Like moths attracted to a bright light, philosophers are drawn to glitz. So in discussing the notions of ‘gauge’, ‘gauge freedom’, and ‘gauge theories’, they have tended to focus on examples such as Yang–Mills theories and on the mathematical apparatus of fibre bundles. But while Yang–Mills theories are crucial to modern elementary particle physics, they are only a special case of a much broader class of gauge theories. And while the fibre bundle apparatus turned out, in retrospect, to be the right formalism to illuminate the structure of Yang–Mills theories, the strength of this apparatus is also its weakness: the fibre bundle formalism is very flexible and general, and, as such, fibre bundles can be seen lurking under, over, and around every bush. What is needed is an explanation of what the relevant bundle structure is and how it arises, especially for theories that are not initially formulated in fibre bundle language.
Here I will describe an approach that grows out of the conviction that, at least for theories that can be written in Lagrangian/Hamiltonian form, gauge freedom arises precisely when there are Lagrangian/Hamiltonian constraints of an appropriate character. This conviction is shared, if only tacitly, by that segment of the physics community that works on constrained Hamiltonian systems.
Physicists who work on canonical quantum gravity will sometimes remark that the general covariance of general relativity is responsible for many of the thorniest technical and conceptual problems in their field. In particular, it is sometimes alleged that one can trace to this single source a variety of deep puzzles about the nature of time in quantum gravity, deep disagreements surrounding the notion of ‘observable’ in classical and quantum gravity, and deep questions about the nature of the existence of spacetime in general relativity.
Philosophers who think about these things are sometimes sceptical about such claims. We have all learned that Kretschmann was quite correct to urge against Einstein that the ‘General Theory of Relativity’ was no such thing, since any theory could be cast in a generally covariant form, and hence that the general covariance of general relativity could not have any physical content, let alone bear the kind of weight that Einstein expected it to. Friedman's assessment is widely accepted: ‘As Kretschmann first pointed out in 1917, the principle of general covariance has no physical content whatever: it specifies no particular physical theory; rather, it merely expresses our commitment to a certain style of formulating physical theories’ (Friedman 1983, p. 44). Such considerations suggest that general covariance, as a technically crucial but physically contentless feature of general relativity, simply cannot be the source of any significant conceptual or physical problems.
Michael Redhead began his Tarner Lectures by allowing that ‘many physicists would dismiss the sort of question that philosophers of physics tackle as irrelevant to what they see themselves as doing’ (1995, p. 1). He argued that, on the contrary, philosophy has much to offer physics: presenting examples and arguments from many parts of physics and philosophy, he led his audience towards his ultimate conclusion that physics and metaphysics enjoy a symbiotic relationship.
By way of tribute to Michael we would like to undertake a related project: convincing philosophers of physics themselves that the philosophy of space and time has something to offer contemporary physics. We are going to discuss the relationship between the interpretative problems of quantum gravity, and those of general relativity. We will argue that classical and quantum theories of gravity resuscitate venerable philosophical questions about the nature of space, time, and change; and that the resolution of some of the difficulties facing physicists working on quantum theories of gravity appears to require philosophical as well as scientific creativity. These problems have received little attention from philosophers. Indeed, scant attention has been paid to recent attempts to quantize gravity. As a result, most philosophers have been unaware of the problem of time in quantum gravity, and its relationship to the knot of philosophical and technical problems surrounding the general covariance of general relativity – so that it has been all too easy to dismiss this latter set of problems as philosophical contrivances. Consequently, philosophical discussion of space and time has suffered.
This point is best illustrated by attending to the contrast between what philosophers and physicists have to say about the significance of Einstein's hole argument.
Over the last few years leading scientific journals have been publishing articles dealing with time travel and time machines. (An unsystematic survey produced the following count for 1990–1992. Physical Review D: 11; Physical Review Letters: 5; Classical and Quantum Gravity. 3; Annals of the New York Academy of Sciences: 2; Journal of Mathematical Physics: 1. A total of 22 articles involving 22 authors.) Why? Have physicists decided to set up in competition with science fiction writers and Hollywood producers? More seriously, does this research cast any light on the sorts of problems and puzzles that have featured in the philosophical literature on time travel?
The last question is not easy to answer. The philosophical literature on time travel is full of sound and fury, but the significance remains opaque. Most of the literature focuses on two matters, backward causation and the paradoxes of time travel. Properly understood, the first is irrelevant to the type of time travel most deserving of serious attention; and the latter, while always good for a chuckle, are a crude and unilluminating means of approaching some delicate and deep issues about the nature of physical possibility. The overarching goal of this chapter is to refocus attention on what I take to be the important unresolved problems about time travel and to use the recent work in physics to sharpen the formulation of these issues.
The plan of the chapter is as follows. Section 1 distinguishes two main types of time travel – Wellsian and Godelian. The Wellsian type is inextricably bound up with backward causation.
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