## Annual Essay Prize Winners

**Suddhasattwa Brahma** *Fudan University*

**Emergence of time in loop quantum gravity**

Loop quantum gravity (LQG) has formalized a robust scheme in resolving classical singularities in a variety of symmetry-reduced models of gravity. In this talk, I shall demonstrate that the quantum correction crucial for singularity resolution is also the same one responsible for the phenomenon of signature change in these models, whereby one effectively transitions from a ‘fuzzy’ Euclidean space to a Lorentzian space-time in deep quantum regimes. Holonomy corrections arising from LQG lead to a deformed notion of covariance, leading to non-singular signature change in these models. How an emergent notion of time naturally arises in this context, as well as its conceptual and mathematical ramifications, shall be main focus of the talk. Robustness of this mechanism, established by comparison across large class of midisuperspace models and allowing for diverse quantization ambiguities, shall also be briefly discussed.

**Sebastian de Haro** *Amsterdam University College, University of Cambridge*

**Spacetime and physical equivalence**

Sebastian de Haro will not present his contribution during the conference, but later during the year.

## Invited Speakers

**Richard Dawid** *Stockholm University*

**Why string theory is philosophically interesting**

In order to understand the role played by string theory in fundamental physics today, it is helpful to relate the theory’s conceptual position within the fabric of physics to the peculiar way the theory’s development has played out. Conceptually, string theory constitutes an attempt to provide a universal theory of all interactions. String theory thus does not fit the canonical view that takes theories as intermediate steps in a continuous process of theory succession towards ever higher universality. On the other hand, the history of string physics over the past fifty years suggests that string theory is enormously difficult to pin down and will not allow for a full formulation in the foreseeable future. Given its peculiar status, string physicists disagree on the question whether string theory should be called a genuine theory at all. In this light, the practice of string physics may indicate that physical theory building works in a fundamentally different way once full universality is aimed at. The talk will discuss the philosophical dimension of this situation.

**Eleanor Knox** *King’s College London*

**Spacetime functionalism and noncommutative gravity**

Spacetime functionalism, the view that spacetime is as spacetime does, allows for an interesting interpretational perspective on both classical and quantum gravitational theories. In this paper, I’ll explore the consequences of a particular kind of spacetime functionalism for a particular variety of non-commutative gravitational theory. The spacetime functionalism I advocate analyses the spacetime concept as a functional one, and holds that whatever defines a structure of inertial frames in a theory just is spacetime. When applied to a kind of noncommutative gravity (one with a constant noncommutativity parameter), the approach yields particularly interesting results. This kind of theory privileges a set of inertial frames in a strong way, breaking diffeomorphism invariance to do so. On the functionalist approach, this means that it postulates a particularly interesting spacetime, and poses an interesting challenge to some widely accepted ideas in the foundations of spacetime theories.

**Daniele Oriti** *Max Planck Institute for Gravitational Physics*

**An emergent universe without fundamental space and time**

We discuss a new perspective on the nature of cosmology from the quantum gravity point of view, and more specifically in an emergent spacetime scenario. It is based on results in quantum gravity that suggest non-spatiotemporal structures as the foundation of our spacetime and on the interpretation of cosmological dynamics as the hydrodynamic description of the microscopic quantum dynamics of such building blocks. In this picture, the universe can be seen as sort of (quantum) fluid, the result of their collective interaction, and its cosmological description as appropriate for its coarsest approximation. Beside outlining this picture and its general implications for quantum gravity and cosmology, we also offer some examples of its realisation taken from current research in group field theory, and related quantum gravity formalisms.

