Addendum to Fast Scramblers

TL;DR

This addendum argues that both de Sitter and Rindler horizons act as fast scramblers, with scrambling governed by a universal bound and realized via matrix quantum mechanics at finite temperature. It develops a naive matrix-Rindler model and a correspondence principle linking de Sitter static patches to matrix degrees of freedom, explaining how horizon entropy and localized masses map to block structures in matrices. It provides a qualitative link between horizon diffusion, information scrambling, and gravitational entropy, and discusses limitations of such holographic descriptions, including observer complementarity and no-go results. The work suggests matrix QM as a candidate dual description for causal patches, offering a framework to understand fast scrambling in curved spacetimes.

Abstract

This paper is an addendum to [arXiv:0808.2096] in which I point out that both de Sitter space and Rindler space are fast scramblers. This fact naturally suggests that the holographic description of a causal patch of de Sitter space may be a matrix quantum mechanics at finite temperature. The same can be said of Rindler space. Some qualitative features of these spaces can be understood from the matrix description.

Figures (2)

• Figure 1: Phenomena at distance ${\cal{R}}$ from the Rindler horizon correspond to the same phenomena at the center of a de Sitter static patch in which the de Sitter radius is ${\cal{R}}.$
• Figure 2: The effect of a mass at ${\cal{R}}$ is to focus light rays from infinity and diminish the area of the horizon.