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.1 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 skeptical 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 the general covariance of general relativity could not have any physical content, let alone bear the kind of weight that Einstein expected it to.2 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” (1984, 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.3 Physicists are, of course, conscious of the weight of Kretschmann’s points against Einstein. Yet they are considerably more ambivalent than their philosophical colleagues. Consider Kuchaˇr’s conclusion at the end of a discussion of this topic. (shrink)

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It has long been a commonplace that there is a problem understanding the role of time when one tries to quantize the General Theory of Relativity (GTR). In his "Thoroughly Modern McTaggart" (Philosophers' Imprint Vol 2, No. 3), John Earman presents several arguments to the conclusion that there is a problem understanding change and the passage of time in the unadorned GTR, quite apart from quantization. His Young McTaggart argues that according to the GTR, no physical magnitude ever changes. A (...) close consideration of Young McTaggart's arguments show that they turn on either a bad choice of formalism or an unwarranted interpretation of the implications of the formalism. This suggests that the problems that arise in quantization may be founded in similar shortcomings. (shrink)

The philosophical literature on time and change is fixated on the issue of whether the B-series account of change is adequate or whether real change requires Becoming of either the property-based variety of McTaggart's A-series or the non-property-based form embodied in C. D. Broad's idea of the piling up of successive layers of existence. For present purposes it is assumed that the B-series suffices to ground real change. But then it is noted that modern science in the guise of Einstein's (...) general theory poses a threat to real change by implying that none of the genuine physical magnitudes countenanced by the theory changes its value with time. The aims of this paper are to explain how this seemingly paradoxical conclusion arises and to assess the merits and demerits of possible reactions to it. (shrink)

Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument from Einstein, we show that spacetime substantivalists are committed to very many more distinct physical states than these theories' equations can determine, even with the most extensive boundary conditions.

I argue that Norton & Earman's hole argument, despite its historical association with General Relativity, turns upon very general features of any linguistic system that can represent substances by names. After exploring various means by which mathematical objects can be interpreted as representing physical possibilities, I suggest that a form of essentialism can solve the hole dilemma without abandoning either determinism or substantivalism. Finally, I identify the basic tenets of such an essentialism in Newton's writings and consider how they can (...) be updated to apply to the case provided by General Relativity. (shrink)

We discuss the relationship between the interpretative problems of quantum gravity and those of general relativity. We 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 would appear to require philosophical as well as scientific creativity.

Relationism claims that our physical theory does not commit us to spacetime points. I consider how a relationist might rewrite physical theories without referring to spacetime points, by appealing to possible objects and possible configurations of objects. I argue that a number of difficulties confront this project. I also argue that a relationist need not be Machian in the sense of claiming that objects' spatiotemporal relations determine whether any object is accelerating.

I reject Norton and Earman's hole argument that spacetime substantivalism is incompatible with determinism. I reconcile these both technically and philosophically. There is a technical definition of determinism that is not violated by pairs of models of the kind used in the hole argument. And technicalities aside, the basic idea of determinism is not violated if we claim that at most one of the two models represents a possible world. This claim can be justified either by metrical essentialism, or by (...) denying transworld identity for points: I prefer the latter. (shrink)

I give an informal outline of the hole argument which shows that spacetime substantivalism leads to an undesirable indeterminism in a broad class of spacetime theories. This form of the argument depends on the selection of differentiable manifolds within a spacetime theory as representing spacetime. I consider the conditions under which the argument can be extended to address versions of spacetime substantivalism which select these differentiable manifolds plus some further structure to represent spacetime. Finally, I respond to the criticisms of (...) Tim Maudlin and Jeremy Butterfield. (shrink)

For the past two decades, Einstein's Hole Argument (which deals with the apparent indeterminateness of general relativity due to the general covariance of the field equations) and its resolution in terms of "Leibniz equivalence" (the statement that pseudo-Riemannian geometries related by active diffeomorphisms represent the same physical solution) have been the starting point for a lively philosophical debate on the objectivity of the point-events of space-time. It seems that Leibniz equivalence makes it impossible to consider the points of the space-time (...) manifold as physically individuated without recourse to dynamical individuating fields. Various authors have posited that the metric field itself can be used in this way , but nobody so far has considered the problem of explicitly distilling the "metrical fingerprint" of point-events from the gauge-dependent elements of the metric field. Working in the Hamiltonian formulation of general relativity, and building on the results of Lusanna and Pauri (2002), we show how Bergmann and Komar's "intrinsic pseudo-coordinates" (based on the value of curvature invariants) can be used to provide a physical individuation of point-events in terms of the true degrees of freedom (the "Dirac observables") of the gravitational field, and we suggest how this conceptual individuation could in principle be implemented with a well-defined empirical procedure. We argue from these results that point-events retain a significant kind of physical objectivity. (shrink)