Limits to the measurement of displacement in an interferometric gravitational radiation detector

Detection of gravitational radiation by some form of Michelson interferometer illuminated by a laser depends on observing the small relative displacements or forces which would be induced in test masses by a gravitational wave. The uncertainty principle would appear to set one limit to the sensitivity for detection of such displacements by a linear position-sensing system such as an optical interferometer. The authors discuss this limit, and also show how one method of treating photon statistics and photon recoil effects yields a similar limit. This is done in the spirit of the 'Heisenberg microscope'.