Respecting boundaries: theoretical equivalence and structure beyond dynamics

Abstract

A standard line in the contemporary philosophical literature has it that physical theories are equivalent only when they agree on their empirical content, where this empirical content is often understood as being encoded in the equations of motion of those theories. In this article, we question whether it is indeed the case that the empirical content of a theory is exhausted by its equations of motion, showing that (for example) considerations of boundary conditions play a key role in the empirical equivalence (or otherwise) of theories. Having argued for this, we show that philosophical claims made by Weatherall (2016) that electromagnetism in the Faraday tensor formalism is equivalent to electromagnetism in the vector potential formalism, and by Knox (2011) that general relativity is equivalent to teleparallel gravity, can both be called into question. We then show that properly considering the role of boundary conditions in theory structure can potentially restore these claims of equivalence and close with some remarks on the pragmatics of adjudications on theory identity.

Conventionalism, Cosmology and Teleparallel Gravity

“…While the boundary term in the action does not affect the field equations in the bulk, it can still play a role in something. For example, the correct account of the black hole entropy and thus the establishment of generalised thermodynamics wholly depends on the boundary term in the GR action [28]. The investigation into black hole thermodynamics in the teleparallel context has barely begun [45,46,63,64], and we do not know whether a consistent account can be given in all the formulations.…”

“…Her complicated deliberations demonstrate that identity of theories is not an easy problem. Recently, Wolf and Read [28] investigated isolated gravitational systems and systems with boundaries and argued that in this respect, GR and TEGR are equivalent.…”

Symmetries and Representation

“…8 8 It is worth noting that there could be additional distinctions among models, such as that between the dynamical models that satisfy the boundary conditions or the initial conditions of a problem, and those that do not. See Wolf and Read (2023) and Murgueitio Ramírez (2021, Ch. 4) for recent work exploring the importance of boundary conditions when thinking of the models of a theory. …”

“…For a thorough treatment, seeOlver (2000).8 It is worth noting that there could be additional distinctions among models, such as that between the dynamical models that satisfy the boundary conditions or the initial conditions of a problem, and those that do not. SeeWolf andRead (2023) and Murgueitio Ramírez (2021, Ch. 4) for recent work exploring the importance of boundary conditions when thinking of the models of a theory.9 Hence, an invertible transformation that does not preserve the underlying structure is not a symmetry, despite what Dasgupta (2016) seems to suggest with some examples that change the number of objects.10 We are using 'state of affairs' here as a bit of a placeholder.…”