I begin by reviewing some recent work on the status of the geodesic principle in general relativity and the geometrized formulation of Newtonian gravitation. I then turn to the question of whether either of these theories might be said to ``explain'' inertial motion. I argue that there is a sense in which both theories may be understood to explain inertial motion, but that the sense of ``explain'' is rather different from what one might have expected. This sense of explanation is (...) connected with a view of theories---I call it the ``puzzleball view''---on which the foundations of a physical theory are best understood as a network of mutually interdependent principles and assumptions. (shrink)

This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories? How do we judge, objectively, which is the “best” theory? Is there even a unique answer to this question? -/- The goal of the workshop, and of this book, (...) is to contribute to the development of a meta-theory of spacetime theories. Such a meta-theory would reveal insights about specific spacetime theories by distilling their essential similarities and differences, deliver a framework for a class of theories that could be helpful as a blueprint to build other meta-theories, and provide a higher-level viewpoint for judging which theory most accurately describes nature. But rather than drawing a map in broad strokes, the focus is on particularly rich regions in the “space of spacetime theories.” -/- This work will be of interest to physicists, as well as philosophers and historians of science working with or interested in General Relativity and/or Space, Time and Gravitation more generally. (shrink)

I discuss several issues related to "classical" spacetime structure. I review Galilean, Newtonian, and Leibnizian spacetimes, and briefly describe more recent developments. The target audience is undergraduates and early graduate students in philosophy; the presentation avoids mathematical formalism as much as possible.

I critically discuss two dogmas of the “dynamical approach” to spacetime in general relativity, as advanced by Harvey Brown [Physical Relativity Oxford:Oxford University Press] and collaborators. The first dogma is that positing a “spacetime geometry” has no implications for the behavior of matter. The second dogma is that postulating the “Strong Equivalence Principle” suffices to ensure that matter is “adapted” to spacetime geometry. I conclude by discussing “spacetime functionalism”. The discussion is presented in reaction to and sympathy with recent work (...) by James Read [“Explanation, geometry, and conspiracy in relativity theory” Thinking about Spacetime Boston: Birkäuser]. (shrink)

As Harvey Brown emphasizes in his book Physical Relativity, inertial motion in general relativity is best understood as a theorem, and not a postulate. Here I discuss the status of the "conservation condition", which states that the energy-momentum tensor associated with non-interacting matter is covariantly divergence-free, in connection with such theorems. I argue that the conservation condition is best understood as a consequence of the differential equations governing the evolution of matter in general relativity and many other theories. I conclude (...) by discussing what it means to posit a certain spacetime geometry and the relationship between that geometry and the dynamical properties of matter. (shrink)

The status of the geodesic principle in General Relativity has been a topic of some interest in the recent literature on the foundations of spacetime theories. Part of this discussion has focused on the role that a certain energy condition plays in the proof of a theorem due to Bob Geroch and Pong-Soo Jang [“Motion of a Body in General Relativity.” Journal of Mathematical Physics16(1) (1975)] that can be taken to make precise the claim that the geodesic principle is a (...) theorem, rather than a postulate, of General Relativity. In this brief note, I show, by explicit counterexample, that not only is a weaker energy condition than the one Geroch and Jang state insufficient to prove the theorem, but in fact a condition still stronger than the one that they assume is necessary. (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)

In General Relativity (GR), it has been claimed that inertia receives a dynamical explanation. This is in contrast to the situation in other theories, such as Special Relativity, because the geodesic principle of GR can be derived from Einstein’s field equations. The claim can be challenged in different ways, all of which question whether the status of inertia in GR is physically different from its status in previous spacetime theories. In this paper I state the original argument for the claim (...) precisely, discuss the different objections to it and then propose a formulation that avoids the problems the original claim encounters. My conclusion is that one can say meaningfully that inertia is dynamically explained in GR. There are two senses in which the derivation of geodetic motion can be said to provide a (more) dynamical explanation of inertia in GR: it holds for any material test body that is a source of the gravitational field; and it is derivable without assuming inertial structures that are fixed independently of matter. (shrink)

I examine two claims that arise in Brown’s account of inertial motion. Brown claims there is something objectionable about the way in which the motions of free particles in Newtonian theory and special relativity are coordinated. Brown also claims that since a geodesic principle can be derived in Einsteinian gravitation, the objectionable feature is explained away. I argue that there is nothing objectionable about inertia and that while the theorems that motivate Brown’s second claim can be said to figure in (...) a deductive-nomological explanation, their main contribution lies in their explication rather than their explanation of inertial motion. (shrink)

Pessimistic meta-induction is a powerful argument against scientific realism, so one of the major roles for advocates of scientific realism will be trying their best to give a sustained response to this argument. On the other hand, it is also alleged that structural realism is the most plausible form of scientific realism; therefore, the plausibility of scientific realism is threatened unless one is given the explicit form of a structural continuity and minimal structural preservation for all our current theories. This (...) essay aims to present what we call expansive structures, which are the structures that can be reconstructed from geometrized Newtonian gravitation and are capable of expanding into general relativity, explicitly. In this way, pessimistic meta-induction will be undermined. (shrink)

In this article, we explore the heuristic power of the theoretical distinction between framework and interaction theories applied to the case of General Relativity. According to the distinction, theories and theoretical elements can be classified into two different groups, each with clear ontological, epistemic and functional content. Being so, to identify the group to which a theory belongs would suffice to know a priori its prospects and limitations in these areas without going into a detailed technical analysis. We make the (...) exercise here with General Relativity, anticipate its ontological, epistemic and functional content and show afterwords that such expectations are justified in this case, being consistent with formal issues of General Relativity. With this, we attempt to make a case for the use of the distinction as a powerful tool for scientific and philosophical analysis. (shrink)

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.

