James Read

Realism about general relativity (GR) seems to imply realism about spacetime curvature. The existence of the teleparallel equivalent of general relativity (TEGR) calls this into question, for (a) TEGR is set in a torsionful but flat spacetime, and (b) TEGR is empirically equivalent to GR. Knox (Stud Hist Philos Sci Part B Stud Hist Philos Mod Phys 42(4):264–275, 2011) claims that there is no genuine underdetermination between GR and TEGR; we call this verdict into question by isolating and addressing her individual arguments. In addition, we anticipate and evaluate two further worries for realism about the torsionful spacetimes of TEGR, which we call the ‘problem of operationalisability’ and the ‘problem of visualisability’.

The nodes of the ‘geometric trinity’ are: (i) general relativity (in which grav itational effects are a manifestation of spacetime curvature), (ii) the ‘teleparallel equivalent’ of general relativity (which trades spacetime curvature for torsion), and(iii) the ‘symmetric teleparallel equivalent’ of general relativity (which trades spacetime curvature for non-metricity). Onepopularreformulationof(iii)is‘co incident general relativity’, but this theory has yet to receive any philosophical attention. This article aims both to introduce philosophers to coincident general relativity, and to undertake a detailed assessment of its features.

String field theory is supposed to stand to perturbative string theory as quantum field theory stands to single-particle quantum theory; as such, it purports to offer a substantially more general and powerful perspective on string theory than the perturbative approach. In addition, string field theory has been claimed for several decades to liberate string theory from any fixed, background spatiotemporal commitments—thereby (if true) rendering it ‘background independent’. But is this really so? In this article, we undertake a detailed interrogation of this claim, finding that the verdict is sensitive both to one’s understanding of the notion of background independence, and also to how one understands string field theory itself. Although in the end our verdicts on the question of the background independence are therefore somewhat mixed, we hope that our study will elevate the levels of systematicity and rigour in these discussions, as well as equip philosophers of physics with a helpful introduction to string field theory and the variety of interesting conceptual questions which it raises.

We discuss affinities and differences between (i) the hole argument in general relativity and (ii) Putnam’s model-theoretic argument against metaphysical realism (‘Putnam’s paradox’). Following Pooley (The Reality of Spacetime, University of Oxford, 2002), we maintain that the hole argument is not a special case of Putnam’s paradox. This notwithstanding, both of these arguments have been responded to through meta-linguistic means. While van Fraassen (Philosophical Perspectives 11:17–42, 1997) claims that Putnam’s paradox dissolves due to our inability to identify a function mapping our theories to objects in the world independent of our total language, Bradley and Weatherall (Philosophy of Science 89(5): 1223–1232, 2022) maintain that the language of general relativity does not allow for the hole argument to be formulated. We compare these responses and assess the extent to which either is successful, concluding that we find van Fraassen’s argument more persuasive precisely because of the greater generality of Putnam’s paradox.

Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? This chapter offers a discussion of the sense in which gauge symmetry can be fruitfully applied to constrain the space of possible dynamical models in such a way that forces and charges are appropriately coupled. It reviews the most well-known application of this kind, known as the ‘gauge argument’ or ‘gauge principle’; discusses its difficulties, and then reconstructs the gauge argument as a valid theorem in quantum theory. The chapter then presents what the authors take to be a better and more general gauge argument, based on Noether’s second theorem in classical Lagrangian field theory, and argues that this provides a more appropriate framework for understanding how gauge symmetry helps to constrain the dynamics of physical theories.

We consider the distinction between ‘qualified’ and ‘unqualified’ approaches introduced by Read (2020a) in the context of the dynamical/geometrical debate. We show that one fruitful way in which to understand this distinction is in terms of what one takes the kinematically possible models of a given theory to represent; moreover, we show that the qualified/unqualified distinction is applicable not only to the geometrical approach (which is the case considered by Read (2020a)), but also to the dynamical approach. Finally, having made these points, we connect them to other discussions of representation and of explanation in this corner of the literature.

