Universal entropy bound and discrete space-time

TL;DR

This paper derives a discrete space-time structure from universal entropy bounds, explaining quantum uncertainty and determining key parameters through black hole entropy and information theory.

Contribution

It introduces a discrete space-time model based on entropy bounds, providing a theoretical foundation for quantum uncertainty and fixing the cutoff parameter.

Findings

Derived a space and time cutoff from entropy bounds.

Connected discrete space-time to the uncertainty principle.

Determined the parameter hi from black hole entropy and information theory.

Abstract

Starting from the universal entropy bounds suggested by Bekenstein and Susskind and applying them to the black-body radiation situation, we get a cut-off of space $ \Delta x \geq \chi l_{\mathrm{P}}$ with $\chi \geq 0.1$. We go further to get a cut-off of time $ \Delta t \geq \chi l_{\mathrm{P}}/c $, thus, the discrete space-time structure is obtained. With the discrete space-time, we can explain the uncertainty principle. Based on the hypothesis of information theory and the entropy of black holes, we get the precise value of the parameter $\chi$ and demonstrate the reason why the entropy bounds hold.