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Aharonov-Bohm effecteffect

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In 1959, Yakir Aharonov and David Bohm theoretically predicted that in quantum mechanics, electromagnetic potentials play a more fundamental role than fields. They proposed a thought experiment: electron interference changes even when they move in a region with zero electric and magnetic fields, if a non-zero vector potential A is present. This challenged the classical view that only fields are physically significant. Experimental confirmation in 1960 proved them right.

How it works

The effect underlies the operation of SQUIDs (superconducting quantum interference devices)—instruments that measure magnetic fields a billion times weaker than Earth's. It also appears in carbon nanotubes and topological insulators.

💡 David Bohm himself, one of the authors, believed it supported his philosophical theory of 'hidden variables' about the implicate order of the universe, but most physicists interpret the effect in the standard way.
\Delta \varphi = \frac{e}{\hbar} \Phi
Δφ — phase difference between two electron paths; e — elementary charge, e ≈ 1.602×10⁻¹⁹ C; ħ — reduced Planck constant, ħ ≈ 1.0546×10⁻³⁴ J·s; Φ — magnetic flux enclosed between the two alternative trajectories (in Webers, Wb). For an isolated solenoid, Φ = B·S, where B is the induction inside and S is the cross-sectional area.
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Discovered by
Yakir AharonovDavid BohmMichael Berry
Related concepts
wave functionquantum entanglement
Related laws
Berry phaseBell's theoremJosephson effect

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