Bordag, Geyer, Klimchitskaya, and Mostepanenko Reply:

The vacuum stresses between a metal half-space and a metal sphere were recently measured at room temperature, in the 0.6-6 &mgr;m range, with an estimated accuracy of 5%. In the interpretation it was assumed that the accuracy was not good enough for observing any thermal effects. We claim that thermal effects are important in this separation range and back up this claim with numerical calculations of the Casimir force at zero temperature and at 300 K, based on tabulated optical data of gold, copper, and aluminum. The effects of dissipation and temperature are investigated and we demonstrate the importance of considering these two corrections together.

We provide a review of both new experimental and theoretical developments in the Casimir effect. The Casimir effect results from the alteration by the boundaries of the zero-point electromagnetic energy. Unique to the Casimir force is its strong dependence on shape, switching from attractive to repulsive as function of the size, geometry and topology of the boundary. Thus the Casimir force is a direct manifestation of the boundary dependence of quantum vacuum. We discuss in depth the general structure of the infinities in the field theory which are removed by a combination of zeta-functional regularization and heat kernel expansion. Different representations for the regularized vacuum energy are given. The Casimir energies and forces in a number of configurations of interest to applications are calculated. We stress the development of the Casimir force for real media including effects of nonzero temperature, finite conductivity of the boundary metal and surface roughness. Also the combined effect of these important factors is investigated in detail on the basis of condensed matter physics and quantum field theory at nonzero temperature. The experiments on measuring the Casimir force are also reviewed, starting first with the older measurements and finishing with a detailed presentation of modern precision experiments. The latter are accurately compared with the theoretical results for real media. At the end of the review we provide the most recent constraints on the corrections to Newtonian gravitational law and other hypothetical long-range interactions at submillimeter range obtained from the Casimir force measurements.