Significance of EM potentials in quantum theory (Aharonov–Bohm)
Aharonov · Bohm
Summary and citation · read the original at the source
In one page
Classically a charged particle feels only the electric and magnetic fields where it actually is, and the potentials that generate those fields are treated as convenient bookkeeping with no reality of their own. Yakir Aharonov and David Bohm showed that quantum mechanics disagrees. In the equation governing an electron's wave it is the potential that appears, not the field — so an electron can travel through a region where every field, and therefore every force on it, is exactly zero, and still be affected. Their example is now in the textbooks: split a coherent electron beam, send the two halves around either side of a long solenoid whose magnetic field is entirely confined inside it, and bring them back together. Neither half ever enters a magnetic field. The interference pattern shifts anyway, by an amount set by the magnetic flux the two paths enclose between them. The paper closes by proposing the experiments and asking what the potentials really are.
Why it matters hereThis is chapter 10's calibrated anchor: the settled, measured case in which an electromagnetic potential does something real in a place where the fields are zero. It is also the discipline the chapter needs — the defensible claim is the one Aharonov and Bohm proved, that the potential controls phase, and the site makes that claim rather than any larger one.
What it claims
01Contrary to the conclusions of classical mechanics, there exist effects of the electromagnetic potentials on charged particles even in the region where all the fields — and therefore all the forces on the particles — vanish.Abstract
Settled physics02The reason is that in the quantum theory it is the potentials, not the field strengths, that enter the equation governing the electron's wave function, so a field-free region carrying a non-zero potential still acts on an electron passing through it.Introduction; formulation of the problem
Settled physics03The observable consequence is a relative phase: a coherent electron beam split so that its two halves pass on either side of a region of confined magnetic flux, and then recombined, shows an interference pattern shifted by an amount fixed by the enclosed flux.The magnetic solenoid case
Settled physics04The line integral of the vector potential around a closed path encircling a long solenoid is not zero even though the magnetic field is zero everywhere along that path — the quantity the electron responds to is the flux the path encloses.The magnetic solenoid case
Settled physics05Aharonov and Bohm set out possible experiments to test these conclusions, and suggest further possible developments in the interpretation of the potentials — the potentials being physically significant rather than a computational convenience.Abstract; proposed experiments and discussion
Settled physics
The way in
https://link.aps.org/doi/10.1103/PhysRev.115.485Published by the American Physical Society as Phys. Rev. 115, 485–491 (1 August 1959). The publisher serves the article free to read at link.aps.org, but under its own terms rather than an open licence, so this sheet carries the summary and citation only.
How to cite it
Aharonov, Bohm (1959) Significance of EM potentials in quantum theory (Aharonov–Bohm). doi:10.1103/PhysRev.115.485
Where it sits in the curriculum
Scalar waves and the field behind the fieldsThe evidence ladder