The Holographic Entropy Bound and Local Quantum Field Theory

TL;DR

This paper demonstrates that the holographic entropy bound can be derived from basic flat-spacetime quantum field theory by imposing a gravitational energy constraint, resulting in an entropy limit consistent with holographic principles.

Contribution

It shows how the holographic bound emerges from elementary quantum field theory with gravitational energy constraints, bridging microphysics and holographic ideas.

Findings

Fock space dimension becomes finite under energy constraints.

Derived entropy limit aligns with holographic bound.

Elementary analysis yields significant insights into entropy limits.

Abstract

The maximum entropy that can be stored in a bounded region of space is in dispute: it goes as volume, implies (non-gravitational) microphysics; it goes as the surface area, asserts the "holographic principle." Here I show how the holographic bound can be derived from elementary flat-spacetime quantum field theory when the total energy of Fock states is constrained gravitationally. This energy constraint makes the Fock space dimension (whose logarithm is the maximum entropy) finite for both Bosons and Fermions. Despite the elementary nature of my analysis, it results in an upper limit on entropy in remarkable agreement with the holographic bound.