Sub-mm gravity: confronting the modified dynamics with higher-dimensional theories

Abstract

We propose that future experiments aiming at the detection of deviations from the inverse square gravitational law on submillimetric scales can be used to test the modified Newtonian dynamics theory (MOND). Current experiments are able to test the gravitational field of masses of approximately 1g at distances around 200 micrometers, implying that they are probing accelerations well above the MOND limit (1.2 X 10^{-8} cms^{-2}). We show that MONDian effects begin to be important at the submillimetric level for masses below 1 mg. MOND makes predictions that are clearly distinguishable from those expected in a scenario with compact extra dimensions. This will enable direct confrontation between the two theories if future experiments can improve their mass scales to the milligram level.