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The non-ideal theory of the Aharonov–Bohm effect

Dougherty, John (2020) The non-ideal theory of the Aharonov–Bohm effect. Synthese. ISSN 1573-0964

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Abstract

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. 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. In this paper I defend the topological interpretation against their criticisms. I consider three types of idealization that might arise in treatments of the effect. 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. But, I argue, the AB effect itself features no singular limits, so it doesn’t involve idealizations in this sense. Second, I argue that Shech and Earman’s emphasis on the role of boundary conditions in the AB effect is misplaced. 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. 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. Finally, I address the role of the non-relativistic approximation usually presumed in discussions of the AB effect. This approximation is essential if—as the topological interpretation supposes—the AB effect constrains and justifies a relativistic theory of the electromagnetic interaction. In this case the ends justify the means. So the topological view presupposes no unjustified idealizations.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Dougherty, Johnjohn.e.dougherty.ii@gmail.com0000-0002-4332-684X
Keywords: idealization; Aharonov–Bohm effect; locality; topology; unitarily inequivalent representations
Subjects: General Issues > Experimentation
Specific Sciences > Physics > Fields and Particles
General Issues > Models and Idealization
Specific Sciences > Physics
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: John Dougherty
Date Deposited: 04 Sep 2020 15:59
Last Modified: 04 Sep 2020 15:59
Item ID: 18057
Journal or Publication Title: Synthese
Publisher: Springer (Springer Science+Business Media B.V.)
Subjects: General Issues > Experimentation
Specific Sciences > Physics > Fields and Particles
General Issues > Models and Idealization
Specific Sciences > Physics
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Symmetries/Invariances
Date: 2020
ISSN: 1573-0964
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/18057

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