An energy condition, in the context of a wide class of spacetime theories, is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be positive". The remarkable fact I will discuss in this paper is that such simple, general, almost trivial seeming propositions have profound and far-reaching import for our understanding of the structure of relativistic spacetimes. It is therefore especially surprising when one also learns that (...) we have no clear understanding of the nature of these conditions, what theoretical status they have with respect to fundamental physics, what epistemic status they may have, when we should and should not expect them to be satisfied, and even in many cases how they and their consequences should be interpreted physically. Or so I shall argue, by a detailed analysis of the technical and conceptual character of all the standard conditions used in physics today, including examination of their consequences and the circumstances in which they are believed to be violated. (shrink)

A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General Relativity." Journal of Mathematical Physics 16, ] provides a sense in which the geodesic principle has the status of a theorem in General Relativity. I have recently shown that a similar theorem holds in the context of geometrized Newtonian gravitation [Weatherall, J. O. "The Motion of a Body in Newtonian Theories." Journal of Mathematical Physics 52, ]. Here I compare the interpretations of these two (...) theorems. I argue that despite some apparent differences between the theorems, the status of the geodesic principle in geometrized Newtonian gravitation is, mutatis mutandis, strikingly similar to the relativistic case. (shrink)

For many years—and with some energy since Laudan’s “Confutation of Convergent Realism” —the scientific realist has sought to accommodate examples of false-yet-successful theories in the history of science. One of the most prominent strategies is to identify ‘success fueling’ components of false theories that themselves are at least approximately true. In this article I develop both sides of the debate, introducing new challenges from the history of science as well as suggesting adjustments to the divide et impera realist strategy. A (...) new ‘recipe’ for the prospective identification of working/idle posits is considered. (shrink)

In this paper I critically review the long history of attempts to formulate and derive the geodesic principle, which claims that massive bodies follow geodesic paths in general relativity theory. I argue that if the principle is interpreted as a dynamical law of motion describing the actual evolution of gravitating bodies as endorsed by Einstein, then it is impossible to apply the law to massive bodies in a way that is coherent with his own field equations. Rejecting this canonical interpretation, (...) I propose an alternative interpretation of the geodesic principle as a type of universality thesis analogous to the universality behavior exhibited in thermal systems during phase transitions. (shrink)

In this paper I critically review the long history of attempts to formulate and derive the geodesic principle, which claims that massive bodies follow geodesic paths in general relativity theory. I argue that if the principle is interpreted as a dynamical law of motion describing the actual evolution of gravitating bodies as endorsed by Einstein, then it is impossible to apply the law to massive bodies in a way that is coherent with his own field equations. Rejecting this canonical interpretation, (...) I propose an alternative interpretation of the geodesic principle as a type of universality thesis analogous to the universality behavior exhibited in thermal systems during phase transitions. (shrink)

Inviting a reappraisal of the status of scientific knowledge, Andrew Pickering suggests that scientists are not mere passive observers and reporters of nature.

I argue that, contrary to folklore, Einstein never really cared for geometrizing the gravitational or the electromagnetic field; indeed, he thought that the very statement that General Relativity geometrizes gravity "is not saying anything at all". Instead, I shall show that Einstein saw the "unification" of inertia and gravity as one of the major achievements of General Relativity. Interestingly, Einstein did not locate this unification in the field equations but in his interpretation of the geodesic equation, the law of motion (...) of test particles. (shrink)

The topics of gravitational field energy and energy-momentum conservation in General Relativity theory have been unjustly neglected by philosophers. If the gravitational field in space free of ordinary matter, as represented by the metric g ab itself, can be said to carry genuine energy and momentum, this is a powerful argument for adopting the substantivalist view of spacetime.This paper explores the standard textbook account of gravitational field energy and argues that (a) so-called stress-energy of the gravitational field is well-defined neither (...) locally nor globally; and (b) there is no general principle of energy-momentum conservation to be found in General Relativity. I discuss the nature and justification of the zero-divergence law for ordinary stress-energy, and its possible connection with the failure of General Relativity to realise Mach's principle. (shrink)

If you wish to learn from the theoretical physicist anything about the methods which he uses, I would give you the following piece of advice: Don't listen to his words, examine his achievements. For to the discoverer in that field, the constructions of his imagination appear so necessary and so natural that he is apt to treat them not as the creations of his thoughts but as given realities.

