Casimir forces without the vacuum radiation field

Abstract

Although the electromagnetic Casimir forces are customarily explained in terms of the vacuum radiation field, they may also be understood in terms of radiation reaction, without explicit reference to the vacuum field. In particular, the Casimir forces may be obtained if one recognizes that the radiation reaction field of a dipole on itself depends on where the dipole is located, for this field is determined by the modal characteristics of the surrounding space. Only in infinite free space does the field of radiation reaction have a spatially invariant meaning. The fact that the Casimir forces may be understood in terms of either the vacuum electromagnetic field or the field of radiation reaction is an example of the general fluctuation-dissipation relation between the two concepts. These ideas are illustrated with derivations of several "vacuum-field effects," including the Casimir-Polder attraction of an atom to a conducting wall and the van der Waals force between two atoms.