  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.
