Philosophy of Physics
"A Raum with a View" (co-authored with Neil Dewar; forthcoming in Einstein Studies—preprint available here)
In this paper, we argue that Hermann Weyl’s analysis of the conception of physical geometry implicit in Einstein’s theory of general relativity offers a novel insight into how geometry represents the world. Following the rapid proliferation of geometries in the nineteenth century, consensus developed around the idea that only constant curvature geometries were candidate physical geometries. However, this idea was unequivocally undermined by the use of a variable curvature geometry in general relativity. Indeed, in the wake of general relativity there is no generally accepted account of which geometrical objects represent spatio-temporal structure: although some argue that spacetime is best represented by a bare topological manifold, others argue that such a manifold must be equipped with a metric—a means of determining distances and angles—in order to represent spacetime. We argue that Weyl’s work reveals a level of geometrical structure intermediate between the manifold and the metric, and that there are good reasons to regard this intermediate structure as the mathematical representation of spacetime in general relativity.
"A Logical Obscurity" (in preparation; draft available on request)
In this paper, I argue that the picture of the world provided by classical mechanics may not be as cohesive as it appears. In particular, I argue that the traditional formulation of mechanics appeals to at least two distinct notions of force which are not obviously compatible with one another. I claim that, as a result of this tension, Newton’s action-reaction principle is not applied in a uniform way to bodies in direct contact (such as the parts of a rigid mechanism) and to bodies acting on each other at a distance (such as celestial objects moving under the influence of gravity). According to standard interpretations of classical mechanics, Newton’s laws are intended to be universal and exceptionless, applying equally well to molecules, chairs, and galaxies. However, I argue that the subtle ambiguity underlying Newton’s action-reaction principle challenges the cogency of this standard interpretation, and that the apparent universality of classical mechanics depends, in part, on the tacit unification of a diverse range of problem-solving strategies.
In this paper, we argue that Hermann Weyl’s analysis of the conception of physical geometry implicit in Einstein’s theory of general relativity offers a novel insight into how geometry represents the world. Following the rapid proliferation of geometries in the nineteenth century, consensus developed around the idea that only constant curvature geometries were candidate physical geometries. However, this idea was unequivocally undermined by the use of a variable curvature geometry in general relativity. Indeed, in the wake of general relativity there is no generally accepted account of which geometrical objects represent spatio-temporal structure: although some argue that spacetime is best represented by a bare topological manifold, others argue that such a manifold must be equipped with a metric—a means of determining distances and angles—in order to represent spacetime. We argue that Weyl’s work reveals a level of geometrical structure intermediate between the manifold and the metric, and that there are good reasons to regard this intermediate structure as the mathematical representation of spacetime in general relativity.
"A Logical Obscurity" (in preparation; draft available on request)
In this paper, I argue that the picture of the world provided by classical mechanics may not be as cohesive as it appears. In particular, I argue that the traditional formulation of mechanics appeals to at least two distinct notions of force which are not obviously compatible with one another. I claim that, as a result of this tension, Newton’s action-reaction principle is not applied in a uniform way to bodies in direct contact (such as the parts of a rigid mechanism) and to bodies acting on each other at a distance (such as celestial objects moving under the influence of gravity). According to standard interpretations of classical mechanics, Newton’s laws are intended to be universal and exceptionless, applying equally well to molecules, chairs, and galaxies. However, I argue that the subtle ambiguity underlying Newton’s action-reaction principle challenges the cogency of this standard interpretation, and that the apparent universality of classical mechanics depends, in part, on the tacit unification of a diverse range of problem-solving strategies.