On the Time Reversal Invariance of Classical Electromagnetic Theory

David Albert claims that classical electromagnetic theory is not time reversal invariant. He acknowledges that all physics books say that it is, but claims they are "simply wrong" because they rely on an incorrect account of how the time reversal operator acts on magnetic fields. On that account, electric fields are left intact by the operator, but magnetic fields are inverted. Albert sees no reason for the asymmetric treatment, and insists that neither field should be inverted. I argue, to the contrary, that the inversion of magnetic fields makes good sense and is, in fact, forced by elementary geometric considerations. I also suggest a way of thinking about the time reversal invariance of classical electromagnetic theory -- one that makes use of the invariant four-dimensional formulation of the theory -- that makes no reference to magnetic fields at all. It is my hope that it will be of interest in its own right, Albert aside. It has the advantage that it allows for arbitrary curvature in the background spacetime structure, and is therefore suitable for the framework of general relativity. The only assumption one needs is temporal orientability.Comment: 24 pages, 3 figure, forthcoming in Studies in History and Philosophy of Modern Physic

A No-Go Theorem About Rotation in Relativity Theory

Within the framework of general relativity, in some cases at least, it is a delicate and interesting question just what it means to say that an extended body is or is not "rotating". It is so for two reasons. First, one can easily think of different criteria of rotation. Though they agree if the background spacetime structure is sufficiently simple, they do not do so in general. Second, none of the criteria fully answers to our classical intuitions. Each one exhibits some feature or other that violates those intuitions in a significant and interesting way. The principal goal of the paper is to make the second claim precise in the form of a modest no-go theorem.Comment: 41 pages including 5 figures, postscript format; to appear in a Festschrift for Howard Stein (The Incomparable Mr. Stein, ed. D. Malament, Open Court Press

On Relative Orbital Rotation in Relativity Theory

We consider the following question within both Newtonian physics and relativity theory. "Given two point particles X and Y, if Y is rotating relative to X, does it follow that X is rotating relative to Y?" As it stands the question is ambiguous. We discuss one way to make it precise and show that, on that reading at least, the answers given by the two theories are radically different. The relation of relative orbital rotation turns out to be symmetric in Newtonian physics, but not in relativity theory

Topics in the Foundations of General Relativity and Newtonian Gravitation Theory

In Topics in the Foundations of General Relativity and Newtonian Gravitation Theory, David B. Malament presents the basic logical-mathematical structure of general relativity and considers a number of special topics concerning the foundations of general relativity and its relation to Newtonian gravitation theory. These special topics include the geometrized formulation of Newtonian theory (also known as Newton-Cartan theory), the concept of rotation in general relativity, and Gödel spacetime. One of the highlights of the book is a no-go theorem that can be understood to show that there i

Does the Causal Structure of Space-Time Determine its Geometry

This essay explores the following problem: to what extent is it possible to construe the causal structure of space-time as basic and from it to reconstruct the topological and metrical structure of space-time? The problem is first examiried within the context of Minkowski space-time (Chapter II) and then generalized to the class of space-time models considered in the general theory of relativity (Chapter III). Much of the essay is technical. But it is motivated by philosophical debate over the viability of causal theories of time and of space-time. By way of introduction, this initial chapter presents a brief discussion of these causal theories. Nothing approaching a thorough analysis is intended. Rather the goal is merely to state what a causal theory time or space-time is supposed to be, outline several objections that have been raised against such theories, and most importantly, suggest why interest in them leads to the questions considered in Chapters II and III. This should set the stage