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Repulsive Casimir forces have been proposed for a variety of shapes and materials. A generalization of Earnshaw's theorem constrains the possibility of levitation by QED Casimir forces in equilibrium. The scattering formalism, which forms the basis of this proof, can be used to study fluctuation-induced forces for different materials, diverse geometries, both in and out of equilibrium. Conformal field theory methods suggest that critical (thermal) Casimir forces are not subject to a corresponding constraint. Host: Robert Ecke |