Influence of the residual gas damping noise in the test of the gravitational inverse-square law

Many theories, such as the unification theories that would include gravitation, predict deviations from Newtonian inverse-square law (ISL) at short range. Many high precision experiments have been performed, but additional experiments are still of high scientific importance. Here, we discuss the torque thermal noise caused by residual gas damping, especially the effect of squeeze-film damping, in a proposed ISL experiment at the range of tens of microns. In such experiments, torsion pendulums are usually used to probe the torque interactions between the detector and the attractor, of which the thermal noise should be considered carefully due to the high sensitivity. By introducing a thermal accommodation coefficient, we can accurately model the torque noise of the residual gas damping as a combination of elastic and inelastic collisions. The results show that the noise will increase significantly at short separations between the pendulum and the surrounding components. In particular, when the separation is smaller than 40 μm, the squeeze-film damping may be larger than the internal damping of the pendulum used in present experiments, and become the fundamental limit for the experiments in the shorter range. (paper)