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
The Physical Significance of Partial Observables: Connecting Gauge and Surplus Structure (Under Review)
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.
Do First-Class Constraints Generate Gauge Transformations? A Geometric Perspective.
Abstract: The standard definition of a gauge transformation in the constrained Hamiltonian formalism traces back to Dirac: a gauge transformation is a transformation generated by the 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, Pitts (2014) argues that in some cases, a first-class constraint does not generate a gauge transformation, but rather “a bad physical change”. Similarly, Pons (2005) argues that Dirac’s analysis of gauge transformations is “incomplete” and does not provide an account of the symmetries between solutions. Both authors conclude that extending the Hamiltonian in the way suggested by Dirac is unmotivated. If correct, these arguments could have implications for other issues in the foundations of the constrained Hamiltonian formalism, including the Problem of Time. In this paper, I use a geometric formulation of the constrained Hamiltonian formalism to show that one can motivate the extension to the Hamiltonian independently from consideration of the gauge transformations, and I argue that this supports the standard definition of a gauge transformation without falling prey to the criticisms of Pitts (2014) and Pons (2005). Therefore, in order to maintain that first-class constraints do not generate gauge transformations, one must reject the claim that the constrained Hamiltonian formalism is fully described by the geometric picture; I suggest two avenues for doing so.
The Many Independence Theses
Abstract: In Mayo-Wilson et al. (2011), a thesis labeled the “Independence Thesis” is defended, and it is argued that this thesis captures the sense in which the individual perspective and the group perspective come apart in several contexts. In this paper, I evaluate whether the Independence Thesis provides a useful framework for thinking about the relationship between individuals and groups. I argue that there are several distinct independence theses conflated in Mayo-Wilson et al. (2011) and that Mayo-Wilson et al. only provide support for an independence thesis that is too weak to support some of the claims made in the paper. I then demonstrate that there are cases that exemplify a kind of tension between the individual perspective and the group perspective that is not captured by the Independence Thesis. I conclude that the Independence Thesis does not have the generality that Mayo-Wilson et al. (2011) take it to have.
A Paper on Conservation of Momentum in AQUAL (with James Owen Weatherall)
Abstract: There is a large amount of evidence suggesting that our best theories of gravity lead to the wrong predictions for several cosmological phenomena. The prevailing theory to account for such discrepancies is the theory of dark matter. However, an alternative theory proposes that it is the theories of gravity that are in fact wrong at certain acceleration scales. The non-relativistic version of such a theory is known as MOND, or “Modified Newtonian Dynamics”. There are several issues facing MOND that have prevented its wider acceptance. One problem is that it fails to satisfy the usual conservation laws. However, Bekenstein & Milgrom (1984) argue that one can make MOND compatible with these conservation laws by reformulating the theory as a Lagrangian theory, known as AQUAL. In this paper, we consider the two arguments for this claim given by Bekenstein & Milgrom (1984) and demonstrate that both are fallacious. The first argument is that the conservation laws automatically follow from AQUAL because of Noether’s Theorem. The second argument is that one can explicitly derive the conservation of momentum and energy using the equation governing the modified gravitational field.