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, Philosophy of Science (Forthcoming)

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.

Works In Progress

Do First-Class Constraints Generate Gauge Transformations? A Geometric Perspective.

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.

The Relationship between Lagrangian and Hamiltonian Mechanics: The Irregular Case

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 characterisation of their structure, the two theories are categorically equivalent. However, Barrett only shows equivalence between “hyperregular” models of Lagrangian and Hamiltonian mechanics. While hyperregularity characterises a large class of theories, it does not characterise 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 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, as well as the definition and interpretation of gauge transformations.

The Extended Hamiltonian is Not Trivial

Abstract: This paper critically analyzes an argument made by Pitts (2022, 2024) that extending the form of the Hamiltonian constitutes a trivial reformulation of a theory, and therefore doesn’t provide insight into the gauge transformations. I argue that a trivial reformulation in the way suggested by Pitts cannot be used to add new gauge transformations to a theory, and I show that the move to a new form of the Hamiltonian is therefore not a trivial reformulation — rather, it is a way of removing structure.

The Physical Significance of Partial Observables: Connecting Gauge and Surplus Structure

Abstract: It is a widely held norm that our best physical theories should be absent of redundancies. But what makes some aspects of a theory redundant? I explore this question by relating two strands of literature — characterizing the notion of a ‘gauge variable’ and characterizing the notion of ‘surplus structure’ in a theory. I present a distinction between two kinds of structure that I call theoretical structure and auxiliary structure, and I argue that understanding the distinctive role that each structure plays resolves debates in both strands of literature regarding the kind of redundancy that certain features of a theory possess.

Conservation Principles in AQUAL (with James Owen Weatherall)

Abstract: We consider conservation of momentum in AQUAL, a field-theoretic extension to Modified Newtonian Dynamics (MOND). We show that while there is a sense in which momentum is conserved, it is only if momentum is attributed to the gravitational field, and thus Newton’s third law fails as usually understood. We contrast this situation with that of Newtonian gravitation on a field theoretic formulation. We then briefly discuss the situation in TeVeS, a relativistic theory that has AQUAL as a classical limit.