Measurement of gravitational coupling between millimetre-sized masses

Abstract

Gravity is the weakest of all known fundamental forces and poses some ofthe most important open questions to modern physics: it remains resistant to unification within the standard model of physics and its underlying concepts appear to be fundamentally disconnected from quantum theory1-4. Testing gravity at all scales is therefore an important experimental endeavour5-7. So far, these tests have mainly involved macroscopic masses at the kilogram scale and beyond8. Here we show gravitational coupling between two gold spheres of 1 millimetre radius, thereby entering the regime of sub-100-milligram sources ofgravity. Periodic modulation ofthe position ofthe source mass allows us to perform a spatial mapping ofthe gravitational force. Both linear and quadratic coupling are observed as a consequence ofthe nonlinearity ofthe gravitational potential. Our results extend the parameter space ofgravity measurements to small, single source masses and low gravitational field strengths. Further improvements to our methodology will enable the isolation ofgravity as a coupling force for objects below the Planck mass. This work opens the way to the unexplored frontier of microscopic source masses, which will enable studies of fundamental interactions9-11 and provide a path towards exploring the quantum nature ofgravity12-15.