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The Emergence of Spacetime in Quantum Gravity

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The Emergence of Spacetime in Quantum Gravity Appearing Out of Nowhere: The Emergence of Spacetime in Quantum Gravity Karen Crowther Thesis submitted for the degree of Doctor of Philosophy Centre for Time Department of Philosophy University of Sydney arXiv:1410.0345v1 [physics.hist-ph] 1 Oct 2014 Australia January 2014 ii iii Abstract Quantum gravity is understood as a theory that, in some sense, unifies general relativity (GR) and quantum theory, and is supposed to replace GR at extremely small distances (high-energies). It may be that quantum gravity represents the breakdown of spacetime geometry described by GR. The relationship between quantum gravity and spacetime has been deemed \emergence", and the aim of this thesis is to investigate and explicate this relation. After finding traditional philosophical accounts of emergence to be inap- propriate, I develop a new conception of emergence by considering physical case studies including condensed matter physics, hydrodynamics, critical phenomena and quantum field theory understood as effective field theory. This new conception of emergence is unconcerned with the ideas of reduction and derivation (i.e. it holds that we may have emergence with reduction or without it). Instead, a low-energy theory (or model) is understood as emergent from a high-energy theory if it is novel and autonomous compared to the high-energy theory, and the low- energy physics is dependent in a particular, minimal sense on the high-energy physics (this dependence is revealed by the techniques of effective field theory and the renor- malisation group). While novelty is construed in a broad sense, the autonomy comes essentially from the underdetermination of the high-energy theory by the low-energy theory, which reflects the minimal way in which the emergent, low-energy theory de- pends on the high-energy one. It results from the scaling behaviour of the theories and the limiting relations between them, and is demonstrated by the renormalisation group and effective field theory techniques, the idea of universality, and the phenomenon of symmetry-breaking. These ideas are important in exploring the relationship between quantum gravity and GR, where GR is understood as an effective, low-energy theory of quantum gravity. Without experimental data or a theory of quantum gravity, we rely on principles and techniques from other areas of physics to guide the way. As well as considering the idea of emergence appropriate to treating GR as an effective field theory, I investigate the emergence of spacetime (and other aspects of GR) in several concrete approaches to quantum gravity, including examples of the condensed matter approaches, the \dis- crete approaches" (causal set theory, causal dynamical triangulations, quantum causal histories and quantum graphity) and loop quantum gravity. iv Acknowledgements An enormous thank you to Dean Rickles and Huw Price for being the best supervisors I ever could have wished for. I am grateful for having benefited not only from their expertise, but their continual support and encouragement. Thank you! This thesis has been improved by the corrections recommended by the amazing Christian W¨uthrich, Eleanor Knox, and Jonathan Bain. I am very appreciative of their thoughtful comments and suggestions. I'd also like to say thanks to my Centre for Time comrades, Karim Th´ebault,Pete Evans and Sam Baron, as well as the awesome Cambridge \phil phys gang", partic- ularly Jeremy Butterfield, Arianne Shahvisi and Lena Zuchowski. I am thankful, too, for the hospitality of Gal and Mr B at the Cambridge Gin Palace on New- market Road. Cheers! Finally, my heartfelt gratitude to my mother, Paula Crowther, and my sister, Anita Crowther, for everything they have done to help me along the way. A note regarding the title of the thesis: I discovered, after I had made the initial submission of this thesis, that Christian W¨uthrich and Nick Huggett have a monograph in the works with a very similar title (being, Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity). We have discussed the coincidence, and have agreed that neither title should need to change. I look forward to reading the book! Contents 1 Introduction: Spacetime and quantum gravity 3 1.1 Quantum gravity . 3 1.2 Spacetime . 12 1.3 Motivations and indications . 14 1.4 Quantum gravity as a physical theory . 17 1.5 The problem of time . 18 1.6 The recovery of spacetime . 22 1.7 Two transitions . 24 1.7.1 The small-scale structure of spacetime . 26 1.7.2 Decoherence . 27 1.8 Emergent gravity . 33 1.8.1 Weinberg-Witten theorem . 35 1.8.2 AdS/CFT duality . 