The Aharonov–Bohm Effect

No field. No force. Yet a measurable change.

Panel A: a coherent electron beam splits and passes on opposite sides of a shielded solenoid; the field is confined inside, the vector potential circulates through the field-free region outside, and switching the flux on displaces the interference pattern by a phase shift. Panel B: in Tonomura’s 1986 proof a toroidal magnet holds the field entirely within the ring, and fringes from the beam through the hole arrive shifted by half a phase against those from outside, peaks meeting troughs.