Echo of the Void: How to Catch the Invisible express

Original: "Beyond the Lorenz Gauge: Probing a Stueckelberg Scalar in the Electric Aharonov-Bohm Effect"
· Renato Vieira dos Santos
arXiv:2605.08148 · 2026-05-03 · CC BY 4.0 · 2 min
The electric version of the Aharonov–Bohm effect with time-varying voltages is finally being prepared for a laboratory test.

A palm hovering over a hot stove feels the heat even when the surrounding air seems cool. Something similar happens to electrons in the Aharonov–Bohm effect: the particle senses an electric voltage even though it enters a region where the field has already been switched off. The electric version of the effect, where a voltage (scalar potential) changes over time and shifts the phase of the electron wave, has so far existed only on paper. No one has run an experiment with shielded, time-varying potentials.

The authors of the new work propose to close this gap. The idea is to send single electrons through an interferometer and apply a short voltage pulse to a shielded region. If the scalar part of the potential is not just a mathematical convenience but a real field, the electron will feel it and produce a characteristic phase shift. This shift depends on the pulse frequency not as a sine (the usual contribution) but as one minus cosine. The two signals are orthogonal: they can be separated by smoothly varying the frequency.

It all comes down to the Lorenz condition — a mathematical rule that “crosses out” one of the components of the electromagnetic potential. But what if nature keeps it as a hidden field?

The experiment will require picosecond precision — the pulse timing is comparable to the electron's transit through the device. Such technology already exists. Essentially, the experiment asks a question that has hung in the air since 1959: Is the Lorenz condition just a convenient choice or a fundamental law? The answer may show that “empty” space is not so empty, and electrons sense what we have grown used to calling invisible. Like a palm over a cooling stove — the heat is gone, but its trace can still be caught.

The electric Aharonov–Bohm effect is like warming your hands over a stove that has been turned off: the heat is already gone, but the wave of warmth hasn't reached your palms yet. Only here, instead of heat, it's electric voltage, and instead of palms, it's an electron.

Scientists
Yakir AharonovDavid BohmMichael BerryKarl SchwarzschildJulian Schwinger
Concepts
Aharonov–Bohm effect bohr magneton anomalous hall effect free electron electric field sensor electric current coulomb constant landau level atomic units scale factor lomb scargle periodogram Lorentz transformations Vlasov equation polarizability polarization measurement bell test scalar charge exchange interaction bohr radius electron charge