Many physicists have thought that absolute time became otiose with the introduction of Special Relativity. William Lane Craig disagrees. Craig argues that although relativity is empirically adequate within a domain of application, relativity is literally false and should be supplanted by a Neo-Lorentzian alternative that allows for absolute time. Meanwhile, Craig and co-author James Sinclair have argued that physical cosmology supports the conclusion that physical reality began to exist at a finite time in the past. However, on their view, the (...) beginning of physical reality requires the objective passage of absolute time, so that the beginning of physical reality stands or falls with Craig's Neo-Lorentzian metaphysics. Here, I raise doubts about whether, given Craig's NeoLorentzian metaphysics, physical cosmology could adequately support a beginning of physical reality within the finite past. Craig and Sinclair's conception of the beginning of the universe requires a past boundary to the universe. A past boundary to the universe cannot be directly observed and so must be inferred from the observed matter-energy distribution in conjunction with auxilary hypotheses drawn from a substantive physical theory. Craig's brand of Neo Lorentzianism has not been sufficiently well specified so as to infer either that there is a past boundary or that the boundary is located in the finite past. Consequently, Neo Lorentzianism implicitly introduces a form of skepticism that removes the ability that we might have otherwise had to infer a beginning of the universe. Furthermore, in analyzing traditional big bang models, I develop criteria that Neo-Lorentzians should deploy in thinking about the direction and duration of time in cosmological models generally. For my last task, I apply the same criteria to bounce cosmologies and show that Craig and Sinclair have been wrong to interpret bounce cosmologies as including a beginning of physical reality. (shrink)

I argue that, contrary to folklore, Einstein never really cared for geometrizing the gravitational or the electromagnetic field; indeed, he thought that the very statement that General Relativity geometrizes gravity "is not saying anything at all". Instead, I shall show that Einstein saw the "unification" of inertia and gravity as one of the major achievements of General Relativity. Interestingly, Einstein did not locate this unification in the field equations but in his interpretation of the geodesic equation, the law of motion (...) of test particles. (shrink)

The problem of motion in general relativity is about how exactly the gravitational field equations, the Einstein equations, are related to the equations of motion of material bodies subject to gravitational fields. This article compares two approaches to derive the geodesic motion of matter from the field equations: the ‘T approach’ and the ‘vacuum approach’. The latter approach has been dismissed by philosophers of physics because it apparently represents material bodies by singularities. I argue that a careful interpretation of the (...) approach shows that it does not depend on introducing singularities at all and that it holds at least as much promise as the T approach. (shrink)

This paper looks at the relationship between spacetime functionalism and Harvey Brown’s dynamical relativity. One popular way of reading and extending Brown’s programme in the literature rests on viewing his position as a version of relationism. But a kind of spacetime functionalism extends the project in a different way, by focussing on the account Brown gives of the role of spacetime in relativistic theories. It is then possible to see this as giving a functional account of the concept of spacetime (...) which may be applied to theories that go beyond relativity. This paper explores the way in which both the relationist project and the functionalist project relate to Brown’s work, despite being incompatible. Ultimately, these should not be seen as two conflicting readings of Brown, but two different directions in which to take his project. (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)

We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum spacetimes; the status of singularity theorems; the non-existence of a Newtonian limit; the status of the cosmological constant; and the character of matter fields, including perfect fluids and electromagnetic fields. We conclude with a discussion of what constrains our understanding of physics in different dimensions.

Ruetsche argues that a problem of unitarily inequivalent representations arises in quantum theories with infinitely many degrees of freedom. I provide an algebraic formulation of classical field theories and show that unitarily inequivalent representations arise there as well. I argue that the classical case helps us rule out one possible response to the problem of unitarily inequivalent representations called Hilbert Space Conservatism.

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)

Substantivalists believe that spacetime and its parts are fundamental constituents of reality. Relationalists deny this, claiming that spacetime enjoys only a derivative existence. I begin by describing how the Galilean symmetries of Newtonian physics tell against both Newton's brand of substantivalism and the most obvious relationalist alternative. I then review the obvious substantivalist response to the problem, which is to ditch substantival space for substantival spacetime. The resulting position has many affinities with what are arguably the most natural interpretations of (...) special and general relativity. I move on to consider and reject two recent antisubstantivalist lines of thought. The interim conclusion is that the best argument for relationalism is an appeal to Ockham's razor. However, for this to be successful there must be genuine relationalist theories that share the theoretical virtues of their substantivalist rivals but without the additional ontological commitment. The bulk of the paper is therefore an investigation of various concrete relationalist proposals. I distinguish three options for the relationalist in the face of the success of Galilean invariant physics and trace how these generalise to relativistic physics. One of the options is particularly promising but, since its basic objects end up being spacetime points, this does not help the prospects of relationalism as traditionally conceived. I end with some reflections on the fate of substantivalism in the aftermath of the Hole Argument, concluding that we have as yet to be given good reasons to abandon the natural, substantivalist interpretation of current physics. (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)

A classic problem in general relativity, long studied by both physicists and philosophers of physics, concerns whether the geodesic principle may be derived from other principles of the theory, or must be posited independently. In a recent paper [Geroch & Weatherall, "The Motion of Small Bodies in Space-Time", Comm. Math. Phys. ], Bob Geroch and I have introduced a new approach to this problem, based on a notion we call "tracking". In the present paper, I situate the main results of (...) that paper with respect to two other, related approaches, and then make some preliminary remarks on the interpretational significance of the new approach. My main suggestion is that "tracking" provides the resources for eliminating "point particles"---a problematic notion in general relativity---from the geodesic principle altogether. (shrink)