Information-theoretic natural ultraviolet cutoff for spacetime

TL;DR

This paper extends an information-theoretic approach to demonstrate that a discrete sampling of spacetime can reconstruct its continuous geometry at a natural ultraviolet cutoff scale, with implications for quantum gravity.

Contribution

It generalizes the sampling framework from fields to entire spacetimes, enabling reconstruction of spacetime geometry from discrete samples at the UV cutoff scale.

Findings

Spacetime can be reconstructed from discrete samples at the UV cutoff.

Sampling at the cutoff scale suffices for full spacetime reconstruction.

Potential applications in quantum gravity approaches.

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.