The Casimir effect revisited

Abstract

Using Wick’s normal-ordered expression for the quantum-mechanical energy of a radiation field, so that in absence of matter the zeropoint energy of a radiation field would vanish, the Casimir effect of attraction between uncharged condenser plates in absence of photons will still follow, due to a nonvanishing but finite zeropoint radiation energy in the presence of these plates. If we assume the plates to be transparent for electromagnetic waves of sufficiently high frequency, the remaining zeropoint energy density itself will be finite (and not merely its variation under a change of the distance between the plates). These results are obtained by a more careful consideration of where in sums over modes of vibration one should use sums over running waves with a periodicity condition, where one should sum over standing waves with nodes at conducting boundaries, and where these sums may be replaced by integrals.