In quantum mechanics, the electromagnetic potential alters the descriptions of charged particles only by shifting their phase--that is, by advancing or retarding the crests and troughs in their quantum wavefunctions. In general, however, such a phase change does not lead to any difference in the measurable properties of a particle.
But in 1959 Yakir Aharonov and David Bohm of the University of Bristol, England, devised a "thought experiment" that linked the potential to a measurable result. In their scenario, a beam of electrons is split, with the two halves made to travel around opposite sides of a cylindrical electromagnet, or solenoid. The magnetic field is concentrated inside the solenoid and can be made arbitrarily weak outside by making the cylinder extremely narrow. So Aharonov and Bohm argued that the two electron paths can travel through an essentially field-free region that surrounds the concentrated field within the electromagnet.
In this field-free region, however, the electromagnetic potential is not zero. Aharonov and Bohm showed theoretically that electrons on the two paths would experience different phase changes, and that recombining the electron beams would produce detectable interference effects. That is, the intensity of the recombined beam would vary according to whether the phase-shifted wavefunctions reinforced or canceled each other--a measurable physical effect directly related to the potential, contrary to standard wisdom. However, the phase shift can also be calculated from the strength of the magnetic field, so that interference can be interpreted as an effect of a magnetic field that the electrons never actually pass through. Aharonov and Bohm argued that physicists must accept that in quantum mechanics the electromagnetic potential has genuine physical significance. They expanded on this point in a second paper in 1961.
This effect now bears their names. It's a triumph of theoretical physics and of quantum mechanics. This discovery is a Nobel Prize caliber.
P.S. I think the link gives you a free download of the actual paper.