Quantum non-locality vs. quasi-local measurements in the conditions of the Aharonov-Bohm effect

Abstract

Theoretical explanation of the Meissner effect involves proportionality between current density and vector potential, which has many deep consequences. As noticed by de Gennes, superconductors in a magnetic field "find an equilibrium state where the sum of kinetic and magnetic energies is minimum" and this state "corresponds to the expulsion of the magnetic field". This statement still leaves an open question: from which source is the superconducting current acquiring its kinetic energy? A naïve answer, perhaps, is from the energy of the magnetic field. However, one can consider situations (Aharonov-Bohm effect), where the classical magnetic field is locally absent in the area occupied by the current. Experiments demonstrate that despite the local absence of the magnetic field, current is, nevertheless, building up. From what source is it acquiring its energy then? Locally, only a vector potential is present. How does the vector potential facilitate the formation of the current? Is the current formation a result of a truly non-local quantum action, or does the local action of the vector potential have experimental consequences? We discuss possible experiments with a hybrid normal-metal superconductor circuitry, which can clarify this puzzling situation. Experimental answers will be important for further developments.