In this framework, the gravitational and gauge interactions become united at the weak scale, which we take as the only fundamental short distance scale in nature. The observed weakness of gravity on distances mm is due to the existence of new compact spatial dimensions large compared to the weak scale. The Planck scale is not a fundamental scale; its enormity is simply a consequence of the large size of the new dimensions. While gravitons can freely propagate in the new dimensions, at sub-weak energies the Standard Model (SM) fields must be localized to a 4-dimensional manifold of weak scale "hickness" in the extra dimensions. This picture leads to a number of striking signals for accelerator and laboratory experiments. For the case of n = 2 new dimensions, planned sub-millimeter measurements of gravity may observe the transition from Newtonian gravitation. For any number of new dimensions, the LHC and NLC could observe strong quantum gravitational interactions. Furthermore, SM particles can be kicked off our 4 dimensional manifold into the new dimensions, carrying away energy, and leading to an abrupt decrease in events with high transverse momentum . For certain compact manifolds, such particles will keep circling in the extra dimensions, periodically returning, colliding with and depositing energy to our four dimensional vacuum with frequencies of or larger. As a concrete illustration, we construct a model with SM fields localised on the 4-dimensional throat of a vortex in 6 dimensions, with a Pati-Salam gauge symmetry in the bulk.