I recently read somewhere that the predictions of QED in the classical limit haven't been nearly as well-studied as, say, the classical limit of quantum mechanics. This is a little confusing: doesn't QED just reduce to Maxwellian electrodynamics with additional small nonlinear quantum mechanical terms? If that's the case, it would seem that classical QED has been studied. Does the comment imply that Maxwell's equations with the nonlinear terms haven't been deeply investigated? What else might remain of classical QED predictions to study?