A mirror scattering vacuum fields is submitted to a quantum fluctuating
radiation pressure. It also experiences a motional force, related to force
fluctuations through fluctuation-dissipation relations. The resulting position
fluctuations of the coupled mirror are related to the dissipative part of the
mechanical admittance. We compute the time dependent position commutator, which
makes apparent the difference between the low-frequency and high-frequency
masses, and the anticommutator noise spectrum, which describes the ultimate
sensitivity in a length measurement using mirrors.Comment: 12 page
