Limits on the Applicability of Classical Electromagnetic Fields as   Inferred from the Radiation Reaction
  Can the wavelength of a classical electromagnetic field be arbitrarily small, or its electric field strength be arbitrarily large? If we require that the radiation-reaction force on a charged particle in response to an applied field be smaller than the Lorentz force we find limits on the classical electromagnetic field that herald the need for a better theory, i.e., one in better accord with experiment. The classical limitations find ready interpretation in quantum electrodynamics. The examples of Compton scattering and the QED critical field strength are discussed. It is still open to conjecture whether the present theory of QED is valid at field strengths beyond the critical field revealed by a semiclassical argument. 
Kirk T. McDonald