On Fields with Finite Information Density

TL;DR

This paper proves mathematical conjectures related to modeling a natural ultraviolet cutoff at the Planck scale as an information density bound, using generalized communication theory methods.

Contribution

It provides rigorous proof for conjectures on modeling ultraviolet cutoff as an information density limit in physical theories.

Findings

Mathematically validated the conjectures on information density bounds.

Established a formal link between ultraviolet cutoff and information theory.

Enhanced understanding of fundamental limits in physical models.

Abstract

The existence of a natural ultraviolet cutoff at the Planck scale is widely expected. In a previous Letter, it has been proposed to model this cutoff as an information density bound by utilizing suitably generalized methods from the mathematical theory of communication. Here, we prove the mathematical conjectures that were made in this Letter.