Microscopic origin of Casimir-Polder forces

We establish a general relation between dispersion forces. First, based on QED in causal media, leading-order perturbation theory is used to express both the single-atom Casimir-Polder and the two-atom van der Waals potentials in terms of the atomic polarizabilities and the Green tensor for the body-assisted electromagnetic field. Endowed with this geometry-independent framework, we then employ the Born expansion of the Green tensor together with the Clausius-Mosotti relation to prove that the macroscopic Casimir-Polder potential of an atom in the presence of dielectric bodies is due to an infinite sum of its microscopic many-atom van der Waals interactions with the atoms comprising the bodies. This theorem holds for inhomogeneous, dispersing, and absorbing bodies of arbitrary shapes and arbitrary atomic composition on an arbitrary background of additional magnetodielectric bodies.