Test of the gravitational inverse square law at millimeter ranges.

We report a new test of the gravitational inverse square law at millimeter ranges by using a dual-modulation torsion pendulum. An I-shaped symmetric pendulum and I-shaped symmetric attractors were adopted to realize a null experimental design. The non-Newtonian force between two macroscopic tungsten plates is measured at separations ranging down to 0.4 mm, and the validity of the null experimental design was checked by non-null Newtonian gravity measurements. We find no deviations from the Newtonian inverse square law with 95% confidence level, and this work establishes the most stringent constraints on non-Newtonian interaction in the ranges from 0.7 to 5.0 mm, and a factor of 8 improvement is achieved at the length scale of several millimeters.