**Karim Thébault** *University of Bristol*

**Cosmic singularity resolution via quantum evolution**

Classical models of the universe generically feature a big bang singularity. That is, when we consider progressively earlier and earlier times, physical quantities stop behaving in a mathematically reasonable way. A particular problem is that physical quantities related to the curvature of spacetime become divergent. A long standing hope is that a theory of quantum gravity would `resolve? the big bang singularity by providing quantum models of the early universe in which all physical quantities are always finite. Unfortunately, not only does the conventional Wheeler-DeWitt approach to quantum gravity fail to resolve the big bang singularity in this sense (without the addition of fundamental discreteness or exotic matter), but it also renders the universe fundamentally timeless. We offer a new proposal for singularity resolution in quantum cosmology based upon quantum evolution. In particular, we advocate a new approach to quantum cosmology based upon a Schrödinger equation for the universe. For simple models with a massless scalar field and positive cosmological constant we show that: i) well-behaved quantum observables can be constructed; ii) generic solutions to the universal Schrödinger equation are singularity-free; and iii) specific solutions display novel phenomenology including a cosmic bounce.

**Alastair Wilson** *University of Birmingham*

**How does spacetime emerge in quantum gravity?**

Metaphysicians typically distinguish sharply between causation and grounding, but there has been surprisingly little discussion of how exactly to draw this distinction, or of how it relates to the relationship between causal and non-causal explanation in philosophy of science. In recent work I have proposed that we can distinguish between different kinds of objective explanatory dependency by reference to principles mediating the dependencies. In this talk I explore the application of this criterion to the status of emergent spacetime in quantum gravity. The key diagnostic question is: does the emergence of spacetime depend on dynamical laws of nature, or on constitutive metaphysical principles? I will argue that if standard assumptions about the range of possible laws and spacetime structures are correct, then in typical approaches to quantum gravity spacetime must be caused by, as opposed to grounded in, the underlying non-spatiotemporal reality. This surprising result may be avoided by adopting the functionalist conception of spacetime recently developed by Eleanor Knox and others. To properly classify emergence of spacetime in the functionalist setting, we will need to investigate how exactly the successful realization of the spacetime role depends on features of the realizer.

## Contributed Papers

**Karen Crowther** *University of Geneva*

**Understanding the emergence of spacetime from quantum gravity**

An acceptable theory of quantum gravity (QG) must recover general relativity (GR), with its conception of spacetime, in the regimes where GR is known to be successful. What this recovery amounts to, however, is an open question, and concerns the inter-theory relations of correspondence, reduction, and emergence. In this talk, I explore these relations both in general, and from the perspective of particular approaches to QG, with a focus on articulating the appropriate notion of emergence. I argue that the traditional conceptions of emergence in philosophy&emdash;particularly those of “strong emergence” versus “weak emergence” are not applicable. I also argue that the more-or-less standard notion of emergence adopted in the philosophy of QG literature, of novelty and robustness (of the emergent theory compared to the more fundamental one), needs further refinement in order to be clearly distinguished from the&emdash;also important&emdash;relations of reduction and correspondence.

Commentator: Joshua Norton (American University of Beirut)

**Juliusz Doboszewski** *Jagiellonian University*

**Merging, splitting and tunnelling: a comment on quantum black holes**

White holes are time-reversed counterparts of black holes. I will discuss three known problematic features of white holes: (1) that no viable candidates for white holes have ever been observed; (2) that a form of indeterminism is associated with white holes; and (3) that white holes violate of the second law of horizon thermodynamics. Then I will introduce and discuss a novel feature: (4) if white holes are possible, so should be white hole splitters – that is, time reversed counterparts of black hole mergers. White hole splitters raise new conceptual challenges, some of which become particularly pressing in the context of recently proposed black-to-white hole tunnelling.

Commentator: Henrique Gomes (Perimeter Institute for Theoretical Physics)

**Simon Friederich** *University of Groningen*

**The asymptotic safety scenario for quantum gravity – a methodological appraisal**

This contribution has two aims: first, to make the asymptotic safety-based approach to quantum gravity better known to the philosophy of physics community by outlining its motivation, core tenets, and successes so far; second, to give a methodological appraisal of it by assessing it in terms of well-established criteria of theory choice. In addition, I deflate any apparently profound metaphysical implications of the fact that, according to the asymptotic safety scenario, space-time has fractal dimension 2 at short length scales.

