Retarded van der Waals Forces at All Distances Derived from Classical Electrodynamics with Classical Electromagnetic Zero-Point Radiation

Abstract

The van der Waals forces between a polarizable particle and a conducting wall and between two polarizable particles are calculated within the theory of classical electrodynamics with classical electromagnetic zero-point radiation. This theory assumes the differential equations of traditional classical electrodynamics but changes the homogeneous boundary condition on Maxwell's equations to correspond to the presence of random classical electromagnetic radiation with a Lorentz-invariant spectrum. The van der Waals force calculations are performed exactly within the nonrelativistic equations of motion for the particles represented as point-dipole oscillators. The classical results are found to agree identically to all orders in the fine-structure constant $\ensuremath{\alpha}$ with the nonrelativistic quantum electrodynamic calculations of Renne. To fourth order, there is agreement with the perturbation-theory work of Casimir and Polder.