Debates about the ontological implications of the general theory of relativity have long oscillated between spacetime substantivalism and relationism. I evaluate such debates by claiming that we need a third option, which I refer to as “structural spacetime realism.” Such a tertium quid sides with the relationists in defending the relational nature of the spacetime structure, but joins the substantivalists in arguing that spacetime exists, at least in part, independently of particular physical objects and events, the degree of “independence” being (...) given by the extent to which geometrical laws exist “over and above” physical events exemplifying them. By showing that structural spacetime realism is the natural outcome of a semantic, model-theoretic approach to the nature of scientific theories, I conclude by arguing that the notion of partial isomorphic representation is the most plausible candidate to connect spacetime models with reality. (shrink)

I argue that the best spacetime setting for Newtonian gravitation (NG) is the curved spacetime setting associated with geometrized Newtonian gravitation (GNG). Appreciation of the ‘Newtonian equivalence principle’ leads us to conclude that the gravitational field in NG itself is a gauge quantity, and that the freely falling frames are naturally identified with inertial frames. In this context, the spacetime structure of NG is represented not by the flat neo-Newtonian connection usually made explicit in formulations, but by the sum of (...) the flat connection and the gravitational field. 1 Introduction2 Newtonian Gravity: The Orthodox Approach3 Newtonian Gravity: Additional Symmetries4 Cosmological Considerations5 A Newtonian Equivalence Principle: Inertial Frames in Newtonian Gravitation6 Theory Equivalence?7 Conclusion. (shrink)

It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying Newton’s methods in Principia is neo-Newtonian or Galilean space-time. I argue to the contrary that inertial frames are not needed in Newton’s theory of motion, and that the right space-time structure for Newton’s Principia requires the notion of parallelism of spatial directions at different times and nothing more. Only relative motions are definable in this framework, never absolute (...) ones. (shrink)

I reject Norton and Earman's hole argument that spacetime substantivalism is incompatible with determinism. I reconcile these both technically and philosophically. There is a technical definition of determinism that is not violated by pairs of models of the kind used in the hole argument. And technicalities aside, the basic idea of determinism is not violated if we claim that at most one of the two models represents a possible world. This claim can be justified either by metrical essentialism, or by (...) denying transworld identity for points: I prefer the latter. (shrink)

I describe how relativistic field theory generalizes the paradigm property of material systems, the possession of mass, to the requirement that they have a mass–energy–momentum density tensor T µ associated with them. I argue that T µ does not represent an intrinsic property of matter. For it will become evident that the definition of T µ depends on the metric field g µ in a variety of ways. Accordingly, since g µ represents the geometry of spacetime itself, the properties of (...) mass, stress, energy, and momentum should not be seen as intrinsic properties of matter, but as relational properties that material systems have only in virtue of their relation to spacetime structure. (shrink)

Intuitively, a classical field theory is background-in- dependent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion. Background-independence is not a not formal property of theories: the question whether a theory is background-independent depends upon how the theory is interpreted. Under the approach proposed here, a theory is fully background-independent relative to an interpretation (...) if each physical possibility corresponds to a distinct spacetime geometry; and it falls short of full background-independence to the extent that this condition fails. (shrink)

This paper sketches a taxonomy of forms of substantivalism and relationism concerning space and time, and of the traditional arguments for these positions. Several natural sorts of relationism are able to account for Newton's bucket experiment. Conversely, appropriately constructed substantivalism can survive Leibniz's critique, a fact which has been obscured by the conflation of two of Leibniz's arguments. The form of relationism appropriate to the Special Theory of Relativity is also able to evade the problems raised by Field. I survey (...) the effect of the General Theory of Relativity and of plenism on these considerations. (shrink)

Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument from Einstein, we show that spacetime substantivalists are committed to very many more distinct physical states than these theories' equations can determine, even with the most extensive boundary conditions.

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)

I discuss the relationship between different versions of the equivalence principle in general relativity, among them Einstein's equivalence principle, the weak equivalence principle, and the strong equivalence principle. I show that Einstein's version of the equivalence principle is intimately linked to his idea that in GR gravity and inertia are unified to a single field, quite like the electric and magnetic field had been unified in special relativistic electrodynamics. At the same time, what is now often called the strong equivalence (...) principle, related to the local validity of special relativity, can also be found in Einstein's writings, albeit by a different name and clearly separated from what he calls the equivalence principle. I discuss both the development of Einstein's thoughts on the different versions of the equivalence principle, their relationship to the relativity principle, as well as later reflections and variants proposed. (shrink)

By mass-energy equivalence, the gravitational field has a relativistic mass density proportional to its energy density. I seek to better understand this mass of the gravitational field by asking whether it plays three traditional roles of mass: the role in conservation of mass, the inertial role, and the role as source for gravitation. The difficult case of general relativity is compared to the more straightforward cases of Newtonian gravity and electromagnetism by way of gravitoelectromagnetism, an intermediate theory of gravity that (...) resembles electromagnetism. (shrink)

In the following paper, I review and critically assess the four standard routes commonly taken to establish that gravitational waves possess energy-momentum: the increase in kinetic energy a GW confers on a ring of test particles, Bondi/Feynman’s Sticky Bead Argument of a GW heating up a detector, nonlinearities within perturbation theory, taken to reflect the fact that gravity contributes to its own source, and the Noether Theorems, linking symmetries and conserved quantities. Each argument is found to either to presuppose controversial (...) assumptions or to be outright spurious. I finally examine the standard interpretation of binary systems, according to which orbital decay is explained in terms of the system’s energy being via GW energy- momentum transport. I contend that a better interpretation, drawing only on the general-relativistic Equations of Motions and the Einstein Equations, is available - and in fact preferable; thereby also an inference to the best explanation for the vindication of GW energy-momentum is blocked. (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.

