Shearing the vacuum - quantum friction

We consider two perfectly smooth featureless surfaces at T = 0, defined only by their respective dielectric functions, separated by a finite distance, and ask the question of whether they can experience any friction when sheared parallel to their interface. We find large frictional effects comparable to everyday frictional forces provided that the materials have resistivities of the order of 1 m Omega and that the surfaces are in close proximity. The friction depends solely on the reflection coefficients of the surfaces for electromagnetic waves and its detailed behaviour with shear velocity and separation is dictated by the dispersion of the reflectivity with frequency.