Publications
Do First-Class Constraints Generate Gauge Transformations? A Geometric Resolution (Forthcoming) The British Journal for the Philosophy of Science. (preprint)
Abstract: In the Hamiltonian formalism, a gauge transformation is typically defined as a transformation generated by an arbitrary combination of first-class constraints. But gauge transformations are also understood as marking physical equivalence: they relate states or solutions that represent the same physical situation. Whether these two characterizations coincide has been a matter of debate. Pitts (2014), for example, contends that first-class constraints can generate a “bad physical change”. This paper defends the standard view, arguing that it correctly identifies both states and solutions that are equivalent from the perspective of the geometric structure of the Hamiltonian formalism. In doing so, it clarifies the relationship between mathematical and interpretational perspectives on gauge transformations.
Excess Structure in the Constrained Hamiltonian Formalism (Forthcoming) Philosophy of Science. (preprint)
Abstract: Gauge theories are often characterized as possessing ‘redundancy’ or ‘excess structure’. This, in turn, motivates reducing the gauge symmetries, commonly through ‘symplectic reduction’ in the Hamiltonian framework. However, there are multiple ways to formulate a Hamiltonian gauge theory. This paper examines the relationship between the formulation of a Hamiltonian gauge theory and the attribution of excess structure. I argue that one can formulate a Hamiltonian gauge theory such that symplectic reduction does not remove structure, and therefore that the role of symplectic reduction cannot be purely to remove ‘excess structure’. I discuss in what sense symplectic reduction is thereby motivated.
The Relationship between Lagrangian and Hamiltonian Mechanics: The Irregular Case (2025) Philosophy of Physics, 3(1): 9, 1–23.
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.
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.
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 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.
Book Reviews
“Background Independence in Classical and Quantum Gravity” by James Read (2025) Philosophy of Science, 92(4):1034-1038.