Short-range test of the universality of gravitational constant $G$ at the millimeter scale using a digital image sensor

Abstract

The composition dependence of gravitational constant $G$ is measured at the millimeter scale to test the weak equivalence principle, which may be violated at short range through new Yukawa interactions such as the dilaton exchange force. A torsion balance on a turning table with two identical tungsten targets surrounded by two different attractor materials (copper and aluminum) is used to measure gravitational torque by means of digital measurements of a position sensor. Values of the ratios ${\tilde{G}}_{Al-W}/{\tilde{G}}_{Cu-W}-1$ and ${\tilde{G}}_{Cu-W}/G_N-1$ were $(0.9\pm 1.1_{\mathrm{sta}}\pm 4.8_{\mathrm{sys}})\times 10^{-2}$ and $(0.2\pm 0.9_{\mathrm{sta}}\pm 2.1_{\mathrm{sys}})\times 10^{-2}$ , respectively; these were obtained at a center to center separation of 1.7 cm and surface to surface separation of 4.5 mm between target and attractor, which is consistent with the universality of $G$. A weak equivalence principle (WEP) violation parameter of $\hat{I}{\cdot }_{Al-Cu}(r\sim 1\mathrm{cm})=(0.9\pm 1.1_{\mathrm{sta}}\pm 4.9_{\mathrm{sys}})\times 10^{-2}$ at the shortest range of around 1 cm was also obtained.

submitted to Class. Quantum Grav