Apparatus to probe the influence of the Mott-Anderson metal-insulator transition in doped semiconductors on the Casimir effect

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 submicron 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, such as 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.