A ‘duality’ is a formal mapping between the spaces of solutions of two empirically equivalent theories. In recent times, dualities have been found to be pervasive in string theory and quantum field theory. Naïvely interpreted, duality-related theories appear to make very different ontological claims about the world—differing in e.g. space-time structure, fundamental ontology, and mereological structure. In light of this, duality-related theories raise questions familiar from discussions of underdetermination in the philosophy of science: in the presence of dual theories, what (...) is one to say about the ontology of the world? In this paper, we undertake a comprehensive and non-technical survey of the landscape of possible ontological interpretations of duality-related theories. We provide a significantly enriched and clarified taxonomy of options—several of which are novel to the literature. (shrink)

We review the dynamical approach to spacetime theories---in particular, its origins in the development of special relativity, its opposition to the contemporary `geometrical' approach, and the manner in which it plays out in general relativity. In addition, we demonstrate that the approach is compatible with the `angle bracket school'.

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.

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)

A common adage runs that, given a theory manifesting symmetries, the syntax of that theory should be modified in order to construct a new theory, from which symmetry-variant structure of the original theory has been excised. Call this strategy for explicating the underlying ontology of symmetry-related models reduction. Recently, Dewar has proposed an alternative to reduction as a means of articulating the ontology of symmetry-related models—what he calls sophistication, in which the semantics of the original theory is modified, and symmetry-related (...) models of that theory are treated as if they are isomorphic. In this paper, we undertake a critical evaluation of sophistication about symmetries—we find the programme underdeveloped in a number of regards. In addition, we clarify the interplay between sophistication about symmetries, and a separate debate to which Dewar has contributed—viz., that between interpretational versus motivational approaches to symmetry transformations. (shrink)

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)

For Knox, ‘spacetime’ is to be defined functionally, as that which picks out a structure of local inertial frames. Assuming that Knox is motivated to construct this functional definition of spacetime on the grounds that it appears to identify that structure which plays theoperationalrole of spacetime—i.e., that structure which is actually surveyed by physical rods and clocks built from matter fields—we identify in this paper important limitations of her approach: these limitations are based upon the fact that there is a (...) gap between inertial frame structure and that which is operationally significant in the above sense. We present five concrete cases in which these two notions come apart, before considering various ways in which Knox’s spacetime functionalism might be amended in light of these issues. (shrink)

We make some remarks on the mathematics and metaphysics of the hole argument, in response to a recent article in this journal by Weatherall ([2018]). Broadly speaking, we defend the mainstream philosophical literature from the claim that correct usage of the mathematics of general relativity `blocks' the argument.

We analyse the possibility that string-theoretic dualities present a genuine case of strong underdetermination of theory by evidence. Drawing on the parallel discussion of the hole argument, we assess the possible interpretations of dualities. We conclude that there exist at least two defensible interpretations on which dualities do not present a worrying case of underdetermination per se.

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)

For Knox, ‘spacetime’ is to be defined functionally, as that which picks out a structure of local inertial frames. Assuming that Knox is motivated to construct this functional definition of spacetime on the grounds that it appears to identify that structure which plays the operational role of spacetime—i.e., that structure which is actually surveyed by physical rods and clocks built from matter fields—we identify in this paper important limitations of her approach: these limitations are based upon the fact that there (...) is a gap between inertial frame structure and that which is operationally significant in the above sense. We present five concrete cases in which these two notions come apart, before considering various ways in which Knox’s spacetime functionalism might be amended in light of these issues. (shrink)

It is now well-known that Newton–Cartan theory is the correct geometrical setting for modelling the quantum Hall effect. In addition, in recent years edge modes for the Newton–Cartan quantum Hall effect have been derived. However, the existence of these edge modes has, as of yet, been derived using only orthodox methodologies involving the breaking of gauge-invariance; it would be preferable to derive the existence of such edge modes in a gauge-invariant manner. In this article, we employ recent work by Donnelly (...) and Freidel in order to accomplish exactly this task. Our results agree with known physics, but afford greater conceptual insight into the existence of these edge modes: in particular, they connect them to subtle aspects of Newton–Cartan geometry and pave the way for further applications of Newton–Cartan theory in condensed matter physics. (shrink)

We discuss what we take to be three possible misconceptions in the foundations of general relativity, relating to: the interpretation of the weak equivalence principle and the relationship between gravity and inertia; the connection between gravitational redshift results and spacetime curvature; and the Einstein equivalence principle and the ability to ``transform away" gravity in local inertial coordinate systems.

