Historical research guide · 0579 · 2025
Topological schemes in spacetime for the electrodynamic Aharonov-Bohm effect
P. L. Saldanha · H. Batelaan
In one minute
Pablo Saldanha of the Federal University of Minas Gerais and Herman Batelaan of the University of Nebraska take the Aharonov–Bohm effect, one of the strangest confirmed facts in physics, and show three new ways to stage it. In each, an electron travels both arms of an interferometer at once, and while it sits inside two metal boxes that cancel every field it could feel, the current in a nearby solenoid is switched. The electron never touches an electric or magnetic field, yet its interference pattern shifts. The authors show the shift is fixed by the shape — the topology — of the fields and the electron’s two histories in spacetime, not by any distance or geometry. Two of their results are striking: adding a wire between the boxes makes the answer depend on which side of the solenoid the wire runs, and winding that wire N times around the solenoid multiplies the phase shift by N. That amplification, they argue, could finally put the electric version of the effect within experimental reach for free electrons.
Connection
Chapter 10 rests on the Aharonov–Bohm effect: the potentials are physical, and what they control is phase. This paper is the current front edge of that argument — the phase can be set by a field the particle never meets, the bookkeeping is topological in spacetime, and the authors give a wound-wire scheme that multiplies the effect until it can be measured.
From the source
The Aharonov–Bohm phase difference in any scheme can be written in one form: the particle charge divided by h-bar, multiplied by the magnetic flux through a spacetime surface bounded by the two interfering world lines, minus the corresponding electric term integrated over that same surface. The answer depends on the topology of the field configuration and of the particle trajectories in spacetime, not on the specific geometry.Equation 1, First topological scheme
In every scheme treated, the interfering particle is subjected to null electromagnetic fields for the whole of its passage — the Faraday cages cancel the field in their interiors — and a nonzero phase shift is accumulated anyway. These are type-I Aharonov–Bohm effects, and experiments with several different systems have confirmed the underlying effect.Introduction
In the first scheme, with the solenoid inside the interferometer and its flux switched from an initial to a final value, the total phase difference is the particle charge times the sum of the initial and final flux, divided by twice h-bar — the average flux enclosed during the passage. To the authors’ knowledge this is the first Aharonov–Bohm scheme in which the electric and the magnetic field configurations both necessarily contribute, whatever spacetime surface is chosen: a truly electromagnetic Aharonov–Bohm effect.First topological scheme, closing paragraph
Connect the two Faraday cages with a metallic wire and the phase difference depends on which side of the solenoid the wire is routed: run it one way and the answer is set by the initial flux alone, run it the other way and it is set by the final flux alone. The spacetime diagram predicts this immediately, where the conventional accumulation picture requires three separate contributions to be added.Second topological scheme, figs. 2(b) and 2(c)
With the solenoid outside the interferometer and the connecting wire wound N turns around it, the phase difference becomes N times the charge times the change in flux, divided by h-bar — an amplification by the number of turns, with the sign set by the winding direction.Third topological scheme, fig. 3
A demonstration of the electric Aharonov–Bohm effect for free electrons has remained elusive. What to watch: the N-turn amplification is offered as the route that could make it observable, together with the dispersionless nature of the effect.Third topological scheme; Discussion and conclusion
The way in
https://doi.org/10.1209/0295-5075/add416How to cite it
P. L. Saldanha, H. Batelaan (2025) Topological schemes in spacetime for the electrodynamic Aharonov-Bohm effect doi:10.1209/0295-5075/add416