Gordon Belot

From metaphysics to physics

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 Einsteins hole argument.

Whose Devil? Which Details?

Batterman has recently argued that fundamental theories are typically explanatorily inadequate, in that there exist physical phenomena whose explanation requires that the conceptual apparatus of a fundamental theory be supplemented by that of a less fundamental theory. This paper is an extended critical commentary on that argument: situating its importance, describing its structure, and developing a line of objection to it. The objection is that in the examples Batterman considers, the mathematics of the less fundamental theory is definable in terms of the mathematics of the fundamental theory, and that only the latter need be given a physical interpretation—so we can view the desired explanation as drawing only upon resources internal to the more fundamental physical theory.

The hawking information loss paradox: the anatomy of controversy

Stephen Hawking has argued that universes containing evaporating black holes can evolve from pure initial states to mixed final ones. Such evolution is non-unitary and so contravenes fundamental quantum principles on which Hawkings analysis was based. It disables the retrodiction of the universes initial state from its final one, and portends the time-asymmetry of quantum gravity. Small wonder that Hawkings paradox has met with considerable resistance. Here we use a simple result for C*-algebras to offer an argument for pure-to-mixed state evolution in black hole evaporation, and review responses to the Hawking paradox with respect to how effectively they rebut this argument.

The Representation of Time and Change in Mechanics

This paper is concerned with the representation of time and change in classical (i.e., non-quantum) physical theories. One of the main goals is to attempt to clarify the nature and scope of the so-called problem of time: a knot of technical and interpretative problems that appear to stand in the way of attempts to quantize general relativity, and which have their roots in the general covariance of that theory. The most natural approach to these questions is via a consideration of more clear cases. So much of the paper is given over to a discussion of the representation of time and change in other, better understood theories, starting with the most straightforward cases and proceeding through a consideration of cases that lead up to the features of general relativity that are responsible for the problem of time.

Is Classical Electrodynamics an Inconsistent Theory

A critical discussion of Mathias Frischs recent book. I discuss Frischs argument for the inconsistency of classical electrodynamcis and the methodological morals that he draws from it.

Dust, Time, and Symmetry

Two symmetry arguments are discussed, each purporting to show that there is no more room for a preferred division of spacetime into instants of time in general relativistic cosmology than in Minkowski spacetime. The first argument is due to Gödel, and concerns the symmetries of his famous rotating cosmologies. The second turns upon the symmetries of a certain space of relativistic possibilities. Both arguments are found wanting. 1. Introduction2. Symmetry arguments3. Gödels argument 3.1 Time in special relativity 3.2 Time in the standard cosmological models 3.3 Time in Gödels stationary rotating solutions 3.4 Gödels argument for the significance of these results 3.5 Is Gödels argument successful?4. Another argument 4.1 Time-translation invariance in classical mechanics 4.2 Time-translation invariance in general relativity? 4.3 Time-translation invariance in dust cosmology 4.4 Is this second argument successful?5. Conclusion Introduction Symmetry arguments Gödels argument 3.1 Time in special relativity 3.2 Time in the standard cosmological models 3.3 Time in Gödels stationary rotating solutions 3.4 Gödels argument for the significance of these results 3.5 Is Gödels argument successful? 3.1 Time in special relativity 3.2 Time in the standard cosmological models 3.3 Time in Gödels stationary rotating solutions 3.4 Gödels argument for the significance of these results 3.5 Is Gödels argument successful? Another argument 4.1 Time-translation invariance in classical mechanics 4.2 Time-translation invariance in general relativity? 4.3 Time-translation invariance in dust cosmology 4.4 Is this second argument successful? 4.1 Time-translation invariance in classical mechanics 4.2 Time-translation invariance in general relativity? 4.3 Time-translation invariance in dust cosmology 4.4 Is this second argument successful? Conclusion

Why General Relativity Does Need an Interpretation

There is a widespread impression that General Relativity, unlike Quantum Mechanics, is in no need of an interpretation. I present two reasons for thinking that this is a mistake. The first is the familiar hole argument. I argue that certain skeptical responses to this argument are too hasty in dismissing it as being irrelevant to the interpretative enterprise. My second reason is that interpretative questions about General Relativity are central to the search for a quantum theory of gravity. I illustrate this claim by examining the interpretative consequences of a particular technical move in canonical quantum gravity.

New Work for Counterpart Theorists: Determinism

Recently Carolyn Brighouse and Jeremy Butterfield have argued that David Lewiss counterpart theory makes it possible both to believe in the reality of spacetime points and to consider general relativity to be a deterministic theory, thus avoiding the ‘hole argument’ of John Earman and John Norton. Butterfields argument relies on Lewiss own counterpart-theoretic analysis of determinism. In this paper, I argue that this analysis is inadequate. This leaves a gap in the Butterfield–Brighouse defence against the hole argument.

Determinism and ontology

Abstract In the philosophical literature, there are two common criteria for a physical theory to be deterministic. The older one is due to the logical empiricists, and is a purely formal criterion. The newer one can be found in the work of John Earman and David Lewis and depends on the intended interpretation of the theory. In this paper I argue that the former must be rejected, and something like the latter adopted. I then discuss the relevance of these points to the current debate over the hole argument.