Equivalence and Duality in Electromagnetism

Abstract

In this paper I bring the recent philosophical literature on theoretical equivalence to bear on dualities in physics. Focusing on electromagnetic duality, which is a simple example of S-duality in string theory, I will show that the duality fits naturally into at least one framework for assessing equivalence-that of categorical equivalence-but that it fails to meet a necessary condition for equivalence on that account. The reason is that the duality does not preserve "empirical content" in the required sense; instead, it takes models to models with "dual" empirical content. I conclude by discussing how one might react to this.

Theoretical equivalence and duality

“…(They also lead to the same quantities.) 55 For some references where these interpretative questions are studied in detail, see Dieks et al (2015), Huggett (2017, 2019, Read and Møller-Nielsen (2018), De , Butterfield (2018).…”

“…Thus the pathologies seem pervasive: and so, the theory-as currently formulated-is inconsistent: it does not make any predictions beyond a certain point. 34 This may be no problem for 32 Recently, Weatherall (2019) has discussed a similar view in the context of classical electric-magnetic duality, where he introduces an 'empirical significance functor' that relates the empirical substructures of the domains of application of the dual models. Weatherall, too, discusses the empirical inequivalence of electric-magnetic duals on their ordinary (in my language, 'external') interpretations vs. their empirical equivalence once an empirical significance functor is introduced (in my language, on an 'internal' interpretation, restricted to the observational conditionals).…”

“…2 Earlier work relating duality and the recent literature on theoretical equivalence is in De Haro (2016: Section 1.4), Butterfield (2018), Read and Møller-Nielsen (2018: Section 4.1). See also Weatherall (2019).…”