The asymptotic safety scenario, originating from a suggestion due to Steven Weinberg, is based on the idea that non-perturbative renormalization techniques may reveal a quantum version of general relativity to be asymptotically safe in the sense of being well-defined at arbitrarily high energies by having a non-trivial ultraviolet fixed point with finite-dimensional critical surface in the parameter space of flowing couplings. The present contribution argues that the asymptotic safety approach to quantum gravity is attractive in the light of virtues such as methodological conservativeness, ontological parsimony, metaphysical conservativeness, and predictive force, which can all be linked to Kuhn’s celebrated five criteria of theory choice.

Commentator: Kian Salimkhani (University of Bonn)

**Richard Healey** *University of Arizona*

**The measurement problem for emergent spacetime in loop quantum gravity**

Any quantum theory of gravity faces the measurement problem. Carlo Rovelli sees his relational interpretation as offering a solution to this problem when applied to his favored loop quantum gravity (LQG). I examine the prospects of Rovelli’s relationalism in LQG. In the context of non-relativistic quantum mechanics Rovelli makes the problematic claim that quantum theory must be understood as an account of the way distinct physical systems affect one another when they interact, and not the way physical systems `are’. The difficulty is compounded in loop quantum gravity. Ordinary quantum mechanics models an observer as a quantum system O, and measurement as an interaction between O and another quantum system S, signaled by a non-zero interaction Hamiltonian. In quantum field theory on a fixed spacetime, interaction is usually understood as non-linearity of the Euler-Lagrange equations derived from the field Lagrangian (density). Implementing Rovelli’s relational interpretation in the context of LQG requires an account of interaction and a model of observer systems whose relational states represent determinate outcomes. Lessons learned by examining the prospects of Rovelli’s relationism in LQG may help us to see how spacetime emerges according to other relational interpretations of this and other quantum theories of gravity.

Commentator: Vincent Lam (University of Geneva)

**Casey D. McCoy** *University of Edinburgh*

**On a quantum-gravity-concerning heuristic viewpoint**

A famous result of Jacobson ostensibly is the derivation of the Einstein equation from the thermodynamics of spacetime. Jacobson argues that the Einstein equation is an equation of state and for this reason should not be quantized as if it were a fundamental field. Recently Chrico et al. have disputed Jacobson’s interpretation, arguing instead that his result is entirely consistent with a derivation from quantum gravity and, hence, does not depend on the introduction of `hidden’ degrees of freedom, i.e. non-gravitational ones. We see this debate as an important one for questions concerning the emergence of spacetime for how it directs attention on two important conceptual issues, namely the roles of quantization and entropy in quantum gravity. In this paper we link the emergence of spacetime to these issues and argue for the inadequacy of current accounts that address these issues.

Commentator: Niels Linnemann (University of Geneva)

**Tushar Menon** *University of Oxford*

**Rebuilding Neurath’s boat planck by planck: Algebraic spacetime functionalism and the ontology of spacetime in quantum gravity**

According to Harvey Brown, the behaviour of rods and clocks is explained by the dynamical symmetry structure of their laws. Brown’s presentation lends itself to an emergent conception of spacetime that is consonant with much modern research in quantum gravity. Building on Brown’s dynamical view and Eleanor Knox’s spacetime functionalism, I propose a non-geometric fundamental ontology, taking the metric field to be primitive, but not primitively chronogeometric. I argue that the chronogeometric significance, which is a necessary feature of any object which claims to represent spacetime, can be arrived at by dynamical considerations related to notions of universality of field transformation and coupling behaviour. How, then, might one go about arguing for a fields-first ontology? And, equally importantly, what are the metaphysical commitments that such a view might entail? In this talk, I argue for a conception of spacetime that does not privilege geometry, but instead, the structural features of a geometric theory which can be encoded just as well algebraically. That such an algebraic reformulation is possible was demonstrated, in the case of GR, by Robert Geroch. I conclude that an emergent conception of spacetime, characterised by the algebraically encoded dynamical symmetry structure of the laws, together with a broadly ontic structural realist metaphysics is a promising option for identifying spacetime in theories of quantum gravity.

