Evidence for an entropy bound from fundamentally discrete gravity

TL;DR

This paper proposes a measure for maximal entropy in spherically symmetric regions within causal set quantum gravity, deriving bounds consistent with known entropy bounds like Susskind's, thus linking discrete spacetime to information limits.

Contribution

It introduces a new entropy measure in the causal set approach, connecting discrete quantum gravity with established entropy bounds in a novel way.

Findings

Derives a bound for entropy based on counting degrees of freedom at the Cauchy horizon.

Shows that the proposed measure reproduces Susskind's spherical entropy bound in the continuum limit.

Supports the idea that spacetime discreteness underpins fundamental entropy limits.

Abstract

The various entropy bounds that exist in the literature suggest that spacetime is fundamentally discrete, and hint at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered, but should manifest itself in a theory of quantum gravity. We present a measure for the maximal entropy of spherically symmetric spacelike regions within the causal set approach to quantum gravity. In terms of the proposal, a bound for the entropy contained in this region can be derived from a counting of potential "degrees of freedom" associated to the Cauchy horizon of its future domain of dependence. For different spherically symmetric spacelike regions in Minkowski spacetime of arbitrary dimension, we show that this proposal leads, in the continuum approximation, to Susskind's well-known spherical entropy bound.