The electron was slightly more magnetic than expected
An electron behaves like a tiny magnet. Relativistic quantum theory predicted most of its magnetic strength, yet careful atomic measurements in the 1940s found a small excess. At the same time, Willis Lamb and Robert Retherford measured an unexpected separation between two hydrogen energy levels. These were small differences with unusually large consequences: the interaction of an electron with the electromagnetic field needed a more complete quantum treatment.
Quantum electrodynamics, or QED, treats both charged matter and the electromagnetic field quantum mechanically. Light comes in photons, and emission, absorption and scattering are described by probabilities calculated from the theory. Even an electron that emits no real light is affected by quantum electromagnetic processes. Those processes alter the energy levels and magnetic response we measure.
Improving the calculation first produced infinities
The first approximation describes the simplest interaction. More accurate calculations add processes involving additional electromagnetic interactions. In a diagrammatic description, some appear as loops. Summing over the virtual momenta inside them can produce divergent expressions, making a direct calculation seem meaningless.
Sin-Itiro Tomonaga, Julian Schwinger and Richard Feynman developed workable relativistic methods in different forms. Freeman Dyson clarified their relation. The practical breakthrough was not to delete troublesome terms at will. It was to define the theory using quantities an experiment can measure, including the electron’s physical mass and charge, and to organize the remaining corrections consistently.
Sources: [2]
Renormalization turns measured inputs into new predictions
This procedure is renormalization. A useful way to picture it is that the mass and charge assigned to a theoretical symbol must match a stated measurement, after the quantum corrections are included. Once those few inputs are fixed, the theory must predict many other outcomes with the same values. It cannot choose a new electron charge for each spectral line.
A regulator can temporarily make intermediate expressions finite. The important test is whether observable predictions become independent of that temporary device after the measured inputs are fixed. QED supports this organization order by order in its small coupling. This makes successive corrections calculable and makes agreement across different experiments meaningful.
A correction of about one part in a thousand
Schwinger’s 1948 calculation gave a leading excess magnetic moment of about 0.00116 times the basic unit, roughly one part in a thousand. That size explained the direction and scale of the discrepancy. Higher-order calculations and improved experiments later made the comparison far more demanding.
A precision test also needs an independently determined electromagnetic coupling. If the electron magnetic moment is used to extract that coupling, the same comparison cannot then be advertised as an independent test with that input. Atomic recoil measurements and other determinations make such cross-checks possible. The logic is simple: a theory becomes compelling when one measurement fixes an input and another comes out right.
Sources: [1]
Three methods became one durable theory
The 1965 Nobel Prize recognized Tomonaga, Schwinger and Feynman for their fundamental QED work. Their achievement joined relativistic quantum mechanics to a predictive treatment of electromagnetic interactions. The theory’s success lies in relationships among many observables, not in the visual appeal of its diagrams.
Hydrogen spectroscopy and magnetic-moment measurements show the same physical lesson from different sides: an electron’s interaction with the quantum electromagnetic field leaves small, measurable traces. QED provides a way to calculate those traces and to keep improving the calculation as experiments improve.
Sources: [3]