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Does the Feigel effect break the first law?

A recent theory posits that the quantum vacuum can transfer momentum to magnetoelectric media (the Feigel effect). Several related theories of vacuum momentum transfer to media have since been proposed. Neither these, nor the original theory have been observed experimentally, the existence a Feigel effect remaining highly contentious. Some investigations predict a measurable effect; others conclude vacuum momentum transfer to magnetoelectric media is not physically possible. Most analyses, including the original Fiegel theory, do not model experimentally realistic geometries and boundary conditions. I recently provided an alternative derivation of Feigel theory applied to realistic geometries, proposing experimental tests. I show here that in such geometries the existence of a steady Feigel effect (time-independent magnetoelectric susceptibilities) is equivalent to a violation of the first law of thermodynamics. A steady Feigel effect should not exist, as confirmed by a semi-classical quantum electrodynamic analysis. However, unsteady Feigel effects compatible with QED and thermodynamics are possible, and two such new effects are proposed.