Precision limits of the modern Cavendish device: thermal noise measurement regimes and strategies in the torsion pendulum

The lightly damped torsion pendulum is among the most sensitive of mechanical force detectors. Major limits to its sensitivity arise from horizontal gravitational gradients, seismic disturbance and thermal fluctuations. Unlike the other sources, the more fundamental thermal noise can serve as a common theoretical 'standard' against which much of the pendulum's performance can be measured. Nevertheless, its 'pure' statistical character from molecular bombardment is not retained through the processes of pendulum action and those of its measurement, as will be shown. Sensitivity limit studies using thermal fluctuation theory apply to most types of sensitive measurement, not just the torsion pendulum. This theory originated in the context of Brownian motion as developed by Einstein, and incorporates ideas involving random walks. The lightly damped pendulum, however, does not execute a random walk under practical observing conditions. We present a brief history of noise theory, followed by its application to the torsion pendulum. A simple measurement strategy for the static mode pendulum is adopted to develop the subject. Intrinsic noise of the pendulum couple is discussed, in which a natural damping limit appears. Spectral behaviour is seen to be important in understanding the system noise. The spectral character is developed, along with a method of analysis used in precision frequency standards, which can be seen to have useful self-evaluation within it. The equilibrium situation of the lightly damped pendulum presents a practical difficulty in the application of noise theory to lightly damped pendula. Negative derivative feedback is seen as a means of handling this, and of optimizing the measurement conditions.