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In the electron's inertial frame the solenoid moves past it in the Aharonov-Bohm Effect. That means the electron sees a time varying vector potential which, by:

$\vec{E}$ = -$\partial\vec{A}/\partial t$

means it also sees an electromotive force during the transit of the solenoid.

The usual narrative of the Aharonov-Bohm Effect is that the only thing affected by the static $\vec{A}$ through which it passes is the electron's quantum phase. However, if, from its inertial frame, it experiences a period of electromotive force, it necessarily means a change in position. Doesn't this mean that, in the solenoid's inertial frame, there is a change in the electron's trajectory?

James Bowery
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  • Speaking of "the electrons frame" is only valid classically. In the quantum theory, it is wholly unclear what that would be. 2. Outside of the ideal solenoid, the potential is pure gauge, i.e. $\vec A = \vec \nabla \Lambda$ for some function of space $\Lambda$. So the temporal derivative vanishes.
    • – ACuriousMind Jun 01 '15 at 15:48
  • Would it clarify the question to change "frame" to "quantum reference frame"? http://en.wikipedia.org/wiki/Quantum_reference_frame#Quantum_reference_frame – James Bowery Jun 01 '15 at 17:03
  • No, because there is no "quantum reference frame" - quantumly, the electron does not have a determined velocity, so there is no uniquely determined "frame of the electron". – ACuriousMind Jun 01 '15 at 17:06
  • @JamesBowery You might find this question interesting. – Mark Mitchison Jun 01 '15 at 18:57