Role of potentials in the Aharonov-Bohm effect

Abstract

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.PACS numbers: 03.65.Vf, 03.65.Ta, 03.65.Ud Before the Aharonov-Bohm effect [1] (AB) was discovered, the general consensus was that particles can change their motion only due to fields at their locations, fields which were created by other particles. The main revolutionary aspect of the AB effect was that this is not generally true, and that in certain setups two particles, prepared in identical states, move in the same fields but end up in different final states. In particular, the electromagnetic field can vanish at every place where the electron has been, yet the electron motion is affected by the electromagnetic interaction. The AB effect states that the motion of an electron is completely defined by the potentials in the region of its motion and not just by the fields. The potentials depend on the choice of gauge, which cannot affect the motion of particles, but there are gauge invariant properties of the potentials (apart from the fields) that specify the motion of particles. The validity and the meaning of the AB effect has been extensively discussed [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. I argue that there is an alternative to commonly accepted mechanism which leads to the effect, and that we might change our understanding of the nature of physical interactions back to that of the time before the AB effect was discovered. The quantum wave function changes due to local actions of fields.The discussion will be on the level of gedanken experiments, without questioning the feasibility of such experiments in today's laboratory. Consider a Mach-Zehnder interferometer for electrons tuned in such a way that the electron always ends up in detector B, see Fig. 1. We can change the electric potential in one arm of the interferometer such that there will be no electromagnetic field at the location of the wave packets of the electron but, nevertheless, the electron will change its behavior and sometimes (or it can be arranged that always) will end up in detector A. This is the electric AB effect. Alternatively, in the magnetic AB effect, the interference picture can be changed due to a solenoid inside the interferometer which produces no electromagnetic field at the arms of the interferometer.Let us start our analysis with the electric AB effect. In the original proposal, the potential was created using conductors, capacitors etc. While those are closer...

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