36 1.9 The world in a grain of sand . 39 1.10 Synopsis . 41 2 Emergence and reduction 47 2.1 Introduction . 47 2.2 Emergence . 50 2.2.1 Distinguishing in principle from in practice . 53 2.2.2 A varied landscape where less is different . 54 2.2.3 The problem of defining \derivation" . 56 2.3 The Anderson/Weinberg debate . 57 2.4 Emergence in physics . 60 2.5 Reduction . 63 2.6 Emergence as dependence plus novelty and autonomy . 66 2.7 Fundamentality . 71 2.8 Conclusion . 72 v vi Contents 3 Effective field theory 75 3.1 Introduction . 75 3.2 Quantum field theory and renormalisation . 76 3.3 Renormalisation group and the re-conceptualisation of QFT . 81 3.3.1 Block-spin RG . 84 3.3.2 Fixed points . 85 3.4 Effective field theory . 87 3.4.1 Basic formalism . 89 3.4.2 Appelquist-Carazzone decoupling theorem . 91 3.5 Tower of theories . 91 3.5.1 Bottom-up . 92 3.5.2 Top-down . 95 3.5.3 Wilsonian versus Continuum EFTs . 96 3.6 Reconceptualising the cutoff . 97 3.7 Philosophy of EFT: Cao and Schweber (1993) . 99 3.7.1 Epistemological antifoundationalism . 100 3.7.2 Final theory . 100 3.7.3 Methodological antireductionism . 103 3.7.4 Ontological pluralism . 106 3.7.5 Emergence: quasi-autonomous domains . 107 3.7.6 Emergence: relations between the layers . 111 3.8 EFT as effective . 112 3.8.1 Effective EFT and high-energy physics . 114 3.8.2 Effective QFT . 116 3.8.3 Axiomatic quantum field theory . 119 3.8.4 Underdetermination . 121 3.8.5 Taking EFT effectively . 126 3.9 Conclusion: Emergence . 127 4 Universality, higher-organising principles and emergence 133 4.1 Introduction . 133 4.2 Multiple-realisability . 135 4.3 Higher organising principles . 139 4.4 Universality and emergence . 140 Contents vii 4.5 Fixed points and critical phenomena . 142 4.6 Batterman's account of emergence . 149 4.7 Morrison's account of emergence . 151 4.8 Comparing the accounts . 158 4.8.1 Universality and EFT . 158 4.8.2 Symmetry breaking and higher-organising principles . 160 4.8.3 Universality and reduction-based definitions of emergence . 162 4.8.4 Hydrodynamics . 165 4.9 Singularities, limiting relations and emergence . 168 4.10 Conclusion . 170 5 Spacetime as described by EFT 173 5.1 Introduction . 173 5.2 Top-down: Analogue models of (and for) gravity . 176 5.2.1 Gravity in superfluid superfluid3 He − A . 177 5.2.2 The quantisation of gravity . 181 5.2.3 Analogue models of gravity? . 181 5.2.4 Emergence . 183 5.3 Bottom-up: GR as an EFT . 184 5.3.1 Kinetic theory approach . 186 5.3.2 Emergence . 187 5.4 Asymptotic safety in quantum gravity . 187 5.5 Conclusion . 191 6 Discrete approaches to quantum gravity 193 6.1 Introduction . 193 6.2 Discreteness . 195 6.3 Non-perturbative approaches . 197 6.4 Background independence . 199 6.5 Causal set theory . 205 6.5.1 Emergence in causal set theory . 210 6.6 Causal dynamical triangulations (CDT) . 213 6.6.1 Emergence in CDT . 219 6.7 Pre-geometric approaches . 222 Contents 1 6.7.1 Emergence in quantum graphity and QCH . 227 6.8 Conclusion . 230 7 Loop quantum gravity 233 7.1 Introduction . 233 7.2 Spacetime in LQG . 239 7.2.1 Micro-structure of space: Spin networks . 240 7.2.2 Semiclassical limit: Weaves . 245 7.2.3 Micro-structure of spacetime: Spin foams . 247 7.3 Emergence . 253 7.4 Conclusion . 260 8 Conclusion: Now here from nowhere 263 2 Contents Chapter 1 Introduction: Spacetime and quantum gravity The search for a theory of quantum gravity is the pursuit of a more unified picture of the world. It is a quest to push beyond what is known, one that perhaps leads into the inaccessible. It is a journey guided by principles rather than experiment: principles gleaned from known physics, but which we cannot be sure will carry us as far as we want to travel. One of these principles states that we must be able to return from our journey|if we reach a theory from which we cannot arrive back at the firm ground of established physics, then, whatever we have reached, it is not quantum gravity. Moving to a theory of quantum gravity might represent the breakdown of space- time, in the sense that it is possible that our current conception of spacetime will not feature in the fundamental description of such a theory. If spacetime does not appear fundamentally in quantum gravity, but is to be recovered at some larger-distance (or lower-energy scale), then spacetime is emergent. The \return" to current physics will represent the process of recovering spacetime. This thesis is concerned with the nature of the breakdown, the process of recovery, and the different conceptions of emergence that it might entail. 1.1 Quantum gravity Quantum theory, or, more specifically, quantum field theory (QFT), provides an account of all the known fundamental forces of nature|except for one.
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