Philosophy of Physics
Classical mechanics is often regarded as relatively tractable, providing a complete (although false) description of the world. However, I argue that this view belies the true contours of the theory. Mechanics encompasses a vast array of phenomena, including the motions of planets, fluids, mechanisms, and everyday objects. To do all this, mechanics knits together a battery of problem-solving strategies, computational techniques, and tried and tested rules-of-thumb. Some of the resources that classical mechanics deploys today took centuries to develop, frequently prompting important developments in mathematics. Nevertheless, mechanics is often treated as though the content of the theory follows straightforwardly from Newton’s three laws of motion. This remains the case despite the fact that careful commentators have long noted that Newton’s statement of his third law (the famous ‘action-reaction’ principle) is unhelpfully vague. Although the standard way to make the third law precise limits its strict application to point-masses, it continues to be routinely applied to rigid bodies and continuous media. My manuscript, A Logical Obscurity, explores the tensions that this situation gives rise to. In future research, I want to pursue the implications of the claim that Newton’s laws of motion do not provide rigorous foundations for mechanics as generally conceived.
A separate research project concerns the representational capacities of geometry. Although the development of non-Euclidean geometries in the nineteenth century challenged the assumed relationship between Euclidean geometry and physical space, it was only following the development of the theory of general relativity that Euclidean geometry’s status as the default description of space was finally overthrown. In the aftermath, there has been much philosophical activity concerning physical geometry. For example, a recent proposal is that physical geometry could be an emergent property of fundamental physics. In my manuscript, The Problem of Space, I argue that such proposals expose an underlying question that remains unanswered. In the rapid proliferation of geometries in the nineteenth century, many leading philosophers and physicists questioned which of these mathematical structures provided candidate descriptions of physical space. Consensus developed around the following answer: only the geometries with a congruence structure that captured the free translation of rigid bodies—the geometries of constant curvature—were candidate physical geometries. However, this idea was unequivocally undermined by the use of variably curved geometry in general relativity. Although Weyl and Cartan both grappled with this new problem, their work in this area remains relatively unexplored, and there is currently no generally accepted principled approach to the question of which mathematical structures are candidate descriptions of physical space. In considering whether physical geometry could be an emergent property of fundamental physics, this underlying question is particularly pressing.
A separate research project concerns the representational capacities of geometry. Although the development of non-Euclidean geometries in the nineteenth century challenged the assumed relationship between Euclidean geometry and physical space, it was only following the development of the theory of general relativity that Euclidean geometry’s status as the default description of space was finally overthrown. In the aftermath, there has been much philosophical activity concerning physical geometry. For example, a recent proposal is that physical geometry could be an emergent property of fundamental physics. In my manuscript, The Problem of Space, I argue that such proposals expose an underlying question that remains unanswered. In the rapid proliferation of geometries in the nineteenth century, many leading philosophers and physicists questioned which of these mathematical structures provided candidate descriptions of physical space. Consensus developed around the following answer: only the geometries with a congruence structure that captured the free translation of rigid bodies—the geometries of constant curvature—were candidate physical geometries. However, this idea was unequivocally undermined by the use of variably curved geometry in general relativity. Although Weyl and Cartan both grappled with this new problem, their work in this area remains relatively unexplored, and there is currently no generally accepted principled approach to the question of which mathematical structures are candidate descriptions of physical space. In considering whether physical geometry could be an emergent property of fundamental physics, this underlying question is particularly pressing.