Gordon Belot

Gordon Belot investigates the distinctive notion of geometric possibility that relationalists rely upon. He examines the prospects for adapting to the geometric case the standard philosophical accounts of the related notion of physical possibility, with particular emphasis on Humean, primitivist, and necessitarian accounts of physical and geometric possibility. This contribution to the debate concerning the nature of space will be of interest not only to philosophers and metaphysicians concerned with space and time, but also to those interested in laws of nature, modal notions, or more general issues in ontology.

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.

Under so-called primitive ontology approaches, in fully describing the history of a quantum system, one thereby attributes interesting properties to regions of spacetime. Primitive ontology approaches, which include some varieties of Bohmian mechanics and spontaneous collapse theories, are interesting in part because they hold out the hope that it should not be too difficult to make a connection between models of quantum mechanics and descriptions of histories of ordinary macroscopic bodies. But such approaches are dualistic, positing a quantum state as well as ordinary material degrees of freedom. This paper lays out and compares some options that primitive ontologists have for making sense of the quantum state

Intuitively, a classical field theory is background-in- dependent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion. Background-independence is not a not formal property of theories: the question whether a theory is background-independent depends upon how the theory is interpreted. Under the approach proposed here, a theory is fully background-independent relative to an interpretation if each physical possibility corresponds to a distinct spacetime geometry; and it falls short of full background-independence to the extent that this condition fails.

This chapter is concerned with the representation of time and change in classical (i.e., non-quantum) physical theories. One of the main goals of the chapter 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 chapter 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.

This paper is concerned with the relation between two notions: that of two solutions or models of a theory being related by a symmetry of the theory and that of solutions or models being physically equivalent. A number of authors have recently discussed this relation, some taking an optimistic view, on which there is a suitable concept of the symmetry of a theory relative to which these two notions coincide, others taking a pessimistic view, on which there is no such concept. The present paper arrives at a cautiously pessimistic conclusion.

ABSTRACTA popular strategy for understanding the probabilities that arise in physics is to interpret them via reductionist accounts of chance—indeed, it is sometimes claimed that such accounts are uniquely well-suited to make sense of the probabilities in classical statistical mechanics. Here it is argued that reductionist accounts of chance carry a steep but unappreciated cost: when applied to physical theories of the relevant type, they inevitably distort the relations of probability that they take as input.

This short and engaging book, based upon Sklar’s 1998 Locke Lectures, addresses three sorts of considerations which have been thought to undercut any claim physics has, or could have, to be getting at the truth. The overarching theme is that these considerations gain their plausibility from being deployed in arguments concerning the representational fidelity of particular physical theories, and that much is lost in the philosophical process of globalisation which converts them into doubts about the representational fidelity of all physical theory. Theory and Truth ought to generate some overdue discussion among philosophers of physics and general philosophers of science concerning the relation between their respective specialties.

It is often said that the Aharonov-Bohm effect shows that the vector potential enjoys more ontological significance than we previously realized. But how can a quantum-mechanical effect teach us something about the interpretation of Maxwell's theory—let alone about the ontological structure of the world—when both theories are false? I present a rational reconstruction of the interpretative repercussions of the Aharonov-Bohm effect, and suggest some morals for our conception of the interpretative enterprise.

The classical field theories that underlie the quantum treatments of the electromagnetic, weak, and strong forces share a peculiar feature: specifying the initial state of the field determines the evolution of some degrees of freedom of the theory while leaving the evolution of some others wholly arbitrary. This strongly suggests that some of the variables of the standard state space lack physical content-intuitively, the space of states of such a theory is of higher dimension than the corresponding space of genuine physical possibilities. The structure of such theories can helpfully be characterized in terms of the action of symmetry groups on their space of states; and the conceptual problems surrounding their strange behavior can be sharpened in light of the observation that it is usually possible to eliminate the redundant variables associated with these symmetries-which turn out to be precisely those variables whose evolution is unconstrained by the dynamical laws of the theory. This paper discusses this approach, uses it to frame questions about the interpretation of classical gauge theories, and to reflect (pessimistically) on our prospects of reaching satisfactory answers to these questions.

A conservation principles tell us that some quantity, quality, or aspect remains constant through change. Such principles appear already in ancient and medieval natural philosophy. In one important strand of Greek cosmology, the rotatory motion of the celestial orbs is eternal and immutable. In optics, from at least the time of Euclid, the angle of reflection is equal to the angle of incidence when a ray of light is reflected. According to some versions of the medieval impetus theory of motion, impetus remains in a projected body (and the associated motion persists) permanently unless the body is subject to outside interference. These examples could be multiplied. But it was in the seventeenth century that conservation principles began to play an absolutely central role in scientific theories. Each of Galileo Galilei, René Descartes, Christiaan Huygens, Gottfried Leibniz, and Isaac Newton founded his approach to physics upon the principle of inertia—that unless interfered with a body will undergo uniform rectilinear motion. A multitude of other conservation principles gained currency during the seventeenth century—some still with us, some long ago left behind. Descartes provides an interesting example of an author who attempted to derive all of his physical principles from conservation laws (Principles of Philosophy, see especially articles 36 to 42 of Part II). Descartes believed that the principles of his physics could be derived from the immutability of God, supplemented only by very weak assumptions about the existence of change in the world. He claims, in fact, that we ought to postulate the strongest conservation laws consistent with such change. These include.