Coordinate-based approaches to physical theories remain standard in mainstream physics but are largely eschewed in foundational discussion in favour of coordinate-free differential-geometric approaches. I defend the conceptual and mathematical legitimacy of the coordinate-based approach for foundational work. In doing so, I provide an account of the Kleinian conception of geometry as a theory of invariance under symmetry groups; I argue that this conception continues to play a very substantial role in contemporary mathematical physics and indeed that supposedly ``coordinate-free'' differential geometry (...) relies centrally on this conception of geometry. I discuss some foundational and pedagogical advantages of the coordinate-based formulation and briefly connect it to some remarks of Norton on the historical development of geometry in physics during the establishment of the general theory of relativity. (shrink)

Background independence begins life as an informal property that a physical theory might have, often glossed as 'doesn't posit a fixed spacetime background'. Interest in trying to offer a precise account of background independence has been sparked by the pronouncements of several theorists working on quantum gravity that background independence embodies in some sense an essential discovery of the General Theory of Relativity, and a feature we should strive to carry forward to future physical theories. This paper has two goals. (...) The first is to investigate what a world must be like in order to be truly described by a background independent theory given extant accounts of background independence. The second is to argue that there are no non-empirical reasons to be more confident in theories that satisfy extant accounts of background independence than in theories that don't. The paper concludes by drawing a general moral about a way in which focussing primarily on mathematical formulations of our physical theories can adversely affect debates in the metaphysics of physics. (shrink)

It has been claimed, recently, that the fact that all the non-gravitational fields are locally Poincaré invariant and that these invariances coincide, in a certain regime, with the symmetries of the spacetime metric is miraculous in general relativity. In this paper I show that, in the context of GR, it is possible to account for these so-called miracles of relativity. The way to do so involves integrating the realisation that the gravitational field equations impose constraints on the behaviour of matter (...) in a novel interpretation of the equivalence principle, which dictates the determination of local inertial frames through gravitational interaction. This proposed explanation of the miracles can also deal with the problematic cases for attempts at explaining them in the context of the standard geometrical perspective on relativity theory. (shrink)

This paper engages with the following closely related questions that have recently received some attention in the literature: what is the status of the equivalence principle in general relativity?; how does the metric field obtain its property of being able to act as a metric?; and is the metric of GR derivative on the dynamics of the matter fields? The paper attempts to complement these debates by studying the spin-2 approach to gravity. In particular, the paper argues that three lessons (...) can be drawn from the spin-2 approach: different from what is sometimes claimed in the literature, central aspects of the non-linear theory of GR are already derivable in classical spin-2 theory; in particular, ‘universal coupling’ can be considered a derived ‘theorem’ in both the classical and the quantum spin-2 approach; this provides new insights for the investigation of the equivalence principle; the ‘second miracle’ that Read et al. argue characterises GR is explained in the classical as well as in the quantum version of the spin-2 approach; the spin-2 approach allows for an ontological reduction of the metrical part of spacetime to the dynamics of matter fields. (shrink)

We approach the physics of \emph{minimal coupling} in general relativity, demonstrating that in certain circumstances this leads to violations of the \emph{strong equivalence principle}, which states that, in general relativity, the dynamical laws of special relativity can be recovered at a point. We then assess the consequences of this result for the \emph{dynamical perspective on relativity}, finding that potential difficulties presented by such apparent violations of the strong equivalence principle can be overcome. Next, we draw upon our discussion of the (...) dynamical perspective in order to make explicit two `miracles' in the foundations of relativity theory. We close by arguing that the above results afford us insights into the nature of special relativity, and its relation to general relativity. (shrink)

In a recent article in this journal, Sus purports to account for what have been identified as the ‘two miracles’ of general relativity—that (1) the local symmetries of all dynamical equations for matter fields coincide, and (2) the symmetries of the dynamical equations governing matter fields coincide locally with the symmetries of the metric field—by application of the familiar result that every symmetry of the action is also a symmetry of the resulting equations of motion. In this reply, we argue (...) that, while otherwise exemplary in its clarity, Sus’ paper fails in this regard, for it rests upon a illegitimate application of the aforementioned result. Thus, we conclude, pace Sus, that these two miracles persist in general relativity. (shrink)

There exists a common view that for theories related by a ‘duality’, dual models typically may be taken ab initio to represent the same physical state of affairs, i.e. to correspond to the same possible world. We question this view, by drawing a parallel with the distinction between ‘interpretational’ and ‘motivational’ approaches to symmetries.