How to articulate the common ontological commitments of symmetry-related models of physical theories? This is a central (perhaps the central) question in the philosophical literature on symmetry transformations in physics; recently, Dewar (British Journal for the Philosophy of Science, 70, 2019) has proposed a strategy for answering this question which goes by the name of ‘external sophistication’. And yet: this strategy has been accused of being hopelessly obscure by, among others, Martens and Read (Synthese, 199, 2020). In this article, I demonstrate that not all cases of external sophistication are subject to this charge—for reasons which will become clear, the cases for which this is not so give us what I’ll call ‘good VIBES’. Having established this, I then go on to consider good VIBES in the context of the analysis of hidden symmetries, in dialogue with recent work on that topic by Bielińska and Jacobs (2024).

The programme of ‘constructive axiomatics’, promulgated by Hans Reichenbach in 1924, seeks to build up the architecture of our best theories of physics from basic axioms supposedly imbued with immediate and indubitable empirical content. Taking inspiration from Reichenbach, Hermann Weyl proposed his own ‘causal-inertial’ approach to the constructive axiomatisation of Einstein’s general relativity, according to which a relativistic spacetime can be constructed solely from the trajectories of light rays and freely-falling particles; this project, however, came to fruition only in 1972, with the constructive axiomatisation of general relativity due to Ehlers, Pirani, and Schild (‘EPS’).One century since Reichenbach, and fifty years since EPS, this book is a celebration of the constructive axiomatic methodology. It achieves four main tasks. First, it provides a thoroughgoing presentation of the EPS axiomatisation, closing missing loopholes, identifying problematic axioms, and so forth—in this way, one gains a much-improved appreciation of the extent to which a causal-inertial approach to general relativity might succeed, and of what such an approach might offer. Second, it synthesises and assesses the vast but disparate literature on constructive axiomatics which has arisen over the past century and sets the methodology in its proper philosophical context. Third, it generalises the approach to apply to quantum spacetimes. And fourth, it applies the approach to the context of non-relativistic spacetime physics. All in all, the book demonstrates that constructive axiomatics is live-and-kicking; the book will become the go-to resource for this way of philosophising about the nature of space and time.

This Element presents the philosophy of special relativity: from the foundations of the theory in Newtonian mechanics, through its birth out of the ashes of 19th Century ether theory, through the various conceptual paradoxes which the theory presents, and finally arriving at some of its connections with Einstein's later theory of general relativity. It illustrates concepts such as inertial frames, force-free motion, and dynamical versus geometrical understandings of physics, the standard hierarchy of classical spacetimes, the concept of a symmetry of a physical theory, Poincaré invariant, Einstein's 1905 derivation of the Lorentz transformations, spacetime structure from Aristotle to Minkowski, general covariance, dynamical and geometrical approaches to spacetime, the conventionality of simultaneity, Frame-dependent effects, and the twin paradox.

Famously, Adrian Moore has argued that an absolute representation of reality is possible: that it is possible to represent reality from no particular point of view. Moreover, Moore believes that such absolute representations are a desideratum of physics. Recently, however, debates in the philosophy of physics have arisen regarding the apparent impossibility of an absolute representation of certain aspects of nature in light of our current best theories of physics. Throughout this article, we take gravitational energy as a particular case study of an aspect of nature that seemingly does not admit of an absolute representation. There is, therefore, a prima facie tension between Moore’s a priori case on the one hand, and the state-of-play in modern physics on the other. This article overcomes this tension by demonstrating how, when formulated in the correct way, modern physics admits of an absolute representation of gravitational energy after all. In so doing, the article offers a detailed case study of Moore’s argument for absolute representation, clarifying its structure and bringing it into contact with the distinction drawn by philosophers of physics between coordinate-freedom and coordinate-independence, as well as the philosophy of spacetime physics.

Over the past decade, the physics literature on torsionful non-relativistic gravity has burgeoned; more recently, philosophers have also begun to explore this topic. As of yet, however, the connections between the writings of physicists and philosophers on torsionful non-relativistic gravity remain unclear. In this article, we seek to bridge the gap, in particular by situating within the context of the existing physics literature a recent theory of non-relativistic torsionful gravity developed by philosophers Meskhidze and Weatherall (Philos Sci, https://doi.org/10.1017/psa.2023.136, 2023) we also discuss the philosophical significance of that theory.