Commentator: John Dougherty (University of Illinois at Chicago)

**Joshua Rosaler** *RWTH Aachen University*

**Limits of Bronstein’s cube: Mapping the inter-model reductions of modern physics in the search for quantum gravity**

What sort of relationship should general relativity and the Standard Model bear to any theory of quantum gravity? This relationship is sometimes called ?reduction,? though the term has been given many different meanings. One important sense of reduction in physics requires one theory to encompass the full range of empirical successes of another. I argue that a prominent attempt to characterise the mathematical mechanisms for this type of reduction between theories in physics, associated with the so-called `Bronstein Cube’ of theories, paints an oversimplified picture of these mechanisms. While limits often play a critical role in reduction, reduction in the sense considered here is often not as simple a matter as taking the specific sorts of limits invoked by the Bronstein Cube. I describe an alternative approach to reduction based on a particular type of mathematical relationship between two models of the same physical system and demonstrate this type of connection in the context of examples that include the relationships between classical and quantum theories and between high- and low-energy effective field theories. I then suggest how the mathematical template for reduction described here might be extended to the relationships between current established theories and quantum gravity.

Commentator: Augustin Baas (University of Geneva)

**Mark Shumelda** *University of Toronto*

**A tale of two Machs: Relationalism in quantum gravity**

In my paper I begin a philosophical analysis of time in the light of two relatively new and very different approaches to quantum gravity: geometrogenesis and shape dynamics. Both claim to be motivated by temporal relationalism. In my analysis I contrast the opposing ways in which geometrogenesis and shape dynamics implement the basic tenets of Machian temporal relationalism. It turns out that far from removing time altogether from the fundamental theory, both geometrogenesis and shape dynamics posit an ontologically robust sense of temporal passage albeit in very different ways. While geometrogenesis retains an absolute time in the form of the Hamiltonian of the fundamental quantum theory, shape dynamics requires one to concede to what amounts to (at least as far as classical general relativity is concerned) a preferred foliation of spacetime. I argue that while each approach has its philosophical merits, neither is able to describe time as a fully emergent concept. Time, it seems, is here to stay in the fundamental theory even given a Machian, relationalist approach to dynamics.

Commentator: James Read (University of Oxford)

**Ward Struyve** *Ludwig Maximilian University of Munich*

**Must space-time be singular?**

According to Einstein’s theory of general relativity space-time singularities such as a big bang typically occur. It is believed that a quantum theory for gravity may eliminate such singularities. Whether this is indeed the case may of course depend on which approach to quantum gravity, for example the Wheeler-DeWitt theory or loop quantum gravity. But it may also depend on the approach to quantum mechanics itself, for example the standard quantum approach, consistent histories or Bohmian mechanics. For the case of mini-superspace models, it has been claimed in the context of standard quantum theory that the Wheeler-DeWitt theory does not eliminate the singularities, while loop quantum gravity does. However, the analysis is plagued by a number of conceptual problems: the measurement problem, the problem of time and the problem of what exactly it means to have a singularity. In my talk, I will explain the Bohmian approach to the Wheeler-DeWitt theory and loop quantum gravity and how this approach solves these conceptual problems. I will show for mini-superspace models that in the Wheeler-DeWitt theory the answer to the question of singularities depends on the wave function and the initial metric, and that in loop quantum gravity there are no singularities.

