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James Owen Weatherall

Publications and source records attributed to James Owen Weatherall.

At least 19 recordsLinked to original sources
arXiv2026

We Have Never Been Sophisticated

Many philosophers of physics maintain that a physical theory that exhibits (certain kinds of) symmetries is flawed, on the grounds that such theories posit "excess structure". In an influential paper, Dewar [2019, "Sophistication about Symmetries", \emph{Brit. J. Phil. Sci.} \textbf{70}: 485-521] introduces a distinction between "reduction" and "sophistication" as alternative ways of removing excess structure. In this paper we re-examine the distinction as Dewar draws it, and we argue that there is no physically or philosophically important distinction between what Dewar calls "reduction" and what he calls "internal sophistication". We then argue that there are multiple notions of "reduction" in the literature that ought to be distinguished, both in motivation and in outcome.

physics.hist-ph↗
arXiv2026

Ceci n'est pas un gluon

We discuss and then resolve a tension between how physicists treat gauge bosons and the celebrated "Wu-Yang dictionary", which identifies particle physics terminology with that of principal bundles and principal connections. We show how this tension leads to an interpretative choice that is not widely discussed in the physics literature. We then show how the same considerations present a dilemma for a recent "particle-first" approach to Yang-Mills theory due to Henrique Gomes. Either the particle-first approach has surplus structure as compared to principal-bundle-based approaches, or gauge bosons are not sections of vector bundles.

physics.hist-ph↗
arXiv2026

Correctness, Artificial Intelligence, and the Epistemic Value of Mathematical Proof

We argue that it is neither necessary nor sufficient for a mathematical proof to have epistemic value that it be "correct", in the sense of formalizable in a formal proof system. We then present a view on the relationship between mathematics and logic that clarifies the role of formal correctness in mathematics. Finally, we discuss the significance of these arguments for recent discussions about automated theorem provers and applications of AI to mathematics.

math.HO↗
arXiv2026

Deterministic Theories

Determinism is (roughly) the thesis that the past determines the future. But efforts to define it precisely have exposed deep methodological disagreements. Standard possible-worlds formulations of determinism presuppose an "agreement" relation between worlds,but this relation can be understood in multiple ways, none of which is particularly clear. We critically examine the proliferation of definitions of determinism in the recent literature, arguing that these definitions fail to deliver clear verdicts about actual scientific theories. We advocate a return to a formal approach, in the logical tradition of Carnap, that treats determinism as a property of scientific theories, rather than an elusive metaphysical doctrine. We highlight two key distinctions: (1) the difference between qualitative and "full" determinism, as emphasized in recent discussions of physics and metaphysics, and (2) the distinction between weak and strong formal conditions on the uniqueness of world extensions. We argue that defining determinism in terms of metaphysical notions such as haecceities is unhelpful, whereas rigorous formal criteria such as Belot's D1 and D3 offer a tractable and scientifically relevant account. By clarifying what it means for a theory to be deterministic, we set the stage for a fruitful interaction between physics and metaphysics.

physics.hist-ph↗
arXiv2025

Determinism and Asymmetry in General Relativity

This paper concerns the question of which collections of general relativistic spacetimes are deterministic relative to which definitions. We begin by considering a series of three definitions of increasing strength due to Belot (1995). The strongest of these definitions is particularly interesting for spacetime theories because it involves an asymmetry condition called ``rigidity'' that has been studied previously in a different context (Geroch 1969; Halvorson and Manchak 2022; Dewar 2024). We go on to explore other (stronger) asymmetry conditions that give rise to other (stronger) forms of determinism. We introduce a number of definitions of this type and clarify the relationships between them and the three considered by Belot. We go on to show that there are collections of general relativistic spacetimes that satisfy much stronger forms of determinism than previously known. We also highlight a number of open questions.

physics.hist-ph↗
arXiv2025

Spacetime Models for Cosmology

I revisit Roberto Torretti's "Spacetime Models for the World" [SHPMP 31 (2):171-186 (2000)] in the light of more recent work in (philosophy of) cosmology. I discuss the motivations for FLRW spacetimes as a natural starting point for inquiry, and I suggest contemporary cosmologists can avoid the rationalism that Torretti attributes to Einstein's early work in relativistic cosmology. I then discuss the senses in which FLRW models are idealized, and I show how those idealizations (and partial de-idealizations) have contributed to our understanding of the universe.

physics.hist-ph↗
arXiv2025

On (Some) Gauge Theories of Gravity

I consider the sense in which teleparallel gravity and symmetric teleparallel gravity may be understood as gauge theories of gravity. I first argue that both theories have surplus structure. I then consider the relationship between Yang-Mills theory and Poincare Gauge Theory and argue that though these use similar formalisms, there are subtle disanalogies in their interpretation.

