FIGURE 1. The Aharonov–Bohm effect.

From the following article:

Quantum physics: Disturbance without the force

Akira Tonomura & Franco Nori

Nature 452, 298-299(20 March 2008)



In Aharonov and Bohm's original theoretical formulation of their effect, an electron beam is split into two, passing on either side of an (infinitely) long, perfectly shielded magnet. The result is a phase-shift evident in an interference pattern formed when the electron beams are recombined. It seems that the electrons 'feel' the non-local presence of the magnetic field through its associated vector potential, which permeates the space around the coil. An analogous effect, the Aharonov–Casher effect, which applies to 'quantum magnetic dipoles' (spins), can be demonstrated by replacing the magnet by an electrically charged cylinder. Caprez and colleagues' experiments1 with a pulsed electron beam passed through a toroidal magnet seem to confirm that no unknown forces are involved in the Aharonov–Bohm effect — it is a purely quantum-mechanical phenomenon.