N ov 2 00 1 Sub - mm gravity : confronting the modified dynamics with higher - dimensional theories

We propose that future experiments aiming at the detection of deviations from the 1/r 2 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 m ≈ 1g at distances r ≈ 200 µm, implying that they are probing accelerations well above the MOND limit (a 0 ≈ 1.2 × 10 −8 cms −2). We show that MONDian effects begin to be important at the submillimetric level for masses m ≤ 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.