HERE’S a nice piece of quantum nonsense. Take a doughnut-shaped magnet and wrap a metal shield round its inside edge so that no magnetic field can leak into the hole. Then fire an electron through the hole. There is no field in the hole, so the electron will act as if there is no field, right? Wrong. The wave associated with the electron’s movement suffers a jolt as if there were something there. Werner Ehrenberg and Raymond Siday were the first to note that this behaviour lurks in the Schrödinger equation (see “Quantum wonders: The Hamlet effect “). That was in 1949, but their result remained unnoticed. Ten years later Yakir Aharonov and David Bohm, working at the University of Bristol in the UK, rediscovered the effect and for some reason their names stuck. So what is going on? The Aharonov-Bohm effect is proof that there is more to electric and magnetic fields than is generally supposed. You can’t calculate the size of the effect on a particle by considering just the properties of the electric and magnetic fields where the particle is. You also have to take into account the properties where it isn’t. Casting about for an explanation, physicists decided to take a look at a property of the magnetic field known as the vector potential. For a long time, vector potentials were considered just handy mathematical tools – a shorthand for electrical and magnetic properties that didn’t have any real-world significance. As it turns out,