Does the gravitational field described in general relativity possess genuine stress-energy? We answer this question in the affirmative, in a weak sense applicable in a certain class of frames of a certain class of models of the theory, and arguably also in a strong sense, applicable in all frames of all models of the theory. In addition, we argue that one can be a realist about gravitational stress-energy in general relativity even if one is a relationist about spacetime ontology. In (...) each case, our reasoning rests upon a functionalist approach to the definition of physical quantities. (shrink)

Consensus in the contemporary philosophical literature has it that conserved quantity theories of causation such as that of Dowe [2000]—according to which causation is to be analysed in terms of the exchange of conserved quantities (e.g., energy)—face damning problems when confronted with contemporary physics, where the notion of conservation becomes delicate. In particular, in general relativity it is often claimed that there simply are no conservation laws for (say) total-stress energy. If this claim is correct, it is difficult to see (...) how conserved quantity theories of causation could survive. In this article, we resist the above consensus and defend conserved quantity theories from this conclusion, at least when focusing on the apparent problems posed by general relativity. We argue that this approach to causation can continue to be defended in general relativity, once one appreciates (a) the availability of approximate symmetries in generic general relativistic spacetimes, and (b) the role of modelling and idealisation in that theory. Given these points, conserved quantity theories of causation must stand or fall on other grounds. (shrink)

In the recent philosophical literature, several counterexamples to the interpretative principle that symmetry-related models are physically equivalent have been suggested The Oxford handbook of philosophy of physics, Oxford University Press, Oxford, 2013, Noûs 52:946–981, 2018; Fletcher in Found Phys 50:228–249, 2020). Arguments based on these counterexamples can be understood as arguments from scientific practice of roughly the following form: because in scientific practice such-and-such symmetry-related models are treated as representing distinct physical situations, these models indeed represent distinct physical situations. In (...) this paper, a strategy for analysing arguments of this type is presented and applied to the examples that can be found in the literature. I argue that if we are exclusively interested in models understood as representing entire possible worlds, arguments from scientific practice should involve some additional assumptions to guarantee they are relevant for models understood in this way. However, none of the examples presented in the literature satisfy all these additional assumptions, which leads to the conclusion that arguments from scientific practice based on these examples do not undermine the interpretative principle that different symmetry-related models represent the same possible world. (shrink)

The present paper revisits the debate between realists about gravitational energy in GR and anti-realists/eliminativists. I re-assess the arguments underpinning Hoefer’s seminal eliminativist stance, and those of their realist detractors’ responses. A more circumspect reading of the former is proffered that discloses where the so far not fully appreciated, real challenges lie for realism about gravitational energy. I subsequently turn to Lam and Read’s recent proposals for such a realism. Their arguments are critically examined. Special attention is devoted to the (...) adequacy of Read’s appeals to functionalism, imported from the philosophy of mind. (shrink)

There are well-known problems associated with the idea of gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian gravitation. We show that there is a natural candidate for the energy density of a Newtonian gravitational field. But we observe that this quantity is gauge dependent, and that it cannot be defined in the geometrized theory without introducing further structure. We then address a potential response by showing that (...) there is an analogue to the Weyl tensor in geometrized Newtonian gravitation. (shrink)

This is an essay about general covariance, and what it says about spacetime structure. After outlining a version of the dynamical approach to spacetime theories, and how it struggles to deal with generally covariant theories, I argue that we should think about the symmetry structure of spacetime rather differently in generally-covariant theories compared to non-generally-covariant theories: namely, as a form of internal rather than external symmetry structure.

We advocate an account of dualities between physical theories: the basic idea is that dual theories are isomorphic representations of a common core. We defend and illustrate this account, which we call a Schema, in relation to symmetries. Overall, the account meshes well with standard treatments of symmetries. But the distinction between the common core and the dual theories prompts a distinction between three kinds of symmetry: which we call ‘stipulated’, ‘accidental’ and ‘proper’.

In this paper I develop a framework for relating dualities and emergence: two notions that are close to each other but also exclude one another. I adopt the conception of duality as 'isomorphism', from the physics literature, cashing it out in terms of three conditions. These three conditions prompt two conceptually different ways in which a duality can be modified to make room for emergence; and I argue that this exhausts the possibilities for combining dualities and emergence. I apply this (...) framework to gauge/gravity dualities, considering in detail three examples: AdS/CFT, Verlinde's scheme, and black holes. My main point about gauge/gravity dualities is that the theories involved, qua theories of gravity, must be background-independent. I distinguish two senses of background-independence: minimalistic and extended. I argue that the former is sufficiently strong to allow for a consistent theory of quantum gravity; and that AdS/CFT is background-independent on this account; while Verlinde's scheme best fits the extended sense of background-independence. I argue that this extended sense should be applied with some caution: on pain of throwing the baby out with the bath-water. Nevertheless, it is an interesting and potentially fruitful heuristic principle for quantum gravity theory construction. It suggests some directions for possible generalisations of gauge/gravity dualities. The interpretation of dualities is discussed; and the so-called 'internal' vs. 'external' viewpoints are articulated in terms of: epistemic and metaphysical commitments; parts vs. wholes. I then analyse the emergence of gravity in gauge/gravity dualities in terms of the two available conceptualisations of emergence; and I show how emergence in AdS/CFT and in Verlinde's scenario differ from each other. Finally, I give a novel derivation of the Bekenstein-Hawking black hole entropy formula based on Verlinde's scheme; the derivation sheds light on several aspects of Verlinde's scheme and how it compares to Bekenstein's original calculation. (shrink)

