Aharonov–Bohm EffectElectrons fired through two slits build up the usual striped interference pattern. Hide a thin coil between the slits so no electron ever touches its magnetic field, then switch the coil on: the stripes slide sideways anyway. Something the electrons never physically pass through still steers them.Aharonov and Bohm worked out in 1959 that the electron's phase depends not on the magnetic field B but on the vector potential A, which leaks outside the coil even where B is exactly zero; going around the loop the two paths pick up a phase difference of exactly 2πΦ/Φ₀ set by the enclosed flux. Tonomura's 1986 electron-hologram experiment confirmed the shift to high precision — proof that A is not just bookkeeping, but has its own physical reality.