Mechanical temporal fluctuation induced distance and force systematic errors in Casimir force experiments

The basic theory of temporal mechanical fluctuation induced systematic errors in Casimir force experiments is developed and applications of this theory to several experiments is reviewed. This class of systematic error enters in a manner similar to the usual surface roughness correction, but unlike the treatment of surface roughness for which an exact result requires an electromagnetic mode analysis, time dependent fluctuations can be treated exactly, assuming the fluctuation times are much longer than the zero point and thermal fluctuation correlation times of the electromagnetic field between the plates. An experimental method for measuring absolute distance with high bandwidth is also described and measurement data presented. (paper)