the anomalous magnetic moment (g-2)

An electron behaves like a tiny spinning magnet, and how strong that little magnet is gets summarized in a number called g. The simplest quantum theory, Dirac's equation, predicts g should be exactly 2. Experiment, however, finds g is a hair larger than 2 — by about a tenth of a percent. That tiny excess, the gap between the measured g and the clean prediction of 2, is the 'anomalous' magnetic moment, often written g-2.

Where does the extra bit come from? From the electron constantly interacting with the seething quantum vacuum around it. As it sits in a magnetic field, the electron is forever emitting and reabsorbing virtual photons, and briefly conjuring virtual electron-positron pairs, and each of these processes nudges its effective magnetism. QED lets physicists calculate the anomaly as a series in the fine-structure constant: the leading correction, worked out by Schwinger in 1948, is simply alpha divided by two-pi, and successive terms add ever-smaller refinements computed from thousands of diagrams.

The electron's g-2 is the single most precisely verified prediction in science: theory and experiment agree to roughly twelve significant figures. This staggering match is the crown jewel of QED and a triumph of the whole quantum-field-theory framework. The muon's g-2 is even more interesting today: measurements have hinted at a small discrepancy with the prediction, which — if it holds up — could be the first crack revealing new particles beyond the Standard Model, though the situation remains unsettled.