  Current theory is able to predict the Casimir force between macroscopic
bodies with an accuracy only limited by the knowledge of the material
parameters. Yet surprisingly after almost 70 years of research, while theory
describes the Casimir force between bodies, the force inside macroscopic bodies
is poorly understood. In this paper, we develop from a physically intuitive
picture the macroscopic theory of the Casimir stress inside inhomogeneous
planar media. Our result agrees with a previous ad hoc procedure [T. G. Philbin
et al., Ann. Phys. (New York) 325, 579 (2010)], giving both mathematical and
physical justification to a conjecture that was only tested numerically so far.
Our theory is likely to be extendable; it may open the gate to the computation
of Casimir forces inside arbitrary materials.
