New null experiment to test the inverse square law of gravitation

Abstract

A "source-independent" null experiment for the Newtonian law of gravity is proposed. The new scheme involves detection of the Laplacian of the gravitational potential ${\nabla }^2\phi \left(\overrightarrow{\mathrm{r}}\right)$ in free space, i.e., where $\rho \left(\overrightarrow{\mathrm{r}}\right)=0\mathrm{}$. This quantity should vanish identically regardless of the mass distribution in the rest of the universe if the inverse square law is exact. A departure from null in ${\nabla }^2\phi \left(\overrightarrow{\mathrm{r}}\right)$ could be measured by monitoring the breathing mode of a sphere or by summing three gravity gradients at a single point along any three orthogonal directions. The "source-independent" behavior of the proposed technique will allow a test of the inverse square law in the intermediate range between 1 m and 10 km in which large geological objects might be used as sources.