Publications
The Non-Equivalence of Einstein and Lorentz (2021) The British Journal for the Philosophy of Science, 72(4) (preprint)
This paper was chosen as an Editors’ Choice article.
Abstract: In this article, I give a counterexample to a claim made in (Norton (2008)) that empirically equivalent theories can often be regarded as theoretically equivalent by treating one as having surplus structure, thereby overcoming the problem of underdetermination of theory choice. The case I present is that of Lorentz’s ether theory and Einstein’s theory of special relativity. I argue that Norton’s suggestion that surplus structure is present in Lorentz’s theory in the form of the ether state of rest is based on a misunderstanding of the role that the ether plays in Lorentz’s theory, and that in general, consideration of the conceptual framework in which a theory is embedded is vital to understanding the relationship between different theories.
On Representational Redundancy, Surplus Structure, and the Hole Argument (with James Owen Weatherall, 2020) Foundations of Physics, 50, pp. 270-293 (preprint)
Abstract: We address a recent proposal concerning ‘surplus structure’ due to Nguyen et al. [ ‘Why Surplus Structure is Not Superfluous.’ Br. J. Phi. Sci.] We argue that the sense of ‘surplus structure’ captured by their formal criterion is importantly different from—and in a sense, opposite to—another sense of ‘surplus structure’ used by philosophers. We argue that minimizing structure in one sense is generally incompatible with minimizing structure in the other sense. We then show how these distinctions bear on Nguyen et al.’s arguments about Yang-Mills theory and on the hole argument.
Mathematical Responses to the Hole Argument: Then and Now (with James Owen Weatherall, 2022) Philosophy of Science, 89 (5):1223-1232 (preprint)
Abstract: We argue that several apparently distinct responses to the hole argument, all invoking formal or mathematical considerations, should be viewed as a unified “mathematical response”. We then consider and rebut two prominent critiques of the mathematical response before reflecting on what is ultimately at issue in this literature.
The Representational Role of Sophisticated Theories (2024) Philosophy of Science, 91(5):1478-1487.
Abstract: Dewar (2019) argues that removing excess structure via “sophistication” can have explanatory benefits to removing excess structure via “reduction”. In this paper, I argue that a more robust reason to prefer sophisticated theories is that they have representational benefits.
The Relationship between Lagrangian and Hamiltonian Mechanics: The Irregular Case (Forthcoming) Philosophy of Physics.
Abstract: Lagrangian and Hamiltonian mechanics are widely held to be two distinct but equivalent ways of formulating classical theories. Barrett (2019) makes this intuition precise by showing that under a certain characterization of their structure, the two theories are categorically equivalent. However, Barrett only shows equivalence between “hyperregular” models of Lagrangian and Hamiltonian mechanics. While hyperregularity characterizes a large class of theories, it does not characterize the class of gauge theories. In this paper, I consider whether one can extend Barrett’s results to show that Lagrangian and Hamiltonian formulations of gauge theories are equivalent. I argue that there is a precise sense in which one can, and I illustrate that exploring this question highlights several interesting questions about the way that one can construct models of Hamiltonian mechanics from models of Lagrangian mechanics and vice versa, about the role that constraints play, and the definition and interpretation of gauge transformations.
Book Reviews
“Background Independence in Classical and Quantum Gravity” by James Read (2025) Philosophy of Science.
Works In Progress
Do First-Class Constraints Generate Gauge Transformations? A Geometric Resolution
(under reivew)
Winner of the Justine Lambert Prize.
Abstract: The standard definition of a gauge transformation in the /constrained Hamiltonian formalism traces back to Dirac (1964): a gauge transformation is a transformation generated by an arbitrary combination of first-class constraints. On the basis of this definition, Dirac argued that one should extend the form of the Hamiltonian in order to include all of the gauge freedom. However, there have been some recent dissenters of Dirac’s view. Notably, Pitts (2014) argues that a first-class constraint can generate “a bad physical change” and therefore that extending the Hamiltonian in the way suggested by Dirac is unmotivated. In this paper, I use a geometric formulation of the constrained Hamiltonian formalism to argue that there is a flaw in the reasoning used by both sides of the debate, but that correct reasoning supports the standard definition and the extension to the Hamiltonian. In doing so, I clarify two conceptually different ways of understanding gauge transformations, and I pinpoint what it would take to deny that the standard definition is correct.
Excess Structure in the Constrained Hamiltonian Formalism
(under review)
Abstract: Although gauge theories are ubiquitous in physics, there are disagreements about how to characterize the Hamiltonian formulation of gauge theories. First, there are disagreements about whether the “Total Hamiltonian” or the “Extended Hamiltonian” correctly characterizes the equivalence class of Hamiltonians. Second, there are disagreements about whether symplectic reduction is required to remove redundancy from a Hamiltonian gauge theory. I will argue that progress can be made on these issues by considering the relationship between the mathematical structure of the theory associated with the Total Hamiltonian, the Extended Hamiltonian, and symplectic reduction.
Are Reduction and Sophistication Always Viable Alternatives? (with James Owen Weatherall)
Abstract: Many philosophers of physics maintain that a physical theory that exhibits (certain kinds of) symmetries is flawed. This is because it is believed that a theory with symmetries posits or otherwise invokes “excess structure”. In an influential paper, Dewar (2019) introduces a distinction between “reduction” and “sophistication” as alternative but equivalent ways of removing excess structure. In this paper, we argue that one cannot draw the distinction between sophistication and reduction in a way that maintains the core features of Dewar’s definitions of these terms and that vindicates the idea that 1. the standard formulations of theories such as General Relativity and Yang-Mills theory are sophisticated and that 2. there exists a theoretically equivalent reduced alternative. We use this argument to highlight that there are two notions of “reduction” that ought to be distinguished, both in motivation and in outcome.