Commentator: Donald C. Salisbury (Austen College)

**Daniel Sudarsky** *National Autonomous University of Mexico*

**On the recovery of an effective classical space-time from the quantum gravity realm**

The recovery of classical space-time from theories involving some fundamental space-time discreteness, is a highly non-trivial task. Naturally, the space-time metric that would emerge from a generic fundamental theory of space-time, must play its standard role, namely, it should encode the manner in which `free physical objects’ move, without the need to postulate in an add hoc manner, after the `recovery of geometry’ is accomplished, that free particles should follow the geodesics of a space-time metric. It seems natural to seek to associate with physical objects, suitable world lines, that can be taken to represent the `geodesics of the emergent metric’. The program then calls for `reading the effective metric’ from the collection of all such world lines. This will involve associating with any extended matter distributions of a certain scale, a center of mass’s world-line, and using those to extract what one might identify as `the effective space-time geometry at that scale’. It is well known (Papapetrou and Beiglb\”{ock), that even in classical general relativity, extended objects do not follow geodesics. In fact certain properties of the `center of mass’s worldliness’, will generate difficulties in the program to recover what we might call `the classical space-time metric’.

Commentator: Erik Curiel (Ludwig Maximilian University of Munich)

**Antonio Vassallo** *University of Warsaw*

**Grounding as metaphysical causation in spacetime physics**

In recent literature some strong suggestions have been made that metaphysical grounding and standard causation are in fact two species of the same genus relation. The main constitutive difference between the two is just that standard causation is a partial ordering with respect to time, while metaphysical grounding (or, `metaphysical causation’) is a partial ordering with respect to fundamentality. In this talk, I will defend the view that, in the context of spacetime physics, the way spacetime structures are said to `act’ on matter is not causal in a standard sense, but instead is better described in terms of metaphysical grounding. I will show how this framework (i) defuses the main arguments against viewing spatiotemporal properties in general relativity as causal, (ii) accords a straightforward causal character also to the absolute spatiotemporal structures of pre-general relativistic theories without ascribing to them any `one-way’ physical influence on matter, and (iii) helps in accounting for the appearance of classical spacetime structures from a fundamentally a-spatiotemporal reality in quantum gravity.

Commentator: Carina Prunkl (University of Oxford)

**Tiziana Vistarini** *University of Colorado Boulder*

**Modality after quantum gravity**

This presentation develops further the view I pursued in my book, namely, that string theory is background independent. It is widely held into the quantum gravity circles that string theory is background dependent and that for this reason looking for any notion of spacetime emergence in the theory is a non-starter.

In my book I argued that string theory is background independent insofar as it does not posit any fundamental geometry. The theory also admits emergent spacetime (including general relativistic spacetime).

Space and time are emergent in string theory as they are mechanical byproducts of more fundamental dynamics. My book develops this point mainly along two paths. One revising the traditional notion of mechanical explanation, the other arguing that (consistently with that revision) string dynamics mechanically produce the manifest geometry of the world, regardless whether there exists any fundamental geometry.

In this presentation I take a further step. If the string theory lesson about non fundamentality of spacetime is plausible, what should we also conclude about the nature of modality? The question arises because some sort of modal reasoning seems naturally to arise from the topology of possible worlds locally and globally structuring string theory moduli space. By reading into this topology (along with additional tools) we gain the lesson that spacetime geometry is not fundamental. Then, what kind of modal reasoning arises from this topology? In Lewis’s conception of modality spatiotemporal relations are fundamental, whereas modality is not, although conceived as an objective feature of reality.

Here I try to pursue a view which is transversal to Lewis view. I try to argue that modality may not require spatiotemporal relations among worlds. Rather it may only require some specific class of non-metrical, topological relations already presented in my book. Here I show that the kind of `closeness’ among stringy-worlds I posit is stronger than the familiar similarity relation delivered in classical modality. This presentation tries to revise modal reasoning in light of some deformation theory techniques.

Commentator: Keizo Matsubara (University of Illinois at Chicago)