Role of potentials in the Aharonov-Bohm effect

There is a consensus today that the the main lesson of the Aharonov-Bohm effect is that a picture of electromagnetism based on the local action of the field strengths is not possible in quantum mechanics. Contrary to this statement, it is argued here that when the source of the electromagnetic potential is treated in the framework of quantum theory, the Aharonov-Bohm effect can be explained without the notion of potentials. It is explained by local action of the field of the electron on the source of the potential. The core of the Aharonov-Bohm effect is the same as the core of quantum entanglement: the quantum wave function describes all systems together.

Figure 1

Mach-Zehnder interferometer with electron as a test bed of the AB effect. Introduction of a relative electric potential between the arms of the interferometer or of a solenoid inside the interferometer spoils the destructive interference in detector $A$.

Figure 2

A realization of the electric AB effect. Identical charges brought symmetrically to the electron wave packet in the left arm of the interferometer create a potential for the electron without creating an electric field at its location.

Figure 3

The potential of the mirror forces. The potential energy of the particle as a function of its distance from the mirror. The particle with an energy slightly higher than $V$ spends long time near the mirror.

Figure 4

The magnetic AB effect. The electron wave packet coming directly toward the solenoid splits into a superposition of two wave packets which encircle the solenoid from two sides and come out almost in the same direction, interfering toward detectors $A$ and $B$.