# Classical and Quantum Gravity

### Why Black Hole Information Loss is Paradoxical (2017)

In N. Huggett, K. Matsubara and C. Wuthrich (eds.), *Beyond Spacetime: The Foundations of Quantum Gravity* (CUP, 2020).

I distinguish between two versions of the black hole information-loss paradox. The first arises from apparent failure of unitarity on the spacetime of a completely evaporating black hole, which appears to be non-globally-hyperbolic; this is the most commonly discussed version of the paradox in the foundational and semipopular literature, and the case for calling it `paradoxical' is less than compelling. But the second arises from a clash between a fully-statistical-mechanical interpretation of black hole evaporation and the quantum-field-theoretic description used in derivations of the Hawking effect. This version of the paradox arises long before a black hole completely evaporates, seems to be the version that has played a central role in quantum gravity, and is genuinely paradoxical. After explicating the paradox, I discuss the implications of more recent work on AdS/CFT duality and on the `Firewall paradox', and conclude that the paradox is if anything now sharper. The article is written at a (relatively) introductory level and does not assume advanced knowledge of quantum gravity.

### The Case for Black Hole Thermodynamics, I - Phenomenological Thermodynamics (2017)

*Studies in the History and Philosophy of Modern Physics* 64 (2018) pp. 52-67.

I give a fairly systematic and thorough presentation of the case for regarding black holes as thermodynamic systems in the fullest sense, aimed at students and non-specialists and not presuming advanced knowledge of quantum gravity. I pay particular attention to (i) the availability in classical black hole thermodynamics of a well-defined notion of adiabatic intervention; (ii) the power of the membrane paradigm to make black hole thermodynamics precise and to extend it to local-equilibrium contexts; (iii) the central role of Hawking radiation in permitting black holes to be in thermal contact with one another; (iv) the wide range of routes by which Hawking radiation can be derived and its back-reaction on the black hole calculated; (v) the interpretation of Hawking radiation close to the black hole as a gravitationally bound thermal atmosphere. In an appendix I discuss recent criticisms of black hole thermodynamics by Dougherty and Callender. This paper confines its attention to the thermodynamics of black holes; a sequel will consider their statistical mechanics.

### The Case for Black Hole Thermodynamics, II - Statistical Mechanics (2017)

*Studies in the History and Philosophy of Modern Physics* 66 (2018) pp. 103-118.

I present in detail the case for regarding black hole thermodynamics as having a statistical-mechanical explanation in exact parallel with the statistical-mechanical explanation believed to underly the thermodynamics of other systems. (Here I presume that black holes are indeed thermodynamic systems in the fullest sense; I review the evidence for *that* conclusion in the prequel to this paper.) I focus on three lines of argument: (i) zero-loop and one-loop calculations in quantum general relativity understood as a quantum field theory, using the path-integral formalism; (ii) calculations in string theory of the leading-order terms, higher-derivative corrections, and quantum corrections, in the black hole entropy formula for extremal and near-extremal black holes; (iii) recovery of the qualitative and (in some cases) quantitative structure of black hole statistical mechanics via the AdS/CFT correspondence. In each case I briefly review the content of, and arguments for, the form of quantum gravity being used (effective field theory; string theory; AdS/CFT) at a (relatively) introductory level: the paper is aimed at students and non-specialists and does not presume advanced knowledge of quantum gravity.. My conclusion is that the evidence for black hole statistical mechanics is as solid as we could reasonably expect it to be in the absence of a directly-empirically-verified theory of quantum gravity.

### Interpreting the Quantum Mechanics of Cosmology (2016)

To appear in forthcoming OUP volume on Philosophy of Cosmology, Anna Ijjas and Barry Loewer (ed.)

Quantum theory plays an increasingly significant role in contemporary early-universe cosmology, most notably in the inflationary origins of the fluctuation spectrum of the microwave background radiation. I consider the two main strategies for interpreting (as opposed to modifying or supplementing) standard quantum mechanics in the light of cosmology. I argue that the conceptual difficulties of the approaches based around an irreducible role for measurement - already very severe - become intolerable in a cosmological context, whereas the approach based around Everett's original idea of treating quantum systems as closed systems handles cosmological quantum theory satisfactorily. Contemporary cosmology, which indeed applies standard quantum theory without supplementation or modification, is thus committed - tacitly or explictly - to the Everett interpretation.

