Shech and Earman both level complaints against the “topological view” of the AB effect this view is Shech’s explicit target, while Earman criticizes a general class of analyses to which the topological view belongs.

In this paper I dispute their foundational points and argue that the topological interpretation of the AB effect does not involve unjustified or unusual idealizations. These conclusions about foundations of physics lead to conclusions about modelling and idealization. 4841) in particular, they claim, physicists and philosophers have not sufficiently attended to the domains of definition of relevant operators. On their view, important facts about functional analysis are too often “swept under the carpet as a ‘merely technical’ issue” (Shech 2018a, p. They argue that more careful consideration of the effect can teach us lessons about foundational issues in physics and about modelling and idealization in science more generally. In a number of recent papers, Elay Shech ( 2015, ( 2018a, ( 2018b, ( 2019) and John Earman ( 2019) have argued for a re-evaluation of the AB effect, a phenomenon in the quantum theory of electromagnetically charged particles. So the topological view presupposes no unjustified idealizations. This approximation is essential if-as the topological interpretation supposes-the AB effect constrains and justifies a relativistic theory of the electromagnetic interaction. Finally, I address the role of the non-relativistic approximation usually presumed in discussions of the AB effect. Indeed, the boundary conditions for which Shech and demands justification are incompatible with some instances of the AB effect, so the topological interpretation ought not justify them. The idealizations that are useful in connecting the theoretical description of the AB effect to experiment do interact with facts about boundary conditions, but none of these idealizations are presupposed by the topological interpretation of the effect. Second, I argue that Shech and Earman’s emphasis on the role of boundary conditions in the AB effect is misplaced. But, I argue, the AB effect itself features no singular limits, so it doesn’t involve idealizations in this sense.

First, Shech takes the AB effect to involve an idealization in the form of a singular limit, analogous to the thermodynamic limit in statistical mechanics. I consider three types of idealization that might arise in treatments of the effect. In this paper I defend the topological interpretation against their criticisms. In particular, they argue that an adequate account of the AB effect must address the role of boundary conditions in certain ideal cases of the effect. Elay Shech and John Earman have recently argued that the common topological interpretation of the Aharonov–Bohm (AB) effect is unsatisfactory because it fails to justify idealizations that it presupposes.

John earman structural engineer