Aharonov-Bohm effect
The 1959 prediction (Yakir Aharonov and David Bohm) that quantum charged particles passing through field-free regions still acquire a measurable phase shift Φ = (q/ℏ)Φ_B from the enclosed magnetic flux. Confirmed by Chambers (1960) and decisively by Tonomura (1986). The cleanest demonstration that the EM potential is more fundamental than the field.
Definition
The Aharonov-Bohm effect is the quantum-mechanical phenomenon, predicted by Yakir Aharonov and David Bohm in 1959 and confirmed experimentally by Robert Chambers (1960) and decisively by Akira Tonomura's electron-holography experiment at Hitachi (1986), that a charged particle following a path enclosing a region of magnetic flux acquires a phase shift Φ_AB = (q/ℏ) ∮ A·dℓ — even when the magnetic field B is identically zero everywhere along the particle's worldline. By Stokes's theorem the loop integral equals (q/ℏ)Φ_B where Φ_B is the magnetic flux enclosed by the loop. The effect is the cleanest experimental demonstration that the electromagnetic four-potential A^μ — not just the field tensor F^{μν} — is a fundamental observable in quantum electrodynamics.
The classic experimental setup is two-slit electron interference with a thin solenoid centred between the slits. The solenoid's field is tightly confined to its interior, so the electron paths through both slits pass through regions where B is identically zero. Classically nothing should happen — no force acts on the electrons. Quantum-mechanically, however, the interference pattern on the detection screen shifts laterally as the solenoid's flux is varied; one full flux quantum Φ_0 = h/|q| corresponds to a 2π phase shift and one full fringe-width displacement, and the pattern returns to its original position. Tonomura's 1986 experiment used a permalloy-coated superconducting toroid to confine the field tightly and ruled out every conceivable classical-leakage explanation; the effect is now textbook material in every quantum mechanics course. The deeper consequence is that two configurations of A^μ that differ by a non-zero closed-loop integral are physically distinct in quantum mechanics, even when their F^{μν} are identical — the gauge potential, not just the field, is the right object.
The AB effect generalises in striking ways. The Berry phase (1984) is its differential-geometric extension to arbitrary parameter spaces, with applications across condensed matter (the integer quantum Hall effect, topological insulators, the spin-Hall effect). The Aharonov-Casher effect (1984) is the electric dual: a neutral particle with magnetic moment passing a line charge acquires an analogous phase. Variants involving heavier mesons, neutrons, and macroscopic Cooper pairs in superconducting rings (the SQUID, where AB-like phase quantisation produces the dc Josephson effect) populate condensed-matter and quantum-information experiments to this day. The Aharonov-Bohm effect was Aharonov and Bohm's introduction to physics; it remains, sixty-five years later, one of the most-cited results in twentieth-century theoretical physics.