### Fundamental and Emergent Geometry in Newtonian Physics (2016)

*British Journal for the Philosophy of Science, * 71 (2020) pp.1-32.

Using as a starting point recent and apparently incompatible conclusions by Simon Saunders (Philosophy of Science 80 (2013) pp.22-48) and Eleanor Knox (British Journal for the Philosophy of Science 65 (2014) pp.863-880), I revisit the question of the correct spacetime setting for Newtonian physics. I argue that understood correctly, these two theories make the same claims both about the background geometry required to define the theory, and about the inertial structure of the theory. In doing so I illustrate and explore in detail the view --- espoused by Knox, and also by Harvey Brown (Physical Relativity, OUP 2005) --- that inertial structure is defined by the dynamics governing subsystems of a larger system. This clarifies some interesting features of Newtonian physics, notably (i) the distinction between using the theory to model subsystems of a larger whole and using it to model complete Universes, and (ii) the scale-relativity of spacetime structure.

### More problems for Newtonian cosmology (2016)

*Studies in the History and Philosophy of Modern Physics * 57 (2017), pp.35-40.

I point out a radical indeterminism in potential-based formulations of Newtonian gravity once we drop the condition that the potential vanishes at infinity (as is necessary, and indeed celebrated, in cosmological applications). This indeterminism, which is well known in theoretical cosmology but has received little attention in foundational discussions, can be removed only by specifying boundary conditions at all instants of time, which undermines the theory's claim to be fully cosmological, i.e., to apply to the Universe as a whole. A recent alternative formulation of Newtonian gravity due to Saunders (*Philosophy of Science* 80 (2013) pp.22-48) provides a conceptually satisfactory cosmology but fails to reproduce the Newtonian limit of general relativity in homogenous but anisotropic universes. I conclude that Newtonian gravity lacks a fully satisfactory cosmological formulation.

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### Gravity, Entropy and Cosmology: In Search of Clarity (2009)

*British Journal for the Philosophy of Science* 61 (2010) pp. 513-540

I discuss the statistical mechanics of gravitating systems and in particular its cosmological implications, and argue that many conventional views on this subject in the foundations of statistical mechanics embody significant confusion; I attempt to provide a clearer and more accurate account. In particular, I observe that (i) the role of gravity *in* entropy calculations must be distinguished from the entropy *of* gravity, that (ii) although gravitational collapse is entropy-increasing, this is not usually because the collapsing matter itself increases in entropy, and that (iii) the Second Law of Thermodynamics does not owe its validity to the statistical mechanics of gravitational collapse.

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### The Relativity and Equivalence Principles for Self-Gravitating Systems (2009)

In D Lehmkuhl, G. Schiemann and E. Scholz (eds.), *Towards a Theory of Spacetime Theories* (Springer, 2017).

I criticise the view that the relativity and equivalence principles are consequences of the small-scale structure of the metric in general relativity, by arguing that these principles also apply to systems with non-trivial self-gravitation and hence non-trivial spacetime curvature (such as black holes). I provide an alternative account, incorporating aspects of the criticised view, which allows both principles to apply to systems with self-gravity.

### The quantization of gravity - an introduction (2000)

Online only; cite as arxiv:gr-qc/0004005.

This is an introduction to quantum gravity, aimed at a fairly general audience and concentrating on what have historically been the two main approaches to quantum gravity: the covariant and canonical programs (string theory is not covered). The quantization of gravity is discussed by analogy with the quantization of the electromagnetic field. The conceptual and technical problems of both approaches are discussed, and the paper concludes with a discussion of evidence for quantum gravity from the rest of physics.

The paper assumes some familiarity with non-relativistic quantum mechanics, special relativity, and the Lagrangian and Hamiltonian formulations of classical mechanics; some experience with classical field theory, quantum electrodynamics and the gauge principle in electromagnetism might be helpful but is not required. No knowledge of general relativity or of quantum field theory in general is assumed.

(**Note**: this is a very old paper of mine, and was never intended for (non-electronic) publication. I've left it available since various people have said it's a moderately helpful introduction to the issue for complete non-specialists. It doesn't really say anything that wasn't known in the 1980s.)