Canonically, ‘classic’ tests of general relativity (GR) include perihelion precession, the bending of light around stars, and gravitational redshift; ‘modern’ tests have to do with, _inter alia_, relativistic time delay, equivalence principle tests, gravitational lensing, strong field gravity, and gravitational waves. The orthodoxy is that both classic and modern tests of GR afford experimental confirmation of that theory _in particular_. In this article, we question this orthodoxy, by showing there are classes of both relativistic theories (with spatiotemporal geometrical properties different from those of GR) and non-relativistic theories (in which the lightcones of a relativistic spacetime are ‘widened’) which would also pass such tests. Thus, (a) issues of underdetermination in the context of GR loom much larger than one might have thought, and (b) given this, one has to think more carefully about what exactly such tests in fact _are_ testing.

In his paper, ‘Regarding the ‘Hole Argument”, Weatherall suggests that models of general relativity related by a hole diffeomorphism must be regarded as being physically equivalent. At a later stage in the paper, however, he also argues that there is a sense in which two such models may be regarded as being empirically distinct—a fortiori physically distinct. We attempt to delineate the logic behind these two prima facie contradictory claims. We argue that the latter sense rests upon a misunderstanding of the import of shift arguments in the foundations of spacetime theories.

In a recent article, Halvorson and Manchak (Br J Philos Sci, Forthcoming) claim that there is no basis for the Hole Argument, because (in a certain sense) hole isometries are unique. This raises two important questions: (a) does their argument succeed?; (b) how does this formalist response to the Hole Argument relate to other recent responses to the Hole Argument in the same tradition—in particular, that of Weatherall (Br J Philos Sci 69(2):329–350, 2018)? In this article, _ad_ (a), we argue that Halvorson and Manchak’s claim does not go through; _ad_ (b), we argue that although one _prima facie_ plausible reading would see Halvorson and Manchak as filling an important hole (no pun intended) in Weatherall’s argument, in fact this reading is implausible; there is no need to supplement Weatherall’s work with Halvorson and Manchak’s results.

Supposing that one is already familiar with special relativistic physics, what constitutes the best route via which to arrive at the architecture of the general theory of relativity? Although the later Einstein would stress the significance of mathematical and theoretical principles in answering this question, in this article we follow the lead of the earlier Einstein (circa 1916) and stress instead how one can go a long way to arriving at the general theory via inductive and empirical principles, without invoking presumptions concerning the geometrical structure of the final theory. We focus on the construction of the kinematical structure and the terms describing the coupling of matter to gravity. General covariance, understood and employed as a straightforward extrapolation of empirical considerations, is central to our derivation, together with what we dub the `Methodological Equivalence Principle'. We argue that our approach has a number of virtues, both for one's understanding of the general theory of relativity, but also for pedagogy, since it stresses---to the greatest extent possible (a lesson which we inherit from Bell, [1976])---both the methodological precedence of dynamical considerations to interpretative issues and the theoretical continuity between general relativity and its precursors. We conclude by comparing our approach to other philosophical approaches to general relativity and discussing the significance of empirically motivated methodological principles in the philosophy of science.

Recent work in the physics literature demonstrates that, in particular classes of rotating spacetimes, physical light rays in general do not traverse null geodesics. Having presented this result, we discuss its philosophical significance, both for the clock hypothesis (and, in particular, a recent purported proof thereof for light clocks), and for the operational meaning of the metric field. 1Introduction 2Fletcher's Theorem 2.1Maudlin on the clock hypothesis in special relativity 2.2Fletcher’s result in special relativity 2.3Fletcher’s theorem in general relativity 3Electromagnetism and the Geometrical-Optical Limit 3.1Maxwell’s equations in curved spacetime 3.2The geometrical-optical limit 3.3Rotating spacetimes 3.4Aren’t Gödel spacetimes unphysical? 4The Clock Hypothesis and Chronogeometry 4.1Natural and mathematical observations 4.2Clock registry discord 4.3Chronogeometry 5Conclusion.

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.

Geometric underdetermination (i.e., the underdetermination of the geometric properties of space and time) is a live possibility in light of some of our best theories of physics. In response to this, geometric conventionalism offers a selective anti-realism, refusing to assign truth values to variant geometric propositions. Although often regarded as being dead in the water by modern philosophers, in this article we propose to revitalise the programme of geometric conventionalism both on its own terms, and as an attractive response to the above-mentioned live cases of geometric underdetermination. Specifically, we (1) articulate geometrical conventionalism as we conceive it, (2) anticipate various objections to the view, and defend it against those objections, and (3) demonstrate how geometric conventionalism plays out in the context of a wide variety of spacetime theories, both classical and relativistic.