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.
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.
as written by the authors arXiv:2605.08148
The electric Aharonov-Bohm effect -- a time-dependent scalar potential imparting a measurable phase shift on electrons in a region free of electromagnetic fields -- has never been experimentally tested in its original formulation with shielded, time-dependent potentials. This unexplored regime offers a rare opportunity: the Lorenz condition $$\partial_\mu A^\mu = 0$$, a choice that eliminates a scalar degree of freedom from the electromagnetic potential, may not be the last word. If the Stueckelberg scalar $$B = \partial_\mu A^\mu$$ survives as a physical field and couples to matter, it would produce a phase shift with a distinctive $$1-\cos(\omega T)$$ signature -- orthogonal to the standard $$\sin(\omega T)$$ and separable by a frequency sweep even if both contributions coexist. We propose a measurement protocol based on single-electron interferometry with picosecond time resolution, within reach of current technology. The experiment asks a question that has lingered since 1959: is the Lorenz gauge a matter of convenience, or a matter of principle?
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.