  Using the generalized Langevin equations involving the stress tensor
approach, we study the dynamics of a perfectly reflecting mirror which is
exposed to the electromagnetic radiation pressure by a laser beam in a fluid at
finite temperature. Based on the fluctuation-dissipation theorem, the minimum
uncertainty of the mirror's position measurement from both quantum and thermal
noises effects including the photon counting error in the laser interferometer
is obtained in the small time limit as compared with the "standard quantum
limit".
  The result of the large time behavior of fluctuations of the mirror's
velocity in a dissipative environment can be applied to the laser
interferometer of the ground-based gravitational wave detector.
