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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Aharonov–Bohm effect | 1/5 | https://en.wikipedia.org/wiki/Aharonov–Bohm_effect | reference | science, encyclopedia | 2026-05-05T10:54:30.845762+00:00 | kb-cron |
The Aharonov–Bohm effect, sometimes called the Ehrenberg–Siday–Aharonov–Bohm effect, is a quantum-mechanical phenomenon in which an electrically charged particle is affected by an electromagnetic potential (
φ
{\displaystyle \varphi }
,
A
{\displaystyle \mathbf {A} }
), despite being confined to a region in which both the magnetic field
B
{\displaystyle \mathbf {B} }
and electric field
E
{\displaystyle \mathbf {E} }
are zero. The underlying mechanism is the coupling of the electromagnetic potential with the complex phase of a charged particle's wave function, and the Aharonov–Bohm effect is accordingly illustrated by interference experiments. The most commonly described case, sometimes called the Aharonov–Bohm solenoid effect, takes place when the wave function of a charged particle passing around a long solenoid experiences a phase shift as a result of the enclosed magnetic field, despite the magnetic field being negligible in the region through which the particle passes and the particle's wavefunction being negligible inside the solenoid. This phase shift has been observed experimentally. There are also magnetic Aharonov–Bohm effects on bound energies and scattering cross sections, but these cases have not been experimentally tested. An electric Aharonov–Bohm phenomenon was also predicted, in which a charged particle is affected by regions with different electrical potentials but zero electric field, but this has no experimental confirmation yet. A separate "molecular" Aharonov–Bohm effect was proposed for nuclear motion in multiply connected regions, but this has been argued to be a different kind of geometric phase as it is "neither nonlocal nor topological", depending only on local quantities along the nuclear path. Werner Ehrenberg (1901–1975) and Raymond E. Siday first predicted the effect in 1949. Yakir Aharonov and David Bohm published their analysis in 1959. After publication of the 1959 paper, Bohm was informed of Ehrenberg and Siday's work, which was acknowledged and credited in Bohm and Aharonov's subsequent 1961 paper. The effect was confirmed experimentally while Bohm was still alive (and of course Aharonov as well), first by Robert G. Chambers, with error too large to be generally accepted, and then by Akira Tonomura, with a low enough error.
== Significance == In the 18th and 19th centuries, physics was dominated by Newtonian dynamics, with its emphasis on forces. Electromagnetic phenomena were elucidated by a series of experiments involving the measurement of forces between charges, currents and magnets in various configurations. Eventually, a description arose according to which charges, currents and magnets acted as local sources of propagating force fields, which then acted on other charges and currents locally through the Lorentz force law. In this framework, because one of the observed properties of the electric field was that it was irrotational, and one of the observed properties of the magnetic field was that it was divergenceless, it was possible to express an electrostatic field as the gradient of a scalar potential (e.g. Coulomb's electrostatic potential, which is mathematically analogous to the classical gravitational potential) and a stationary magnetic field as the curl of a vector potential (then a new concept – the idea of a scalar potential was already well accepted by analogy with gravitational potential). The language of potentials generalised seamlessly to the fully dynamic case but, since all physical effects were describable in terms of the fields which were the derivatives of the potentials, potentials (unlike fields) were not uniquely determined by physical effects: potentials were only defined up to an arbitrary additive constant electrostatic potential and an irrotational stationary magnetic vector potential. The Aharonov–Bohm effect is important conceptually because it bears on three issues apparent in the recasting of (Maxwell's) classical electromagnetic theory as a gauge theory, which before the advent of quantum mechanics could be argued to be a mathematical reformulation with no physical consequences. The three issues are:
whether potentials are "real" or just a convenient mathematical tool; whether action principles are fundamental; the principle of locality. The Aharonov–Bohm thought experiments and their experimental realization imply that the issues were not just philosophical. However, the electromagnetic four-potential
A
α
{\displaystyle A^{\alpha }}
overdescribes the physics, as all observable phenomena remain unchanged after a gauge transformation, and conversely, Maxwell's electric and magnetic fields underdescribe the physics, as they do not predict the Aharonov–Bohm effect. Moreover, as predicted by the gauge principle, the quantities that remain invariant under gauge transforms are precisely the physically observable phenomena. Because of reasons like these, the Aharonov–Bohm effect was chosen by the New Scientist magazine as one of the "seven wonders of the quantum world". Chen-Ning Yang considered the Aharonov–Bohm effect to be the only direct experimental proof of the gauge principle.
=== Potentials vs. fields === It is generally argued that the Aharonov–Bohm effect illustrates the physicality of electromagnetic potentials, Φ and A, in quantum mechanics. Classically it was possible to argue that only the electromagnetic fields are physical, while the electromagnetic potentials are purely mathematical constructs, that due to gauge freedom are not even unique for a given electromagnetic field. However, Lev Vaidman has challenged this interpretation by showing that the Aharonov–Bohm effect can be explained without the use of potentials so long as one gives a full quantum mechanical treatment to the source charges that produce the electromagnetic field. According to this view, the potential in quantum mechanics is just as physical (or non-physical) as it was classically. Aharonov, Cohen, and Rohrlich responded that the effect may be due to a local gauge potential or due to non-local gauge-invariant fields. Two papers published in the journal Physical Review A in 2017 have demonstrated a quantum mechanical solution for the system. Their analysis shows that the phase shift can be viewed as generated by a solenoid's vector potential acting on the electron or the electron's vector potential acting on the solenoid or the electron and solenoid currents acting on the quantized vector potential.