A Remark About the "Geodesic Principle" in General Relativity

It is often claimed that the geodesic principle can be recovered as a theorem in general relativity. Indeed, it is claimed that it is a consequence of Einstein's equation (or of the conservation principle that is, itself, a consequence of that equation). These claims are certainly correct, but it may be worth drawing attention to one small qualification. Though the geodesic principle can be recovered as theorem in general relativity, it is not a consequence of Einstein's equation (or the conservation principle) alone. Other assumptions are needed to drive the theorems in question. One needs to put more in if one is to get the geodesic principle out. My goal in this short note is to make this claim precise (i.e., that other assumptions are needed)

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

Notes on Geometry and Spacetime (Version 7.2)

This is a set of unpublished lecture notes for a course on "Geometry and Spacetime" that I taught several times at the University of California in Irvine. I discuss Minkowski spacetime in some detail and consider a number of issues concerning the foundations of (so called) "special relativity". I also discuss connections between Minkowskian geometry and non-Euclidean (= hyperbolic) plane geometry

Notes on Geometry and Spacetime (Version 7.2)

This is a set of unpublished lecture notes for a course on "Geometry and Spacetime" that I taught several times at the University of California in Irvine. I discuss Minkowski spacetime in some detail and consider a number of issues concerning the foundations of (so called) "special relativity". I also discuss connections between Minkowskian geometry and non-Euclidean (= hyperbolic) plane geometry

Stability in Cosmology, from Einstein to Inflation

I investigate the role of stability in cosmology through two episodes from the recent history of cosmology: (1) Einstein’s static universe and Eddington’s demonstration of its instability, and (2) the flatness problem of the hot big bang model and its claimed solution by inflationary theory. These episodes illustrate differing reactions to instability in cosmological models, both positive ones and negative ones. To provide some context to these reactions, I also situate them in relation to perspectives on stability from dynamical systems theory and its epistemology. This reveals, for example, an insistence on stability as an extreme position in relation to the spectrum of physical systems which exhibit degrees of stability and fragility, one which has a pragmatic rationale, but not any deeper one

Stability in Cosmology, from Einstein to Inflation

I investigate the role of stability in cosmology through two episodes from the recent history of cosmology: (1) Einstein’s static universe and Eddington’s demonstration of its instability, and (2) the flatness problem of the hot big bang model and its claimed solution by inflationary theory. These episodes illustrate differing reactions to instability in cosmological models, both positive ones and negative ones. To provide some context to these reactions, I also situate them in relation to perspectives on stability from dynamical systems theory and its epistemology. This reveals, for example, an insistence on stability as an extreme position in relation to the spectrum of physical systems which exhibit degrees of stability and fragility, one which has a pragmatic rationale, but not any deeper one

Classical Relativity Theory

This survey article is divided into two parts. In the first (section 2), I give a brief account of the structure of classical relativity theory. In the second (section 3), I discuss three special topics: (i) the status of the relative simultaneity relation in the context of Minkowski spacetime; (ii) the ``geometrized" version of Newtonian gravitation theory (also known as Newton-Cartan theory); and (iii) the possibility of recovering the global geometric structure of spacetime from its ``causal structure"

On the Status of the "Geodesic Law" in General Relativity

Harvey Brown believes it is crucially important that the "geodesic principle" in general relativity is an immediate consequence of Einstein's equation and, for this reason, has a different status within the theory than other basic principles regarding, for example, the behavior of light rays and clocks, and the speed with which energy can propagate. He takes the geodesic principle to be an essential element of general relativity itself, while the latter are better seen as contingent facts about the particular matter fields we happen to encounter. The situation seems much less clear and clean to me. There certainly is a sense in which the geodesic principle can be recovered as a theorem in general relativity. But one needs more than Einstein's equation to drive the theorems in question. Other assumptions are needed. One needs to put more in if one is to get the geodesic principle out. My goal in this note is to make this claim precise, i.e., that other assumptions are needed