Virtual photon loop: electron jitters ~Δx ≈ α · a₀ · ln(1/α) ≈ 0.001 a₀
Jitter smears the nucleus, reduces binding at s-orbital
2s feels nucleus more → pushed up relative to 2p
In 1947, Willis Lamb and Robert Retherford used microwave techniques to measure the splitting. The result, 1057.77 ± 0.10 MHz, could not be explained by Dirac theory. Hans Bethe made the first theoretical prediction within days using non-relativistic QED — and got 1040 MHz.
The Lamb shift launched modern QED. Today it is computed to 12 significant figures and measured to similar precision. The proton charge radius puzzle (muonic hydrogen Lamb shift) remains an active research topic.