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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.
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The last decades have seen numerous experimental confirmations of Einstein's theory of relativity, our best working theory of gravity, by observing massive astronomical objects and their dynamics5,16. This culminated in the recent direct detection ofgravitational waves from the merger of two black holes17 and the direct imaging of a supermassive black hole18. Meanwhile, Earth-bound experiments have been continuously increasing their sensitivity to gravity phenomena at laboratory scales, including general relativistic effects19,20, tests of the equivalence principle6,21, precision measurements of Newton's constant22-24 and tests of the validity of Newton's law at micrometre-scale distances25-27. Although test masses in such experiments span the whole range from macroscopic objects to individual quantum systems19-21,24,28, the gravitational source is typically either Earth or masses at the kilogram scale and beyond8. This is contrasted by an increasing interest to study gravitational phenomena originating from quantum states of source masses, for example, in the form of 'quantum Cavendish experiments'1,12-14,29. Because quantum coherence is easily lost for increasing system size, it is important to isolate gravity as a coupling force for as small objects as possible.
Experiments with...