All physical theories, from classical Newtonian mechanics to relativistic quantum field theory, entail propositions concerning the geometric structure of spacetime. To give an example, the general theory of relativity entails that spacetime is curved, smooth, and four-dimensional. In this dissertation, I take the structural commitments of our theories seriously and ask: how is such structure instantiated in the physical world? Mathematically, a property like 'being curved' is perfectly well-defined insofar as we know what it means for a mathematical space to (...) be curved. But what could it mean to say that the physical world is curved? Call this the problem of physical geometry. The problem of physical geometry is a plea for foundations--a request for fundamental truth conditions for physical-geometric propositions. My chief claim is that only a substantival theory of spacetime--a theory according to which spacetime is an entity in its own right, existing over and above the material content of the world--can supply the necessary truth conditions. (shrink)

ABSTRACT It has recently been argued that Harvey Brown and Oliver Pooley’s ‘dynamical approach’ to special relativity should be understood as what might be called an ontologically and ideologically relationalist approach to Minkowski geometry, according to which Minkowski geometrical structure supervenes upon the symmetries of the best-systems dynamical laws for a material world with primitive topological or differentiable structure. Fleshing out the details of some such primitive structure, and a conception of laws according to which Minkowski geometry could so supervene, (...) has been referred to by some as the ‘constructivist project’. Here, it is explained that Nick Huggett’s work on ‘regularity relationalism’ provides a framework for such an approach, and a relativistic version of Huggett’s regularity relationalism is outlined for that purpose. Finally, by way of examples, it is shown that this approach fails in the simplest cases. Still, reasons are given for which this should not necessarily discourage an advocate of this interpretation of the dynamical approach. 1 Introduction to the Dynamical Approach 2 Huggett’s Regularity Relationalism 3 The Dynamical Approach as a Form of Regularity Relationalism 4 A Simple Way to Set the Stage 5 A First Attempt 5.1 Complex-valued planewave solutions 5.2 Real-valued planewave solutions 6 More General Solutions 7 Summary and Reflections. (shrink)

This essay explores the use of platonist and nominalist concepts, derived from the philosophy of mathematics and metaphysics, as a means of elucidating the debate on spacetime ontology and the spatial structures endorsed by scientific realists. Although the disputes associated with platonism and nominalism often mirror the complexities involved with substantivalism and relationism, it will be argued that a more refined three-part distinction among platonist/nominalist categories can nonetheless provide unique insights into the core assumptions that underlie spatial ontologies, but it (...) also assists in critiquing alternative uses of nominalism, platonism, and both ontic and epistemic structural realism. (shrink)

This paper explores various metaphysical aspects of Leibniz’s concepts of space, motion, and matter, with the intention of demonstrating how the distinctive role of force in Leibnizian physics can be used to develop a theory of relational motion using privileged reference frames. Although numerous problems will remain for a consistent Leibnizian relationist account, the version developed within our investigation will advance the work of previous commentators by more accurately reflecting the specific details of Leibniz’s own natural philosophy, especially his handling (...) of the dynamical interactions of plenum bodies. (shrink)

Sklar ([1974]) claimed that relationalism about ontology-the doctrine that space and time do not exist-is compatible with Newtonian mechanics. To defend this claim he sketched a relationalist interpretation of Newtonian mechanics. In his interpretation, absolute acceleration is a fundamental, intrinsic property of material bodies; that a body undergoes absolute acceleration does not entail that space and time exist. But Sklar left his proposal as just a sketch; his defense of relationalism succeeds only if the sketch can be filled in. I (...) argue that this cannot be done. There can be no (relationalist) dynamical laws of motion based on Sklar's proposal that capture the content of Newton's theory. So relationalists must look elsewhere for a relationalist interpretation of Newtonian mechanics. (shrink)

This paper considers the implications for the relational-substantival debate of observations of parity nonconservation in weak interactions, a much neglected topic. It is argued that 'geometric proofs' of absolute space, first proposed by Kant (1768), fail, but that parity violating laws allow 'mechanical proofs', like Newton's laws. Parity violating laws are explained and arguments analogous to those of Newton's Scholium are constructed to show that they require absolute spacetime structure--namely, an orientation--as Newtonian mechanics requires affine structure. Finally, it is considered (...) how standard relationist responses to Newton's argument might respond to the new challenge of parity nonconservation. (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)

I argue that there is natural relationist interpretation of Newtonian and relativistic non-quantum physics. Although relationist, this interpretation does not fall prey to the traditional objections based on the existence of inertial effects.

ABSTRACT I explore the viability of a Galilean relational theory of space-time—a theory that includes a three-place collinearity relation among its stock of basic relations. Two formal results are established. First, I prove the existence of a class of dynamically possible models of Newtonian mechanics in which collinearity is uninstantiated. Second, I prove that the dynamical properties of Newtonian systems fail to supervene on their Galilean relations. On the basis of these two results, I argue that Galilean relational space-time is (...) too weak of a structure to support a relational interpretation of classical mechanics. 1.Introduction 2.Completeness 3.Leibnizian Relationalism 4.Galilean Relationalism 5.Inverse-Cube Force Laws 5.1Warm-up 5.2Model 1: Zero angular momentum 5.3Model 2: Non-zero angular momentum 6.Supervenience 7.Incompleteness 8.Conclusion. (shrink)

I will discuss only one of the several entwined strands of the philosophy of space and time, the question of the relation between the nature of motion and the geometrical structure of the world.1 This topic has many of the virtues of the best philosophy of science. It is of long-standing philosophical interest and has a rich history of connections to problems of physics. It has loomed large in discussions of space and time among contemporary philosophers of science. Furthermore, there (...) is, I think, widespread agreement that recent insights here have lead to a genuine deepening of our understanding. (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)

This paper has two goals. (i) I explore the limits of the mathematical theory of spacetime (more generally, differential geometry) as an analytical tool for interpreting early modern thought. While it dramatically clarifies some issues, it can also lead to misunderstandings of some figures, and is a very poor tool indeed for others - Leibniz in particular. (ii) I will show how to blunt a very influential argument against a relational conception of spacetime - the view that the properties and (...) relations of bodies exhaust the spatiotemporal. (shrink)

Julian Barbour's approach to dynamics is reviewed. With a particular focus on questions of explanation and confirmation, the approach is contrasted with standard formulations of dynamics. This paper expands upon my commentary on Lawrence Sklar's paper at the Philosophy of Time Society meeting at the APA's Central Division meeting in Chicago, April 2004. Although a commentary, the current paper is comprehensible without reference to Sklar's paper.