  We measure the fundamental noise processes associated with a continuous
linear position measurement of a micromechanical membrane incorporated in a
microwave cavity optomechanical circuit. We observe the trade-off between the
two fundamental sources of noises that enforce the standard quantum limit: the
measurement imprecision and radiation-pressure backaction from photon shot
noise. We demonstrate that the quantum backaction of the measurement can
overwhelm the intrinsic thermal motion by 24 dB, entering a new regime for
cavity optomechanical systems.
