Reexamination of the Abraham-Minkowski dilemma

Here the Abraham-Minkowski controversy on the correct definition of the light momentum in a macroscopic medium is revisited with the purpose to highlight that an effective medium formalism necessarily restricts the available information on the internal state of a system, and that this is ultimately the reason why the dilemma has no universal solution. Despite these difficulties, it is demonstrated that in the limit of no material absorption and under steady-state conditions, the time-averaged light (kinetic) momentum may be unambiguously determined by the Abraham result, both for bodies at rest and for circulatory flows of matter. The implications of these findings are discussed in the context of quantum optics of moving media, and we examine in detail the fundamental role of the Minkowski momentum in such a context.

Figure 1

(a) A generic circulatory flow of polarizable neutral matter. (b) Simplified mathematical model for the circulatory flow, where the end effects are modeled with periodic boundaries. (c) A cavity formed by two interacting systems $A$ and $B$ separated by a distance $d$. The system $B$ is at rest, while the system $A$ corresponds to a circulatory flow of polarizable neutral matter.