Online research in philosophy

We are used to talking about the “structure” posited by a given theory of physics. We say that relativity is a theory about spacetime structure. Special relativity posits one spacetime structure; different models of general relativity posit different spacetime structures. We also talk of the “existence” of these structures. Special relativity says the world’s spacetime structure is Minkowskian: it posits that this spacetime structure exists. Understanding structure in this sense seems important for understanding what physics is telling us about the world. But it is not immediately obvious just what this structure is, or what we mean by the existence of one structure, rather than another. The idea of mathematical structure is relatively straightforward. There is geometric structure, topological structure, algebraic structure, and so forth. Mathematical structure tells us how abstract mathematical objects t together to form different types of mathematical spaces. Insofar as we understand mathematical objects, we can understand mathematical structure. Of course, what to say about the nature of mathematical objects isn’t easy. But there seems to be no further problem for understanding mathematical structure. Modern theories of physics are formulated in terms of these mathematical structures. In order to understand “structure” as used in physics, then, it seems we must simply look at the structure of the mathematics that is used to state the physics. But it is not that simple. Physics is supposed to be telling us about the nature of the world. If our physical theories are formulated in mathematical language, using mathematical objects, then this mathematics is somehow telling us about the physical make-up of the world. What is..

This essay considers the prospects of modeling spacetime as a phenomenon that emerges in the low-energy limit of a quantum liquid. It evaluates three examples of spacetime analogues in condensed matter systems that have appeared in the recent physics literature, indicating the extent to which they are viable, and considers what they suggest about the nature of spacetime.

This paper offers an alternative view of spacetime different from both substantivalism and relationism. Using basic ideas underlying the fiber bundle formulation of field theories, it illustrates the function of spacetime in individuating local fields. As the system of numerical identities for entities that we can individually refer to, spacetime is an intrinsic, indispensable, and inalienable structure of the physical world with distinct entities.

How do we learn about the nature of the world from the mathematical formulation of a physical theory? One rule we follow, familiar from spacetime theorizing: posit the least amount of spacetime structure required by the fundamental dynamical laws. I think that we should extend this rule beyond spacetime structure. We should extend the rule to statespace structure. Using this rule, I argue that a classical mechanical world has a surprisingly spare amount of structure.

This dissertation concerns the nature of spacetime. It is divided into two parts. The first part, which comprises chapters 1, 2, and 3, addresses ontological questions: does spacetime exist? And if so, are there any other spatiotemporal things? In chapter 1 I argue that spacetime does exist, and in chapter 2 I respond to modal arguments against this view. In chapter 3 I examine and defend supersubstantivalism—the claim that all concrete physical objects (tables, chairs, electrons and quarks) are regions of spacetime. Four-dimensional spacetime, we are often told, ‘unifies’ space and time; if we believe in spacetime, then we do not believe that space and time are separately existing things. But that does not mean that there is no distinction between space and time: we still distinguish between the spatial aspects and the temporal aspects of spacetime. The second part of this dissertation, comprising chapter 4, looks at this distinction. How is it made? In virtue of what are the temporal aspects of spacetime temporal, rather than spatial? The standard view is that the temporal aspects of spacetime are temporal because they play a distinctive role in the geometry of spacetime. I argue that this view is false, and that the temporal aspects are temporal because they play a distinctive role in the geometry of spacetime and in the laws of nature.

The spacetime ontology is considered in General Relativity (GR) in view of the choice of a frame of reference (FR). Various approaches to a description of the FR, such as coordinate systems, monads and tetrads are reviewed. It is shown that any of the existing FR definitions require a preexisting background spacetime, which, if defined independently of the FR, renders the spacetime absolute in violation of the principle of relativity, or, if defined within an inertial FR (IFR), as it is usually done, make the argument circular. Consequently, defining a FR in a preexisting spacetime is unacceptable. We show that a FR defines a differentiable manifold with, generally, non-Euclidean geometry. In a noninertial FR (NIFR) the observer must chose a coordinative definition either admitting existence of a universal – inertial – force or settling for non-Euclidian spacetime. Following Reichenbach, it is preferable to eliminate all universal forces and opt for a non-Euclidean geometry. It is shown that an affine connection with metric is best suited to describe the geometry of spacetime within a FR. Considering a gravitational field in an arbitrary FR, we show within the framework of Einstein’s GR that the gravity is described by nonmetricity of spacetime. This result may shed new light on the nature of the cosmological constant and dark energy.

Abstract Einstein intended the general theory of relativity to be a generalization of the relativity of motion and, therefore, a radical departure from previous spacetime theories. It has since become clear, however, that this intention was not fulfilled. I try to explain Einstein's misunderstanding on this point as a misunderstanding of the role that spacetime plays in physics. According to Einstein, earlier spacetime theories introduced spacetime as the unobservable cause of observable relative motions and, in particular, as the cause of inertial effects of ?absolute? motion. I use a comparative analysis of Einstein and Newton to show that spacetime is not introduced as an explanation of observable effects, but rather is defined through those effects in arguments like Newton's ?water bucket? argument and Einstein's argument for special relativity. I then argue that to claim that a spacetime theory is true, or to claim that a spacetime structure is ?real?, is not to claim that a theoretical object explains the observable. Rather, it is to claim that the fundamental definitions that link spacetime structure to physical phenomena are empirically sound, i.e. that they can be successfully applied empirically. This leads to a new and clearer view of the empirical content of spacetime theories and of the meaning of ?realism? about spacetime.

Discussions of the metaphysical status of spacetime assume that a spacetime theory offers a causal explanation of phenomena of relative motion, and that the fundamental philosophical question is whether the inference to that explanation is warranted. I argue that those assumptions are mistaken, because they ignore the essential character of spacetime theory as a kind of physical geometry. As such, a spacetime theory does notcausally explain phenomena of motion, but uses them to construct physicaldefinitions of basic geometrical structures by coordinating them with dynamical laws. I suggest that this view of spacetime theories leads to a clearer view of the philosophical foundations of general relativity and its place in the historical evolution of spacetime theory. I also argue that this view provides a much clearer and more defensible account of what is entailed by realism concerning spacetime.

I give an informal outline of the hole argument which shows that spacetime substantivalism leads to an undesirable indeterminism in a broad class of spacetime theories. This form of the argument depends on the selection of differentiable manifolds within a spacetime theory as representing spacetime. I consider the conditions under which the argument can be extended to address versions of spacetime substantivalism which select these differentiable manifolds plus some further structure to represent spacetime. Finally, I respond to the criticisms of Tim Maudlin and Jeremy Butterfield.