In many quantum-mechanical measurements, the total uncertainties (\ensuremath{\sigma}) are greater than or equal to the intrinsic uncertainties (${\ensuremath{\sigma}}_{I}$) of the quantities to be measured; the differences are due to the particular measurement processes chosen. In each of these situations, a measurement uncertainty ${\ensuremath{\sigma}}_{M}$ can be defined as ${\ensuremath{\sigma}}_{M}$=(${\ensuremath{\sigma}}^{2}$-${\ensuremath{\sigma}}_{I}$
2)1/2. A question to ask is whether ${\ensuremath{\sigma}}_{M}$ is independent of the initial quantum state of the system to be measured, i.e., whether ${\ensuremath{\sigma}}_{M}$ is only dependent on the measurement process chosen. For a Michelson interferometer, we extend Loudon's model to show that in the model ${\ensuremath{\sigma}}_{M}$ is only dependent on the measurement process chosen for the case with small radiation-pressure fluctuation. When the intensity and radiation-pressure fluctuation are high, there are cross-correlated terms. Some of these terms are negative and give hope to the possibility of uncertainty reductions for appropriate schemes.
We discuss quantum measurements of position and repeated-measurement schemes for monitoring free-mass position to an arbitrary accuracy. Using these schemes, weak classical forces can be monitored to an arbitrary accuracy. To illustrate various measurement uncertainties and intrinsic uncertainties, we consider the case of a Michelson interferometer. In the low-intensity limit, two measurement uncertainties, photon counting error and radiation pressure error, are independent of the intrinsic uncertainty. The uses of squeezed states and number eigenstates are discussed.