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With J. Earman, “Pre-Socratic Quantum Gravity.” In C. Callender and N. Huggett (eds.), Philosophy Meets Physics at the Planck Scale. Cambridge University Press (2001), pp. 213-255.
[preprint]
Abstract. It appears to be a common view among physicists that the physical content of the general covariance of general relativity resides not in the fact that that theory, like every other, can be given a generally covariant formulation, but in the fact that it ought to be so formulated. The idea is that one does some sort of violence to the physical content of general relativity if one breaks its general covariance by introducing preferred coordinates, slicings, or other geometrical structure, in a way in which one does not when one moves from a generally covariant formulation of Newtonian mechanics or special relativity to the standard formulations in which inertial coordinates play a special role. Central to this way of thinking about general covariance is the idea that misjudging the physical content of a given theory can lead one astray in attempts to construct new theories—since, e.g., empirically equivalent formulations of a theory may well lead to inequivalent quantum theories, it is important to begin with the correct formulation. This link between content and method is the source of the sentiment, widespread among physicists working on canonical quantum gravity, that there is a tight connection between the interpretative problems of general relativity and the technical and conceptual problems of quantum gravity. Our goal in this paper is to explicate this connection for a philosophical audience, and to evaluate some of the interpretative arguments which have been adduced in favor of various attempts to formulate quantum theories of gravity. We organize our discussion around the question of the extent to which the general covariance of general relativity can (or should) be understood by analogy to the gauge invariance of theories like classical electromagnetism, and the related questions of the nature of observables in classical and quantum gravity, and the existence of time and change in the quantum theory.
Note. This is a companion paper to “From Metaphysics to Physics.”
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