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arXiv:1303.2137 · WORLD SCIENTIFIC eBooks

On the Aharonov-Bohm Effect and Why Heisenberg Captures Nonlocality Better Than Schrödinger

Yakir Aharonov

Published Apr 1, 2014• 4 citations
arXivHTMLPDF

Abstract

I discuss in detail the history of the Aharonov-Bohm effect in Bristol and my encounters with Akira Tonomura later on. I then propose an idea that developed following the publication of the Aharonov-Bohm effect, namely the importance of modulo momentum and Heisenberg representation in dealing with non-local quantum phenomena.
DOI
10.1142/9789814472906_0009

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At first sight the Aharonov-Bohm effect appears nonlocal, though not in the way EPR/ Bell correlations are generally acknowledged to be nonlocal. This paper applies an analysis of nonlocality to the Aharonov-Bohm effect to show that its peculiarities may be blamed either on a failure of a principle of local action or on a failure of a principle of separability. Different interpretations of quantum mechanics disagree on how blame should be allocated. The parallel between the Aharonov-Bohm effect and violations of Bell inequalities turns out to be so close that a balanced assessment of the nature and significance of quantum nonlocality requires a detailed study of both effects.
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I argue that the metaphysical import of the Aharonov-Bohm effect has been overstated: correctly understood, it does not require either rejection of gauge invariance or any novel form of nonlocality. The conclusion that it does require one or the other follows from a failure to keep track, in the analysis, of the complex scalar field to which the magnetic vector potential is coupled. Once this is recognised, the way is clear to a local account of the ontology of electrodynamics (or at least, to an account no more nonlocal than quantum theory in general requires); I sketch a possible such account.
Abstract This oral history interview provides Yakir Aharonov’s perspective on the theoretical discovery of the Aharonov-Bohm effect in 1959, during his PhD studies in Bristol with David Bohm, the reception of the effect, the efforts to test it empirically (up to Tonomura’s experiment), and some of the debates regarding the existence of the effect and its interpretation. The interview also discusses related later developments until the 1980s, including modular momentum and Berry’s phase. It includes recollections from meetings with Werner Heisenberg, Richard Feynman, and Chen-Ning Yang, also mentioning John Bell, Robert Chambers, Werner Ehrenberg, Sir Charles Frank, Wendell Furry, Gunnar Källén, Maurice Pryce, Nathan Rosen, John Wheeler, and Eugene Wigner.