Special relativity has been understood by many as vindicating a tenseless conception of time, denying the existence of tensed facts and a fortiori objective temporal passage. The reason for this is straightforward: both passage and the obtaining of tensed facts require a universal knife-edge present moment—yet this structure is not easily reconcilable with the relativity of simultaneity. The above being said, the prospects for tense and passage are sometimes claimed to be improved on moving to cosmological solutions of general relativity. (...) In this paper, we evaluate in detail these arguments, finding that there remain several open questions to be addressed if the introduction of tensed facts into the relativistic context is to be compelling. Moreover, we argue that, even setting aside these issues, objective tense stands and falls in relativity for exactly the same reasons that it does in classical philosophical discussions on the matter. (shrink)

Philosophy Compass, Volume 17, Issue 4, April 2022.

We discuss the status of gravitational radiation in Newtonian theories. In order to do so, we consider various options for interpreting the Poisson equation as encoding propagating solutions, reflect on the extent to which limit considerations from general relativity can shed light on the Poisson equation’s conceptual status, and discuss various senses in which the Poisson equation counts as a dynamical equation.

I draw together some recent literature on the debate between dynamical versus geometrical approaches to spacetime theories, in order to argue that there exist defensible versions of the geometr...

Historically, a great deal of attention has been addressed to the question of what it would take to test experimentally the metrical structure of spacetime. Arguably, however, consideration of this question has been at the expense of comparable investigations into what it would take to test other structural features of spacetime. In this article, we critique and expand substantially upon an article by Hadley (Hadley in Class Quantum Gravity, 19:4565–4571, 2002), which constitutes one of the best-known paper-length studies of what (...) it would take to test the orientability of spacetime. In so doing, we seek to clarify a number of matters which remain unclear in the wake of Hadley’s article, thereby allowing the literature on this topic to progress. More positively, we also present, compare, and evaluate a number of other potential approaches to testing the orientability of spacetime which have arisen in the recent physics literature. (shrink)

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 for the operational meaning of the metric field.

We construct a notion of teleparallelization for Newton-Cartan theory, and show that the teleparallel equivalent of this theory is Newtonian gravity; furthermore, we show that this result is consistent with teleparallelization in general relativity, and can be obtained by null-reducing the teleparallel equivalent of a five-dimensional gravitational wave solution. This work thus strengthens substantially the connections between four theories: Newton-Cartan theory, Newtonian gravitation theory, general relativity, and teleparallel gravity.

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)

It is now well-appreciated by philosophers that contemporary large-scale ‘-omics’ studies in biology stand in non-trivial relationships to more orthodox hypothesis-driven approaches. These relationships have been clarified by Ratti (2015); however, there remains much more to be said regarding how an important field of genomics cited in that work—‘genome-wide association studies’ (GWAS)—fits into this framework. In the present article, we propose a revision to Ratti’s framework more suited to studies such as GWAS. In the process of doing so, we introduce (...) to the philosophical literature novel exploratory experiments in (phospho)proteomics, and demonstrate how these experiments interplay with the above considerations. (shrink)

What, if anything, would be wrong with replacing the light postulate in Einstein’s 1905 formulation of special relativity with a ‘sound postulate’, stating that the speed of sound is independent of the speed of the source? After reviewing the historical reasons underlying the particular focus on light in the special theory, we consider the circumstances under which such a theory of ‘sonic relativity’ would be justified on empirical grounds. We then consider the philosophical upshots of ‘sonic relativity’ for four contemporary (...) areas of investigation in the philosophy of spacetime: global versus subsystem symmetries, dynamical versus geometrical approaches to spacetime, the possibility of a preferred frame in theories of quantum gravity, and spacetime functionalism. (shrink)

The equivalence principle has constituted one of the cornerstones of discussions in the foundations of spacetime theories over the past century. However, up to this point the principle has been considered overwhelmingly only within the context of relativistic physics. In this article, we demonstrate that the principle has much broader, super-theoretic significance: to do so, we present a unified framework for understanding the principle in its various guises, applicable to both relativistic and Newtonian contexts. We thereby deepen significantly our understanding (...) of the role played by the equivalence principle in a broad class of spacetime theories. (shrink)

We explore the significance of physical theories set in Euclidean spacetimes. In particular, we explore the use of these theories in contemporary physics at large, and the sense in which there can be a notion of temporal evolution in these theories. Having achieved these tasks, we proceed to reflect on the lessons that one can take from such theories for Knox’s ‘inertial frame’ version of spacetime functionalism, which seems to issue incorrect verdicts in the case of theories with Euclidean metrical (...) structure. (shrink)

Dualities are a pervasive phenomenon in contemporary physics, in which two physical theories are empirically equivalent, yet prima facie make different ontological claims about the world (potentially very different claims—differing in e.g. the number and radius of dimensions of the universe). Dualities thus present a particular instantiation of the well-known notion of underdetermination of theory by evidence. Many different philosophical proposals have been made for how such putative underdetermination might be resolved—this continues to be a programme of active research.

