
Discretization of spacetime is a necessary step in quantizing gauge theories, including gravity, when, as a result of quantization, the gaugegroup becomes finite and infenetezimal transformations sieze to make sense. We identify a minimal set of variables of discretized gravity on which Newtonian interaction between two particles can be calculated. The space is discretized by dividing it into quadrants by three threedimensional surfaces intersecting at the worldlines of the particles. The variables needed for calculating Newtonian potential are the holonomies of $SO(4,1)$ connection dual to the above three surfaces plus the holonomies around the images of the particle worldlines on every surface. The equations of motions for these variables are ordinary differential equations with no spatial derivatives. Newtonian portential in the usual form is reproduced from linearized version of these equations, in which the holonomies of $SO(4,1)$ group are replaced by abelian holonomies of $so(4,1)$ algebra. The full equations with $SO(4,1)$ holonomies indicate the presence of a lower bound on the distance between the particles. In the limit when one particle has much bigger mass than the other, this bound corresponds to the Schwarzschild radius of the heavy particle. We discuss the possible implications of this effect for short dictance physics in quantum theory.
