Fundamental limits to attractive and repulsive Casimir-Polder forces

We derive upper and lower bounds on the Casimir-Polder force between an anisotropic dipolar body and a macroscopic body, separated by vacuum, via algebraic properties of Maxwell's equations. These bounds require only a coarse characterization of the system---the material composition of the macroscopic object, the polarizability of the dipole, and any convenient partition between the two objects---to encompass all structuring possibilities. We...