Rotating Torsion Balance Tests of the Weak Equivalence Principle

Abstract

We used a rotating torsion balance to make the most precise laboratory search for equivalence-principle violation. We used a beryllium-aluminum composition dipole to complement our previous measurement with a beryllium-titanium composition dipole. We improved the tilt stability of the apparatus and reduced the temperature gradient feed-through to improve the uncertainty by 30% compared to our beryllium-titanium result. Using the beryllium-aluminum test bodies, we found $\eta_{\oplus} = (-1.3\pm1.2)\times10^{-13}$. The combined limits using both test bodies pairs generally limit any new equivalence-principle-violating force that couples to ordinary neutral matter. We also measured test-bodies with compositions that mimic the difference in composition between the earth and moon to provide a model-independent weak equivalence principle limit of $\eta_{\rm CD} = (1.2 \pm 1.1) \times 10^{-13}$ for comparison with lunar laser ranging strong equivalence principle measurements. The combined lunar laser ranging and weak equivalence principle measurements limit equivalence-principle violation for gravitational binding energy to $\lesssim 6\times 10^{-4}$ at 1-$\sigma$.