Information-Theoretic Natural Ultraviolet Cutoff for Spacetime

Abstract

Fields in spacetime could be simultaneously discrete and continuous, in the same way that information can. It has been shown that the amplitudes phi(x(n)) that a field takes at a generic discrete set of points x(n) can be sufficient to reconstruct the field phi(x) for all x, namely, if there exists a certain type of natural ultraviolet (UV) cutoff in nature, and if the average spacing of the sample points is at the UV-cutoff scale. Here, we generalize this information-theoretic framework to spacetimes themselves. We show that samples taken at a generic discrete set of points of a Euclidean-signature spacetime can allow one to reconstruct the shape of that spacetime everywhere, down to the cutoff scale. The resulting methods could be useful in various approaches to quantum gravity.