06 — The Disagreement

5.5σ

two of the best measurements of α ever made  —  and they don't agree

This site has already called α⁻¹ = 137.035999177(21) the most precisely known number describing how strongly light and matter interact. That CODATA figure is itself an average, smoothing over something the average hides: the two most careful direct measurements of α ever made, done independently, on opposite sides of an ocean, do not actually agree with each other.

137.035999046(27)  –  137.035999206(11)

In 2018, a team at UC Berkeley led by Holger Müller measured α by watching cesium-133 atoms recoil after absorbing a single photon, using a matter-wave interferometer accurate to 2 parts in 10 billion. In 2020, a team at Laboratoire Kastler Brossel in Paris ran the same kind of experiment on rubidium atoms instead of cesium, reaching 81 parts per trillion — three times finer. Both experiments rest on the same physics and the same basic method. Their two answers differ starting in the ninth decimal place, by more than their combined margin of error allows — about five and a half standard deviations apart, the kind of gap that isn't supposed to happen twice by chance.

A third, unrelated measurement sits between them without settling anything. In 2023, a Harvard group led by Gerald Gabrielse measured the electron's own magnetic moment to 0.13 parts per trillion inside a single-electron trap — the most precisely known property of any elementary particle. Run through the theory of quantum electrodynamics, that number implies α⁻¹ = 137.035999166(15), a value ten times more certain than the gap between Paris and Berkeley, and closer to the rubidium result than the cesium one. It leans toward an answer without being able to referee: it depends on QED itself holding exactly true, which is the very thing all three experiments are ultimately testing.

Researchers on both the Paris and Berkeley teams have said the mismatch probably has nothing to do with the choice of cesium or rubidium — more likely, something in one of the two setups hasn't been accounted for. Both groups have rebuilt parts of their apparatus since and plan to measure again. Until one of those remeasurements moves, nobody knows which number is closer to true, or whether the honest answer is both, in ways not yet understood. A constant this well measured should have stopped surprising anyone. It hasn't.