renormalization in QED

When physicists first pushed quantum electrodynamics past its simplest predictions, disaster struck. The corrections that were supposed to be small refinements came out infinite. A naive calculation of the electron's energy or charge gave answers like 'infinity,' which is obviously nonsense. For a while it looked as though the whole theory was broken. The cure, worked out around 1947 to 1949, is called renormalization, and it rescued QED.

The key insight is that the quantities appearing in the raw equations — the 'bare' mass and charge of the electron — are not the things we actually measure. What we measure is the electron already dressed in its inescapable cloud of virtual photons and pairs. Renormalization carefully absorbs the troublesome infinities into a redefinition of these bare quantities, replacing them with the finite, measured mass and charge. Once you express predictions in terms of what is actually observed rather than the unobservable bare values, every infinity cancels and finite, sensible answers remain.

This was not a swindle but a deep reorganization of the theory, and it works spectacularly — renormalized QED yields the twelve-digit agreement of the electron's g-2. The same procedure was later shown to apply to the weak and strong forces, making renormalizability a guiding requirement for what counts as a sensible fundamental theory in the Standard Model. The modern understanding, via the renormalization group and effective field theory, is that the infinities reflect our ignorance of physics at unreachably short distances, and renormalization is the disciplined way to make reliable predictions anyway.