Measuring Gravity at Sub-Millimeter Distances

Tests of Newtonian gravity play an important role in constraining possible extensions of the Standard Model. Over the past twenty years, many experiments have tested the inverse-square law (ISL) and the Weak Equivalence Principle (WEP) on distance scales ranging from millimeters to astronomical units without finding deviations from the predictions of Newton's law of gravity. Still, very little is known about gravity between 0.1 mm and the Planck length L_Pl ~ 10^-35 m, where quantum gravitational effects are expected to become important. The possibility that new physics lies within this unexplored territory has initiated new experiments to probe gravity at sub-millimeter scales. Here we briefly review the theoretical motivation for these experiments and develop the phenomenology used to describe modifications of Newtonian gravity that would be caused by new forces and extra spatial dimensions.