The Aharonov-Bohm effect is a quantum phenomenon where particles are influenced by electromagnetic potentials in regions with zero field.An electron beam, split in two, bypasses a microscopic coil and, upon recombination, produces fringes — like ripples on water. The shift of these fringes proves: the magnetic force here is zero, yet the coil still affects the electrons. Quantum mechanics describes particles as waves, and when moving in electromagnetic potentials, their wave phase changes. Even if the field (B) itself is zero, but the vector potential (A) is nonzero, the phase still accumulates. The experiment with a solenoid, whose field is confined inside and outside B=0, shows interference fringes shifted in proportion to the magnetic flux through the solenoid. This confirms that potentials are not just a mathematical abstraction but a physical reality.
The idea dates back to discussions on the role of potentials in quantum mechanics. In 1959, Yakir Aharonov and David Bohm published a paper describing a hypothetical experiment. The first experimental confirmation was performed by R. G. Chambers in 1960 using an interferometer with a magnetic whisker. Later, Akira Tonomura and colleagues conducted demonstrative experiments with electron holography that left no doubts. The effect is closely related to the Berry phase and has led to the development of interferometric devices.
In the Schrödinger equation for a charged particle, the vector potential A appears. When traversing a closed loop C, the wave function acquires an additional phase Δφ = (e/ħ) ∮_C A·dl. By Stokes' theorem, this integral equals the flux of the magnetic field B through any surface bounded by C: Φ = ∫ B·dS. If the field B is concentrated inside a solenoid and does not penetrate the region of motion, the flux Φ is nonetheless nonzero, causing a shift in interference fringes. Gauge invariance ensures that only the flux modulo 2π is observable.
Based on this effect, ultra-precise magnetic field sensors and new types of transistors are created.
Oscillations of electrical resistance in thin metal rings in a magnetic field are a direct manifestation of the Aharonov–Bohm effect, used in magnetometers.















