Significance of the Aharonov-Bohm effect

Abstract

It is shown that in an Aharonov-Bohm experiment: i) Due to superposition of the electron’s magnetic field and the solenoid’s interior magnetic field there exists an interaction energyUmwhose gradient represents a force on the electron which has not hitherto been recognized or provided for in the classical formalism, ii) This force is non-Lorentzian, it does do work, and explains the A.B. phase shiftclassically, iii) The long-standing action-reaction difficulty involved in. the application of the Biot-Savart law to unclosed circuits is eliminated by this new force in this context, iv) The same force (−gradUm) is implicitly contained in the Schrodinger equation of the A.B. effect. Thus there is no need to modify the concept of force or vector potential as proposed by Aharonov and Bohm. In the Appendix, detailed calculations are outlined showing that currents generated in the solenoid by a passing electron are negligible.