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It is widely accepted that the Aharonov-Bohm (AB) effect is understood aslocal action of the vector potential generated by the solenoid on the complexphase of a charged particle's wave functions. Nevertheless, because the vectorpotential is a gauge-dependent quantity, there still exist not a fewresearchers who claim that the AB-effect is caused by nonlocal action of themagnetic field confined inside the solenoid. A serious drawback of suchnon-locality explanation is that it is hard to offer definite mechanism of suchnonlocal interaction between separated charge and magnetic field. This is notsurprising, since the locality is the foundation of modern physics includingelectromagnetism and quantum mechanics. On the other hand, there recentlyappear some interesting attempts to explain the AB-effect through theinteraction between the charged particle and the solenoid current mediated bythe exchange of a virtual photon. A vital assumption of this approach is thatAB-phase shift is proportional to the change of the interaction energy betweenthe charged particle and solenoid along the path of the moving charge.Accordingly, they insist that the AB-phase change along a path does not dependon the gauge choice so that the AB-phase shift for a non-closed path is inprinciple measurable. In the present paper, we critically examine thisastonishing conclusion with the utmost care and attention. At the same time, wetry to give refreshed insight into the role of the vector potential in theinterpretation of the AB-effect.

Is the Aharonov-Bohm phase shift for a non-closed path a measurable quantity ?