Does the Aharonov–Bohm Effect Occur?

Timothy H. Boyer

G N Afanasiev, V.M. Shilov

It is shown that different forms of quantum impenetrability lead to different physical consequences. This should be kept in mind in analysing experimental data. The relativistic impenetrability conditions are considered and the corresponding relativistic Aharonov-Bohm cross-sections are obtained. The possibility of the AB effect occurring in simply-connected space regions is discussed.

Daniel M. Greenberger

Kazuyasu Shigemoto, Kunihiko Uehara B

In the original setting of the Aharonov-Bohm, the gauge invariant physical longitudinal mode of the vector potential, which is expressed by the gauge invariant physical current, gives the desired contribution to the Aharonov-Bohm effect. While the scalar mode of the vector potential, which changes under the gauge transformation so that it is the unphysical mode, give no contribution to the Aharonov-Bohm effect. Then Aharonov-Bohm effect really occurs by the physical longitudinal mode in the original Aharonov-Bohm’s setting. In the setting of Tonomura et al., where the magnet is shielded with the superconducting material, not only the magnetic field but also the longitudinal mode of the vector potential become massive by the Meissner effect. Then not only the magnetic field but also the physical longitudinal mode does not come out to the region where the electron travels. In such setting, only the scalar mode of the vector potential exists in the region where the electron travels, but there is no contribution to the Aharonov-Bohm effect from that mode.

Benjamin Liebowitz

Elay Shech

Abstract By appealing to resources found in the scientific understanding literature, I identify in what senses idealisations afford understanding in the context of the (magnetic) Aharonov‐Bohm effect. Three types of concepts of understanding are discussed: understanding‐what, which has to do with understanding a phenomenon; understanding‐with, which has to do with understanding a scientific theory; and understanding‐why, which has to do with the reason some phenomenon occurs. Consequently, I outline an account of understanding‐with that is suggested by the historical controversy surrounding the Aharonov‐Bohm effect.