In classical electromagnetism, electric and magnetic fields are the fundamental entities responsible for all physical effects. There is a compact formulation of electromagnetism that expresses the fields in terms of another quantity known as the electromagnetic potential, which can have a value everywhere in space. The fields are easily derived theoretically from the potential, but the potential itself was taken to be purely a mathematical device, with no physical meaning.

In quantum mechanics, shifts in the electromagnetic potential alter the description of a charged particle only by shifting its phase—that is, by advancing or retarding the crests and troughs in its quantum wave function. 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, UK, 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.