Casimir Effect

Abstract

The Casimir effect is a force associated with the ►zero-point energy of a field. The effect originally considered by Hendrik B. G. Casimir (1909–2000) is the attraction between two uncharged, perfectly conducting plates (Fig. 1). According to quantum theory, there is energy in the electromagnetic field even at the absolute zero of temperature. For a field of frequency ν, this energy is ½hν, identical to the zero-point energy of a harmonic oscillator having the same frequency. The total zero-point energy is then ½h times the sum over all the field frequencies, these being determined by Maxwell’s equations and the boundary conditions. In the example of Fig. 1, Maxwell’s equations allow field modes of arbitrarily large frequency both between the plates and outside them, and therefore the zero-point field energy is infinite when the plates are separated by a finite distance d as well as when they are infinitely far apart. However, the difference in zero-point energy for the two cases is finite, and its dependence on the plate separation d implies a force F = − πhc/480d 4 per unit area.