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Idealizations, Essential Self-Adjointness, and Minimal Model Explanation in the Aharonov-Bohm EffectTwo approaches to understanding the idealizations that arise in the Aharonov-Bohm (AB) effect are presented. It is argued that the standard topological approach, which takes the non-simply connected electron configuration space to be an essential element in the explanation and understanding of the effect, is flawed. An alternative approach is outlined. Consequently, it is shown that the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have important implications for philosophical issues. Also, the alleged indispensable explanatory role of said idealizations is examined via a minimal model explanatory scheme.
Department of Philosophy