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

Making or Breaking Your Billion Dollar Case: U.S. Judicial Assistance to Private International Arbitration Under 28 U.S.C. 1732(a)

With the increasingly globalized economy, arbitration is becoming a popular mechanism for resolving disputes. The total value of international arbitration claims grew over one hundred percent in 2012, from $96 billion in 2011 to$206 billion in 2012. The principal users of international arbitration are corporations. In fact, for the shipping, energy, oil and gas, and insurance industries, international arbitration of multi-billion dollar disputes is the default resolution mechanism. Across all industries, approximately ninety percent of international contracts include an arbitration clause. Importantly, seventy-four percent of international arbitration proceedings involve exclusively private parties-no state entities are parties to the dispute

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

Optimal time travel in the Godel universe

Using the theory of optimal rocket trajectories in general relativity, recently developed in arXiv:1105.5235, we present a candidate for the minimum total integrated acceleration closed timelike curve in the Godel universe, and give evidence for its minimality. The total integrated acceleration of this curve is lower than Malament's conjectured value (Malament, 1984), as was already implicit in the work of Manchak (Manchak, 2011); however, Malament's conjecture does seem to hold for periodic closed timelike curves.Comment: 16 pages, 2 figures; v2: lower bound in the velocity and reference adde

The Motion of a Body in Newtonian Theories

A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General Relativity." Journal of Mathematical Physics 16(1), (1975)] provides the sense in which the geodesic principle has the status of a theorem in General Relativity (GR). Here we show that a similar theorem holds in the context of geometrized Newtonian gravitation (often called Newton-Cartan theory). It follows that in Newtonian gravitation, as in GR, inertial motion can be derived from other central principles of the theory.Comment: 12 pages, 1 figure. This is the version that appeared in JMP; it is only slightly changed from the previous version, to reflect small issue caught in proo