Feynman’s lecture utilizing the Aharonov–Bohm effect

Volume II of The Feynman Lectures on physics is primarily devoted to explicating classical electromagnetism. Quantum theory arises in just one lecture, 15-5, entitled “The vector potential and quantum mechanics”. He emphasizes a remarkable conceptual change that the classically central notion of force “becomes quite secondary—if it is there at all” in quantum physics. He wishes to demonstrate, with as little quantum theory apparatus as possible, how the quantum notion of a wave function’s phase carries information about the classical force. To that end, he uses the Aharonov–Bohm effect in two thought experiments involving a two-slit electron interference pattern and two different configurations of magnetic field. Here I review Feynman’s argument with the benefit of more specificity about the quantum calculation than Feynman wished to give. Tiwari (Phys Rev Lett 113:158901, 2014 , Quantum Stud.: Math. Found. 4:1 2017 ) recently criticized Feynman’s lecture for not providing a classical explanation of the Aharonov–Bohm effect. I believe this criticism is unwarranted because Feynman never set out to do that. What Feynman does is consider a two-slit interference experiment for an electron with a special magnetic field configuration, and he shows in this case that, when the magnetic field is turned on, the interference pattern on the detection screen shifts by the same distance as the classical trajectories emanating from the slit shift due to the magnetic force. That there is such an example, although unique, which suggests how the quantum phase may be connected to the classical trajectory, appears to be all that Feynman wishes to convey. If Feynman’s presentation is to be faulted, it is that this example is unique, that reasonable extensions of this thought experiment do not show this connection.