Except for a few brief periods, Einstein was uninterested in analysing the nature of the spacetime singularities that appeared in solutions to his gravitational field equations for general relativity. The existence of such monstrosities reinforced his conviction that general relativity was an incomplete theory which would be superseded by a singularity-free unified field theory. Nevertheless, on a number of occasions between 1916 and the end of his life, Einstein was forced to confront singularities. His reactions show a strange asymmetry: he (...) tended to be more disturbed by merely apparent singularities and less disturbed by real singularities. Einstein had strong a priori ideas about what results a correct physical theory should deliver. In the process of searching through theoretical possibilities, he tended to push aside technical problems and jump over essential difficulties. Sometimes this method of working produced brilliant new ideas—such as the Einstein–Rosen bridge—and sometimes it lead him to miss important implications of his theory of gravity—such as gravitational collapse. (shrink)

Except for a few brief periods, Einstein was uninterested in analysing the nature of the spacetime singularities that appeared in solutions to his gravitational field equations for general relativity. The existence of such monstrosities reinforced his conviction that general relativity was an incomplete theory which would be superseded by a singularity-free unified field theory. Nevertheless, on a number of occasions between 1916 and the end of his life, Einstein was forced to confront singularities. His reactions show a strange asymmetry: he (...) tended to be more disturbed by merely apparent singularities and less disturbed by real singularities. Einstein had strong a priori ideas about what results a correct physical theory should deliver. In the process of searching through theoretical possibilities, he tended to push aside technical problems and jump over essential difficulties. Sometimes this method of working produced brilliant new ideas—such as the Einstein–Rosen bridge—and sometimes it lead him to miss important implications of his theory of gravity—such as gravitational collapse. (shrink)

Much controversy surrounds the question of what ought to be the proper definition of 'singularity' in general relativity, and the question of whether the prediction of such entities leads to a crisis for the theory. I argue that a definition in terms of curve incompleteness is adequate, and in particular that the idea that singularities correspond to 'missing points' has insurmountable problems. I conclude that singularities per se pose no serious problem for the theory, but their analysis does bring into (...) focus several problems of interpretation at the foundation of the theory often ignored in the philosophical literature. (shrink)

What would it mean to apply quantum theory, without restriction and without involving any notion of measurement and state reduction, to the whole universe? What would realism about the quantum state then imply? This book brings together an illustrious team of philosophers and physicists to debate these questions. The contributors broadly agree on the need, or aspiration, for a realist theory that unites micro- and macro-worlds. But they disagree on what this implies. Some argue that if unitary quantum evolution has (...) unrestricted application, and if the quantum state is taken to be something physically real, then this universe emerges from the quantum state as one of countless others, constantly branching in time, all of which are real. The result, they argue, is many worlds quantum theory, also known as the Everett interpretation of quantum mechanics. No other realist interpretation of unitary quantum theory has ever been found. Others argue in reply that this picture of many worlds is in no sense inherent to quantum theory, or fails to make physical sense, or is scientifically inadequate. The stuff of these worlds, what they are made of, is never adequately explained, nor are the worlds precisely defined; ordinary ideas about time and identity over time are compromised; no satisfactory role or substitute for probability can be found in many worlds theories; they can't explain experimental data; anyway, there are attractive realist alternatives to many worlds. Twenty original essays, accompanied by commentaries and discussions, examine these claims and counterclaims in depth. They consider questions of ontology - the existence of worlds; probability - whether and how probability can be related to the branching structure of the quantum state; alternatives to many worlds - whether there are one-world realist interpretations of quantum theory that leave quantum dynamics unchanged; and open questions even given many worlds, including the multiverse concept as it has arisen elsewhere in modern cosmology. A comprehensive introduction lays out the main arguments of the book, which provides a state-of-the-art guide to many worlds quantum theory and its problems. (shrink)

Indeed, this is the first serious book-length study of the subject by a philosopher of science.

Why did Einstein tirelessly study unified field theory for more than 30 years? In this book, the author argues that Einstein believed he could find a unified theory of all of nature's forces by repeating the methods he used when he formulated general relativity. The book discusses Einstein's route to the general theory of relativity, focusing on the philosophical lessons that he learnt. It then addresses his quest for a unified theory for electromagnetism and gravity, discussing in detail his efforts (...) with Kaluza-Klein and, surprisingly, the theory of spinors. From these perspectives, Einstein's critical stance towards the quantum theory comes to stand in a new light. This book will be of interest to physicists, historians and philosophers of science. (shrink)

There is a striking difference between the methodology of the young Einstein and that of the old. I argue that Einstein’s switch in the late 1910s from a moderate empiricism to an extreme rationalism should at least in part be understood against the background of his crushing personal and political experiences during the war years in Berlin. As a result of these experiences, Einstein started to put into practice what, drawing on Schopenhauer, he had preached for years, namely to use (...) science as his means of escaping from “the merely personal.” Whatever the exact sources of Einstein’s about-face, the older man has left us with a highly misleading picture of how the younger man achieved the successes that we still celebrate today. This has had a harmful influence on theoretical physics. If the young Einstein’s successes are any guide as to how successful theoretical physics is done, close adherence to general features of the empirical data is much more and mathematical elegance is much less important than the old Einstein wanted us to believe. (shrink)

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). (shrink)

This is a self-contained introduction to the Everett interpretation of quantum mechanics. It is the introductory chapter of Many Worlds? Everett, quantum theory, and reality, S. Saunders, J. Barrett, A. Kent, and D. Wallace, Oxford University Press.