Local relative motion in general relativity

The distinction is drawn between problems in which single particle motion has physical significance and those in which relative motion between pairs of particles must be considered. Local relative motion is considered from the standpoint of the equation of geodesic deviation, expressed in arbitrary coordinates and in geodesic Fermi coordinates. A simple alternative approach to geodesic deviation using synchronous reference frames is described. Examples of relative motion in the Schwarzschild field and in a gravitational wave are discussed. Criticism of the efficacy of cryogenic cooling to enhance gravitational wave detector sensitivity is shown to be invalid. However, a cautionary note is expressed with regard to the necessity of a local observer to detect deviations from local planeness.