On the molecular forces acting between macroscopic bodies

The eigenfrequencies are identified for two electromagnetically coupled semi-infinite solids with plane-parallel surfaces (two half-spaces) separated by a third, polarizable body. The corresponding van der Waals-London and Casimir forces are calculated from the zero-point energy (vacuum fluctuations) of the normal modes. It is shown how the results can be extended to bodies of any shape; in particular, the force is given for a sphere interacting with a half-space. The calculations are performed using the well-known Drude-Lorentz (plasma) model of (non-magnetic) polarizable matter. The polarization degrees of freedom are explicitly introduced. It is shown that the polarization dynamical variables for the two bodies are coupled through the electromagnetic field, very similar with two infinite sets of coupled harmonic oscillators.