phase spaces -- 10.8.4 Parametrized systems -- Notes -- 11 The origin of the spacetime metric: Bell's 'Lorentzian pedagogy' and its significance in general relativity -- 11.1 Introduction -- 11.2 Chalk and cheese: Einstein on the status of special relativity theory -- 11.3 The significance of the Lorentzian pedagogy -- 11.4 Einstein's unease about rods and clocks in special relativity -- 11.5 A digression on rods and clocks in Weyl's 1918 unified field theory -- 11.6 The case of general relativity -- Notes -- Part V Quantum Gravity and the Interpretation of Quantum Mechanics -- 12 Quantum spacetime without observers: Ontological clarity and the conceptual foundations of quantum gravity -- 12.1 Introduction -- 12.2 The conceptual problems of quantum gravity -- 12.2.1 The problem of time -- 12.2.2 The problem of 4-diffeomorphism invariance -- 12.2.3 The problem of 'no outside observer' -- 12.2.4 The problem of diffeomorphism-invariant observables -- 12.3 The basic problem of orthodox quantum theory: the lack of a coherent ontology -- 12.4 Bohmian mechanics -- 12.5 Bohmian quantum gravity -- 12.6 A universal Bohmian theory -- Notes -- 13 On gravity's role in quantum state reduction -- 13.1 The problem of quantum state reduction -- 13.2 Stationary states -- 13.3 Preliminary considerations -- 13.4 Superposed gravitational fields -- 13.5 The semiclassical approach -- 13.6 Approximate spacetime point identification -- 13.7 Further considerations -- Notes.

14 Why the quantum must yield to gravity -- 14.1 Introduction: From Schrödinger's cat to Penrose's 'OR' -- 14.2 How spatio-temporal events lost their individuality -- 14.3 Penrose's mechanism for the objective state reduction -- 14.3.1 Motivation via a concrete example -- 14.3.2 The raison d'ˆetre of state reduction -- 14.3.3 Phenomenology of the objective state reduction -- 14.3.4 A different measure of deviation from quantum mechanics -- 14.3.5 Penrose's proposed experiment -- 14.4 A closer look at Penrose's proposal within Newton-Cartan framework -- 14.4.1 An orthodox analysis within strictly Newtonian domain -- 14.4.2 The inadequacy of Penrose's proposed experiment -- 14.4.3 More adequate experiments involving relative rotations -- 14.5 Concluding remarks -- Notes -- References -- Notes on contributors -- Index.