physics.hist-ph↗
arXiv2025

Natural Theories

We consider the class of physical theories whose dynamics are given by natural equations, which are partial differential equations determined by a functor from the category of n-manifolds, for some n, to the category of fiber bundles, satisfying certain further conditions. We show how the theory of natural equations clarifies several important foundational issues, including the status and meaning of minimal coupling, symmetries of theories, and background structure. We also state and prove a fundamental result about the initial value problem for natural equations.

physics.hist-ph↗
arXiv2025

A Puzzle About General Covariance and Gauge

We consider two simple criteria for when a physical theory should be said to be "generally covariant", and we argue that these criteria are not met by Yang-Mills theory, even on geometric formulations of that theory. The reason, we show, is that the bundles encountered in Yang-Mills theory are not natural bundles; instead, they are gauge-natural. We then show how these observations relate to previous arguments about the significance of solder forms in assessing disanalogies between general relativity and Yang-Mills theory. We conclude by suggesting that general covariance is really about functoriality.

physics.hist-ph↗
arXiv2024

Are General Relativity and Teleparallel Gravity Theoretically Equivalent?

Teleparallel gravity shares many qualitative features with general relativity, but differs from it in the following way: whereas in general relativity, gravitation is a manifestation of space-time curvature, in teleparallel gravity, spacetime is (always) flat. Gravitational effects in this theory arise due to spacetime torsion. It is often claimed that teleparallel gravity is an equivalent reformulation of general relativity. In this paper we question that view. We argue that the theories are not equivalent, by the criterion of categorical equivalence and any stronger criterion, and that teleparallel gravity posits strictly more structure than general relativity.

physics.hist-ph↗
arXiv2024

Conservation Principles in AQUAL

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.

physics.hist-ph↗
arXiv2023

Between a Stone and a Hausdorff Space

We consider the duality between General Relativity and the theory of Einstein algebras, in the extended setting where one permits non-Hausdorff manifolds. We show that the duality breaks down, and then go on to discuss a sense in which general relativity, formulated using non-Hausdorff manifolds, exhibits excess structure when compared to Einstein algebras. We discuss how these results bear on a class of algebraically-motivated deflationist views about spacetime ontology. We conclude with a conjecture concerning non-Hausdorff spacetimes with no bifurcate curves.

physics.hist-ph↗
arXiv2023

The Local Validity of Special Relativity, Part 1: Geometry

In this two-part essay, we distinguish several senses in which general relativity has been regarded as "locally special relativistic". Here, in Part 1, we focus on senses in which a relativistic spacetime has been said to be "locally (approximately) Minkowskian". After critiquing several proposals in the literature, we present a result capturing a substantive sense in which every relativistic spacetime is locally approximately Minkowskian. We then show that Minkowski spacetime is not distinguished in this result: every relativistic spacetime is locally approximately every other spacetime in the same sense. In Part 2, we will consider "locally specially relativistic" matter theories.

physics.hist-ph↗
arXiv2023

The Local Validity of Special Relativity, Part 2: Matter Dynamics

In this two-part essay, we distinguish several senses in which general relativity has been regarded as "locally special relativistic". In Part 1, we focused on senses in which a relativistic spacetime may be said to be "locally (approximately) Minkowskian". Here, in Part 2, we consider what it might mean to say that a matter theory is "locally special relativisitc". We isolate and evaluate three criteria in the literature and show that they are incompatible: matter theories satisfying one will generally violate others. We then consider what would happen if any of those criteria failed for a given theory.

physics.hist-ph↗
arXiv2023

Dark Energy or Modified Gravity?

We consider some of the epistemic benefits of exploring "theory space" in the context of modifications of general relativity with intended applications in cosmology. We show how studying modifications of general relativity can help in assessing the robustness of empirical inferences, particularly in inaccessible regimes. We also discuss challenges to sharply distinguishing apparently distinct directions in theory space.

physics.hist-ph↗
arXiv2023

Torsion in the Classical Spacetime Context

Teleparallel gravity, an empirically equivalent counterpart to General Relativity, represents the influence of gravity using torsional forces. It raises questions about theory interpretation and underdetermination. To better understand the torsional forces of Teleparallel gravity, we consider a context in which forces are better understood: classical spacetimes. We propose a method of incorporating torsion into the classical spacetime context that yields a classical theory of gravity with a closed temporal metric and spacetime torsion. We then prove a result analogous to the Trautman degeometrization theorem, that every model of Newton-Cartan theory gives rise, non-uniquely, to a model of this theory.

physics.hist-ph↗
arXiv2022

On Automorphism Criteria for Comparing Amounts of Mathematical Structure

Wilhelm (2021) has recently defended a criterion for comparing structure of mathematical objects, which he calls Subgroup. He argues that Subgroup is better than SYM * , another widely adopted criterion. We argue that this is mistaken; Subgroup is strictly worse than SYM *. We then formulate a new criterion that improves on both SYM * and Subgroup, answering Wilhelm's criticisms of SYM * along the way. We conclude by arguing that no criterion that looks only to the automorphisms of mathematical objects to compare their structure can be fully satisfactory.

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