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)

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)

Using the example of classical electrodynamics, I argue that the concept of fields as mediators of particle interactions is fundamentally flawed and reflects a misguided attempt to retrieve Newtonian concepts in relativistic theories. This leads to various physical and metaphysical problems that are discussed in detail. In particular, I emphasize that physics has not found a satisfying solution to the self-interaction problem in the context of the classical field theory. To demonstrate the superiority of a pure particle ontology, I defend (...) the direct interaction theory of Wheeler and Feynman against recent criticism and argue that it provides the most cogent formulation of classical electrodynamics. (shrink)

Recent decades have seen a revived interest in super-substantivalism, the idea that spacetime is the only fundamental substance and matter some kind of aspect, property or consequence of spacetime structure. However, the metaphysical debate so far has misidentified a particular variant of super-substantivalism with the position per se. I distinguish between a super-substantival core commitment and different ways of fleshing it out. I then investigate how general relativity and alternative spacetime theories square with the different variants of super-substantivalism.

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)

I argue that Norton & Earman's hole argument, despite its historical association with General Relativity, turns upon very general features of any linguistic system that can represent substances by names. After exploring various means by which mathematical objects can be interpreted as representing physical possibilities, I suggest that a form of essentialism can solve the hole dilemma without abandoning either determinism or substantivalism. Finally, I identify the basic tenets of such an essentialism in Newton's writings and consider how they can (...) be updated to apply to the case provided by General Relativity. (shrink)

The story of Einstein's struggle to create a general theory of relativity, and his early discontentment with the final form of the theory , is well known in broad outline. Thanks to the work of John Norton and others, much of the fine detail of the story is also now known. One aspect of Einstein's work in this period has, however, been relatively neglected: Einstein's commitment to Mach's ideas on inertia, and the influence this commitment had on Einstein's work on (...) general relativity from 1907 to 1918. In this paper published writings and archival material are examined, to try to reconstruct the details of Einstein's thinking about inertia and gravitation, and the role that Mach's ideas played in Einstein's crucial work on the general theory. By the end, a clear picture of Einstein's conceptions of Mach's ideas on inertia, and their philosophical motivations, will emerge. Several surprising conclusions also emerge: Einstein's desire for a Machian gravitation theory was the central force driving his work from 1912 to 1915, keeping him going despite numerous frustrating setbacks; Einstein's continued commitment to Mach's ideas in 1916–1917 kept him at work trying various strategies of modification of the field equations, in order to exclude anti-Machian solutions ; and as late as early 1918, Einstein was ready to call the whole General Theory a failure if no way of squaring it with Mach's ideas on inertia could be found. But by 1920 Einstein advocated a view that granted spacetime independent existence with physical qualities of its own, a complete break with his earlier Machian views. (shrink)

Utilizing Einstein’s comparison of General Relativity and Descartes’ physics, this investigation explores the alleged conventionalism that pervades the ontology of substantival and relationist conceptions of spacetime. Although previously discussed, namely by Rynasiewicz and Hoefer, it will be argued that the close similarities between General Relativity and Cartesian physics have not been adequately treated in the literature—and that the disclosure of these similarities bolsters the case for a conventionalist interpretation of spacetime ontology.

A certain argument has been given in the literature to the effect that generalism (the view that all facts about all possible worlds can (in principle) be given in general terms, that is, without resorting to nonqualitative thisnesses) excludes transworld identitism (the view that there are numerical identities through possible worlds). It follows from this argument, among other things, that transworld identitism entails Scotistic haecceitism (acceptance of nonqualitative thisnesses), and that generalists subscribing to de reism (the view that there are (...) true modal statements de re) are committed to counterpartism (the view that sameness through worlds is not numerical identity). The purpose of this paper is to resist the argument in question by constructing generalist transworld identitism, that is, by providing an account involving identities through possible worlds, without resorting to nonqualitative thisnesses. (shrink)

This paper outlines a new interpretation of an argument of Kant's for the existence of absolute space. The Kant argument, found in a 1768 essay on topology, argues for the existence of Newtonian-Euclidean absolute space on the basis of the existence of incongruous counterparts (such as a left and a right hand, or any asymmetrical object and its mirror-image). The clear, intrinsic difference between a left hand and a right hand, Kant claimed, cannot be understood on a relational view of (...) space - for in terms of the spatial relations of their parts, there is no difference to be found. Kant's argument has been interpreted by, among others, Graham Nerlich (in 1973, Hands, Knees and Absolute Space, The Journal of Philosophy). I briefly discuss Nerlich, and then offer a different reconstruction of the argument, one that appears to be closer to Kant's text. The reconstruction, however, essentially involves ascription of primitive identity to parts of space. Comparing the Kantian absolutist account of incongruous counterparts using primitive identity to the correct relationist account, I conclude that the absolutist account pays a heavy metaphysical price, without buying any genuine explanatory advantage over the relationist. I go on to examine recent suggestions that parity-non-conservation phenomena in quantum physics allow a stronger version of Kant's challenge to relationism. On closer examination, it turns out that here too the absolutist or substantivalist must be appealing to space parts with primitive identity in order to claim an advantage over relationists; and here too, I argue the substantivalist story really has no advantage over the correct relationist account. (shrink)

We consider the motion of small bodies in general relativity. The key result captures a sense in which such bodies follow timelike geodesics. This result clarifies the relationship between approaches that model such bodies as distributions supported on a curve, and those that employ smooth fields supported in small neighborhoods of a curve. This result also applies to "bodies" constructed from wave packets of Maxwell or Klein-Gordon fields. There follows a simple and precise formulation of the optical limit for Maxwell (...) fields. (shrink)