  We examine whether fluctuation-induced forces can lead to stable levitation.
First, we analyze a collection of classical objects at finite temperature that
contain fixed and mobile charges, and show that any arrangement in space is
unstable to small perturbations in position. This extends Earnshaw's theorem
for electrostatics by including thermal fluctuations of internal charges.
Quantum fluctuations of the electromagnetic field are responsible for
Casimir/van der Waals interactions. Neglecting permeabilities, we find that any
equilibrium position of items subject to such forces is also unstable if the
permittivities of all objects are higher or lower than that of the enveloping
medium; the former being the generic case for ordinary materials in vacuum.
