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"Malament, David B"
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Norton’s Slippery Slope
In this article, I identify several issues that arise in trying to decide whether Newtonian particle mechanics qualifies as a deterministic theory. I also give a minitutorial on the geometry and dynamical properties of Norton’s dome surface. The goal is to better understand how his example works and also to better appreciate just how wonderfully strange it is.
Journal Article
Is Newtonian Cosmology Really Inconsistent?
John Norton has recently argued that Newtonian gravitation theory (at least as applied to cosmological contexts where one envisions the possibility of a homogeneous mass distribution throughout all of space) is inconsistent. I am not convinced. Traditional formulations of the theory may seem to break down in cases of the sort Norton considers. But the difficulties they face are only apparent. They are artifacts of the formulations themselves, and disappear if one passes to the so-called \"geometrized\" formulation of the theory.
Journal Article
Why Gibbs Phase Averages Work--The Role of Ergodic Theory
We propose an \"explanation scheme\" for why the Gibbs phase average technique in classical equilibrium statistical mechanics works. Our account emphasizes the importance of the Khinchin-Lanford dispersion theorems. We suggest that ergodicity does play a role, but not the one usually assigned to it.
Journal Article
\Time Travel\ in the Gödel Universe
The paper first tries to explain how the possibility of \"time travel\" arises in the Gödel universe. It then goes on to discuss a technical problem conerning minimal acceleration requirements for time travel. A theorem is stated and a conjecture posed. If the latter is correct, time travel can be ruled out as a practical possibility in the Godel universe.
Journal Article
Itamar Pitowsky's Quantum Probability—Quantum Logic
Itamar Pitowsky's book (1989), published in the Springer-Verlag Lecture Notes in Physics series, brings together several extremely interesting component investigations concerning the foundations of quantum mechanics. All deal with issues of probability including, in one case, the relation of probability to logic. It is a significant contribution, offering both new, nontrivial mathematical results, and provocative philosophical remarks about their significance.
Journal Article
Classical General Relativity
This survey paper 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\".
Paper
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.
Paper