In times of crisis, when current theories are revealed as inadequate to task, and new physics is thought to be required—physics turns to re-evaluate its principles, and to seek new ones. This paper explores the various types, and roles of principles that feature in the problem of quantum gravity as a current crisis in physics. I illustrate the diversity of the principles being appealed to, and show that principles serve in a variety of roles in all stages of the crisis, (...) including in motivating the need for a new theory, and defining what this theory should be like. In particular, I consider: the generalised correspondence principle, UV-completion, background independence, and the holographic principle. I also explore how the current crisis fits with Friedman’s view on the roles of principles in revolutionary theory-change, finding that while many key aspects of this view are not represented in quantum gravity, the view could potentially offer a useful diagnostic, and prescriptive strategy. This paper is intended to be relatively non-technical, and to bring some of the philosophical issues from the search for quantum gravity to a more general philosophical audience interested in the roles of principles in scientific theory-change. (shrink)

The philosophy of physics literature contains conflicting claims on the heuristic significance of general covariance. Some authors maintain that Einstein's general relativity distinguishes itself from other theories in that it must be generally covariant, for example, while others argue that general covariance is a physically vacuous and trivial requirement applicable to virtually any theory. Moreover, when general covariance is invested with heuristic significance, that significance as a rule is assigned to so-called “active” general covariance, underwritten by the principle of background (...) independence, rather than to general covriance as Einstein understood it. While agreeing with the latter group of commentators that general covariance indeed carries heuristic significance, I argue that a background independent theory need not be generally covariant and that instead the Principle of Equivalence as Einstein understood it provides the key to understanding the heuristic power of general covariance as a “mathematical sieve” for determining the gravitational field law. However, heuristic significance accrues to general covariance only indirectly, by its encompassing the relativity of frames underwritten by Einstein's principle of equivalence. (shrink)

The word “effective” has become the standard label attached to scientific theories these days. An effective theory allows us to make accurate predictions about a physical system at a certain (energy, length) scale while being largely ignorant of the details at more fundamental levels. One does not need to know anything about the deeper, quantum structure of water molecules to describe the macroscopic behaviour of waves or water in a glass. Although effective descriptions so broadly construed have been part of (...) research in physics since the earliest stages of modern science, it is particle physics that has most clearly relied on and brought to the fore some of the most interesting and admittedly puzzling aspects of this way of looking at theories. Indeed, the effective field theory (EFT) program in QFT has established itself as the most natural way to understand renormalisation and dissipate initial reservations about the status of these techniques by treating higher-order processes as contributions suppressed at lower energy scales. QFT is thus treated as the “effective” framework par excellence with the decoupling of scales constituting its permeating tenet. The goal of this project is to attempt a philosophical appraisal of EFTs as currently used in high energy physics as well as assess the possibility that the whole program eventually breaks down, i.e. fails to apply when certain preconditions do not hold. Accordingly, the dissertation is logically divided into two parts with the first two chapters dedicated to discussion of the relation between EFTs and traditional questions in the philosophy of science concerning the structure of scientific theories, the formulation and defence of scientific realism as well as its connection to possible ontological readings of EFTs. The second part constitutes an analysis of two well-known problems that have been accorded the status of crises in the physics literature: the hierarchy problem and the cosmological constant problem. Our main focus will be to uncover those assumptions responsible for undermining the validity of the EFT techniques in their respective context. In light of this analysis, we will ultimately lean towards a more cautionary or “reserved” approach to EFTs. (shrink)

I discuss the debate between dynamical versus geometrical approaches to spacetime theories, in the context of both special and general relativity, arguing that the debate takes a substantially different form in the two cases; different versions of the geometrical approach—only some of which are viable—should be distinguished; in general relativity, there is no difference between the most viable version of the geometrical approach and the dynamical approach. In addition, I demonstrate that what have previously been dubbed two ‘miracles’ of general (...) relativity admit of no resolution from within general relativity, on either the dynamical or ‘qualified’ geometrical approaches, modulo some possible hints that the second ‘miracle’ may be resolved by appeal to recent results regarding the ‘geodesic principle’ in GR. (shrink)

We analyse the various conceptual notions that go under the umbrella “relationalism/substantivalism”. Our focus will be on evaluating the ontological status of spacetime in General Relativity. To this end we systematically develop the ontological framework that implicitly underlies the traditional debate and common understanding of physics. We submit that spacetime with its chronogeometric and inertial structure, represented by the triple of the bare manifold, the metric and the affine structure, is best construed as the totality of possible and actual spatiotemporal (...) relations of events. This can explain the non-fundamentality of general relativistic gravitational energy and suggests a non-causal, non-interactional understanding of the interdependence of matter in spacetime in GR. (shrink)