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

The lightly damped torsion pendulum is among the most sensitive of mechanic al force detectors. Major limits to its sensitivity arise from horizontal g ravitational gradients, seismic disturbance and thermal fluctuations. Unlik e the other sources, the more fundamental thermal noise can serve as a comm on theoretical 'standard' against which much of the pendulum's performance can be measured. Nevertheless, its 'pure' statistical character from molecu lar bombardment is not retained through the processes of pendulum action an d those of its measurement, as will be shown. Sensitivity limit studies using thermal fluctuation theory apply to most ty pes of sensitive measurement, not just the torsion pendulum. This theory or iginated in the context of Brownian motion as developed by Einstein, and in corporates ideas involving random walks. The lightly damped pendulum, howev er, 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 pen dulum is adopted to develop the subject. Intrinsic noise of the pendulum co uple is discussed, in which a natural damping limit appears. Spectral behav iour is seen to be important in understanding the system noise. The spectra l character is developed, along with a method of analysis used in precision frequency standards, which can be seen to have useful self-evaluation with in it. The equilibrium situation of the lightly damped pendulum presents a practical difficulty in the application of noise theory to lightly damped p endula. Negative derivative feedback is seen as a means of handling this, a nd of optimizing the measurement conditions.