Space-time uncertainty relation from quantum and gravitational principles

TL;DR

This paper derives a space-time uncertainty relation combining quantum and gravitational principles, which has implications for understanding the universe's computational limits, thermodynamics, and dark energy.

Contribution

It introduces a new space-time uncertainty relation based on quantum and gravitational principles, applicable to cosmological and holographic phenomena.

Findings

The relation links space-time uncertainties with universe properties.

It supports discussions on the universe's computational capacity.

It provides insights into holographic dark energy.

Abstract

By collecting both quantum and gravitational principles, a space-time uncertainty relation $(\delta t)(\delta r)^{3}\geqslant\pi r^{2}l_{p}^{2}$ is derived. It can be used to facilitate the discussion of several profound questions, such as computational capacity and thermodynamic properties of the universe and the origin of holographic dark energy. The universality and validity of the proposed relation are illustrated via these examples.