Casimir force acting on magnetodielectric bodies embedded in media

Abstract

Within the framework of macroscopic quantum electrodynamics, general expressions for the Casimir force acting on linearly and causally responding magnetodielectric bodies that can be embedded in another linear and causal magnetodielectric medium are derived. Consistency with microscopic harmonic-oscillator models of the matter is shown. The theory is applied to planar structures and proper generalizations of Casimir's and Lifshitz-type formulas are given.

Comment on “Casimir force acting on magnetodielectric bodies embedded in media”

“…When inserted into the Raabe-Welsch tensor (1), however, the z + z ′ -dependent terms of the Green's function do not cancel, meaning that T RW zz is z dependent as z → z ′ (the authors of [1] presume without comment that the optical theory of [32] is consistent with their proposed theory). Because of this the Casimir attraction between the two slabs separated by medium 1 is not well defined, since it depends on the exact position of the boundaries of the control surface over which the tensor is integrated.…”

“…In [1] the Casimir force on a plate inside a cavity is calculated in this way and further analysed by Tomaš [24]. It may appear surprising that this rather complicated 5-layered geometry is chosen, as it adds considerable mathematical complications as compared to the simpler three-layer geometry considered by Lifshitz [25] and later by numerous others.…”

“…Our purpose has merely been to investigate the practical usefulness of it. (Note that the authors of [1], after deriving the tensor (1) very generally, applies it exclusively to the Casimir force [6], a quantum mechanical phenomenon in contrast with the classical situation considered above and, for example, in [3]). …”

“…Since Raabe and Welsch predict just such a spatially varying momentum flux, there must be balancing forces present which their stress tensor does not account for. Such balancing forces are not considered in [1]. The reply is that these "additional (internal and external) forces" are not taken into account in the force expression because "only electromagnetic contributions are included in the stress tensor" [6].…”

“…In a recent paper [1], Raabe and Welsch suggested a theory for electromagnetic fields in a medium based on the Lorentz force, from which they derived a stress tensor different from the Abraham-Minkowski tensor traditionally applied in systems where electro-and magnetostrictive forces may be neglected. The same tensor was first proposed by Poincelot many years ago [2], and has more recently been supported by Obukhov and Hehl [3].…”