Focusing virtual photons: casimir energies for some pairs of conductors

We consider the Casimir energy E of a pair of conductors, E( parallel) for parallel plates, E(|o) for a plate and a sphere, E(oo) for two separated spheres, and E( middle dot in circle) for one sphere inside the other. We also obtain E((o) for an open shell and a sphere, a configuration which might be experimentally preferable. Semiclassically the Casimir energy is given by the optical properties of the system of coaxial mirrors, with focal lengths f(1) and f(2), a distance l<

Long-Range (Casimir) Interactions

Normally, nonrelativistic electromagnetic theory with two-particle Coulombic interactions adequately determines the interaction potential of systems A and B if the systems are composed of particles with characteristic velocities much less than the speed of light. If, however, the time it takes light to travel between A and B exceeds a characteristic oscillation period of A or B, the way in which the potential function depends on the separation of the systems can be altered. Called the Casimir effect, it has only recently been confirmed, and it arises in physics, chemistry, and biology. It is the clearest physical manifestation of the fact that, even in a vacuum, electromagnetic fields cannot all vanish.