**Adrian Parsegian**

*LPSB/NICHD/NIH**Bethesda, MD 20892 U.S.A.*

Rudi Podgornik

*LPSB/NICHD/NIH and**Univ. Ljubljana, Slovenia*

Most materials are not ideal conductors; interfaces are not
step functions. The Lifshitz formulation liberated Casimir theory
from its ideal-conductor assumption. This talk will consider
interfaces with spatially graded dielectric response in the direction
perpendicular to the parallel faces of interacting planar bodies.
We have recently followed earlier work with Jim Kiefer & George
Weiss to extend the Lifshitz result for any spatial variation
of dielectric response normal to the faces of interacting half-spaces.
Working in a macroscopic-continuum limit, we are able to include
the consequences of retardation and finite temperature. Noisome
contact divergences in the interaction free energy can be made
to disappear. New facility emerges to formulate interactions
involving spatially inhomogeneous systems.