Experimentally Probing the Shape of Extra Dimensions

In recent years, theories with compact extra dimensions have become increasingly popular. In some models, the standard model particles are confined to our four-dimensional world, and only gravity can propagate in the extra dimensions. In such models, the size of the extra dimensions can be as large as hundreds of microns. The functional dependence of the gravitational force on distance is well known at both large and small distances, compared to the size of the extra dimensions; for two extra dimensions, for example, it varies from 1/r to 1/r as the distance decreases. However, the dependence for intermediate distances has not been fully calculated. We determine this dependence as a function of both the size of the extra dimensions and the possible angle between the extra dimensional unit vectors, and show that high precision measurements of the gravitational force will allow the determination of the shape of the extra dimensions. Email: [email protected] Email: [email protected]