A geometrical origin for the covariant entropy bound

TL;DR

This paper proposes a geometric framework linking causal diamond-shaped space-time subsets, operator algebras, and the covariant entropy bound, introducing a non orthomodular net to explain holographic degrees of freedom and light-sheet conditions.

Contribution

It introduces a non orthomodular causal set net that implements a covariant cutoff, offering a new geometric perspective on the covariant entropy bound.

Findings

Non orthomodular net explains non positive expansion condition.

Provides a covariant formulation of the entropy bound.

Links space-time geometry with holographic degrees of freedom.

Abstract

Causal diamond-shaped subsets of space-time are naturally associated with operator algebras in quantum field theory, and they are also related to the Bousso covariant entropy bound. In this work we argue that the net of these causal sets to which are assigned the local operator algebras of quantum theories should be taken to be non orthomodular if there is some lowest scale for the description of space-time as a manifold. This geometry can be related to a reduction in the degrees of freedom of the holographic type under certain natural conditions for the local algebras. A non orthomodular net of causal sets that implements the cutoff in a covariant manner is constructed. It gives an explanation, in a simple example, of the non positive expansion condition for light-sheet selection in the covariant entropy bound. It also suggests a different covariant formulation of entropy bound.