It is plausible that the models of our scientific theories correspond to possibilities. But exactly which models of which scientific theories stand in this correspondence? The answers to this question hinted at so far in the literature are too restrictive: they don't support the idea that the models of many of our best scientific theories correspond to physical possibilities. The paper thus provides a novel proposal for guiding belief about physical possibilities based on physics. The proposal draws on the notion (...) of an effective theory: a theory that applies very well to a particular, restricted domain. We argue that it is the models of effective theories that we should believe correspond, at least in part, to physical possibilities. It is thus effective theories that should guide modal reasoning in science. (shrink)

A standard line in the contemporary philosophical literature has it that physical theories are equivalent only when they agree on their empirical content, where this empirical content is often understood as being encoded in the equations of motion of those theories. In this article, we question whether it is indeed the case that the empirical content of a theory is exhausted by its equations of motion, showing that (for example) considerations of boundary conditions play a key role in the empirical (...) equivalence (or otherwise) of theories. Having argued for this, we show that philosophical claims made by Weatherall (2016) that electromagnetism in the Faraday tensor formalism is equivalent to electromagnetism in the vector potential formalism, and by Knox (2011) that general relativity is equivalent to teleparallel gravity, can both be called into question. We then show that properly considering the role of boundary conditions in theory structure can potentially restore these claims of equivalence and close with some remarks on the pragmatics of adjudications on theory identity. (shrink)

The paper investigates the status of gravitational energy in Newtonian Gravity, developing upon recent work by Dewar and Weatherall. The latter suggest that gravitational energy is a gauge quantity. This is potentially misleading: its gauge status crucially depends on the spacetime setting one adopts. In line with Møller-Nielsen’s plea for a motivational approach to symmetries, we supplement Dewar and Weatherall’s work by discussing gravitational energy–stress in Newtonian spacetime, Galilean spacetime, Maxwell-Huygens spacetime, and Newton–Cartan Theory. Although we ultimately concur with Dewar (...) and Weatherall that the notion of gravitational energy is problematic in NCT, our analysis goes beyond their work. The absence of an explicit definition of gravitational energy–stress in NCT somewhat detracts from the force of Dewar and Weatherall’s argument. We fill this gap by examining the supposed gauge status of prima facie plausible candidates—NCT analogues of gravitational energy–stress pseudotensors, the Komar mass, and the Bel-Robinson tensor. Our paper further strengthens Dewar and Weatherall’s results. In addition, it sheds more light upon the subtle link between sufficiently rich inertial structure and the definability of gravitational energy in NG. (shrink)

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. (shrink)

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. (shrink)

It is well-known that the conformal structure of a relativistic spacetime is of profound physical and conceptual interest. In this note, we consider the analogous structure for Newtonian theories. We show that the Newtonian Weyl tensor is an invariant of this structure.

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. (shrink)

As a candidate theory of quantum gravity, the popularity of string theory has waxed and waned over the past four decades. One current source of scepticism is that the theory can be used to derive, depending upon the input geometrical assumptions that one makes, a vast range of different quantum field theories, giving rise to the so-called landscape problem. One apparent way to address the landscape problem is to posit the existence of a multiverse; this, however, has in turn drawn (...) heightened attention to questions regarding the empirical testability and predictivity of string theory. We argue first that the landscape problem relies on dubious assumptions and does not motivate a multiverse hypothesis. Nevertheless, we then show that the multiverse hypothesis is scientifically legitimate and could be coupled to string theory for other empirical reasons. Looking at various cosmological approaches, we offer an empirical criterion to assess the scientific status of multiverse hypotheses. (shrink)

Philosophy Compass, Volume 17, Issue 10, October 2022.

We highlight and resolve what we take to be three common misconceptions in general relativity, relating to the interpretation of the weak equivalence principle and the relationship between gravity and inertia; the connection between gravitational redshift results and spacetime curvature; and the strong equivalence principle and the local recovery of special relativity in curved, dynamical spacetime.

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. (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)

It has been remarked that there is a tendency in all Governments to an augmentation of power at the expense of liberty. But the remark as usually understood does not appear to me well founded.... It is a melancholy reflection that liberty should be equally exposed to danger whether the Government have too much or too little power, and that the line which divides the extremes should be so inaccurately drawn by experience. -/- Madison, letter to Jefferson, October 17, 1788.

It has been remarked that there is a tendency in all Governments to an augmentation of power at the expense of liberty. But the remark as usually understood does not appear to me well founded.... It is a melancholy reflection that liberty should be equally exposed to danger whether the Government have too much or too little power, and that the line which divides the extremes should be so inaccurately drawn by experience. Madison, letter to Jefferson, October 17, 1788.

The arts of rule cover the exercise of power by princes and popular sovereigns, but they range beyond the domain of government itself, extending to civil associations, political parties, and religious institutions. Making full use of political philosophy from a range of backgrounds, this festschrift for Harvey Mansfield recognizes that although the arts of rule are comprehensive, the best government is a limited one.