Barrow entropy and spacetime foam

TL;DR

This paper explores the relationship between quantum fluctuations, spacetime discreteness, and measurement limitations using Barrow entropy to model fractal spacetime structure, linking it to information processing speed.

Contribution

It introduces a novel connection between Barrow entropy parameters and spacetime measurement accuracy, emphasizing the fractal nature of quantum foam.

Findings

Barrow entropy characterizes spacetime fractality.

Measurement inaccuracy relates to Barrow entropy parameter.

Spacetime fractality influences information processing speed.

Abstract

Quantum gravitational effects, on the one hand, lead to a limitation in the accuracy of measuring spatial and time intervals, and, on the other hand, they generate a discrete of spacetime structure (quantum foam). The common source of both measurement limitations and discreteness of space-time are quantum fluctuations, so their characteristics must be related to each other. We study such a relationship using Barrow entropy as a source of fractal space-time structure. The minimum inaccuracy in measuring space-time intervals is expressed through the Barrow entropy parameter. The connection between the level of fractality and the speed of information processing is considered.