I propose that the phase of an electron's wave function changes by π when the electron goes around a loop maintaining phase coherence. Equivalently, that the minimum orbital angular momentum of an electron in a ring is ℏ/2 rather than zero as generally assumed, hence that the electron in a ring has azimuthal zero point motion. This proposal provides a physical explanation for the origin of electronic `quantum pressure', it implies that a spin current exists in the ground state of aromatic ring molecules, and it suggests an explanation for the ubiquitousness of persistent currents observed in mesoscopic rings.