Submillimeter tests of the gravitational inverse-square law

Motivated by a variety of theories that predict new effects, we tested the gravitational 1/r² law at separations between 10.77 mm and 137μm using two different 10-fold azimuthally symmetric torsion pendulums and rotating 10-fold symmetric attractors. Our work improves upon other experiments by up to a factor of about 100. We found no deviation from Newtonian physics at the 95% confidence level and interpret these results as constraints on extensions of the standard model that predict Yukawa or power-law forces. We set a constraint on the largest single extra dimension (assuming toroidal compactification and that one extra dimension is significantly larger than all the others) of R_*<~160μm, and on two equal-sized large extra dimensions of R_*<~130μm. Yukawa interactions with |α|>~1 are ruled out at 95% confidence for λ>~197μm. Extra-dimensions scenarios stabilized by radions are restricted to unification masses M_*>~3.0TeV/c², regardless of the number of large extra dimensions. We also provide new constraints on power-law potentials V(r)∝r^-k with k between 2 and 5 and on the γ₅ couplings of pseudoscalars with m<~10meV/c².