  We describe an isoelectronic differential apparatus designed to observe the
influence on the Casimir force of the Mott-Anderson metal-insulator transition
in doped semiconductors. Alternative theories of dispersion forces lead to
different predictions for this effect. The investigation of this problem by
standard apparatus, based on absolute measurements of the Casimir force, is
very difficult because the effect is small in the region of sub-micron
separations, where the Casimir force can be measured precisely. The
differential apparatus described here is immune by design to several sources of
error that blur the interpretation of Casimir experiments, like electrostatic
patches, inaccurate determination of plates separation, surface roughness and
errors in the optical data. With the help of the proposed setup it should be
possible to establish conclusively which among the alternative theories of the
Casimir effect for semiconducting test bodies is correct.
