Why Emergence of Gravity in Matrix Theories is Entropic

TL;DR

This paper proposes that gravity emerges as an entropic force in matrix theories due to a hierarchy of timescales, linking fast chaotic modes to the gravitational potential and force in a novel way.

Contribution

It introduces a new perspective that gravity arises from entropic considerations of fast modes in matrix theories, connecting spacetime emergence to entropy.

Findings

Derives gravitational potential energy from the density matrix of the system.

Shows the emergent gravitational force is an entropic force related to fast mode entropy.

Identifies the regime with super-Planckian distances in dual supergravity.

Abstract

Matrix theories exhibit the phenomenon of spacetime emergence in certain regimes of their dynamics. In this work, I posit that the key to this emergence is a hierarchy between two timescales -- very slow modes that an observer measures plus a chaotic cloud of very fast modes; this then leads to a natural operator algebra for measurements for the slow modes and an associated density matrix for the full system. I show that this density matrix implies the same gravitational potential energy that has been identified previously in the literature; furthermore, I show that the corresponding emergent gravitational force is nothing but the entropic force associated with the entropy of the fast modes of the system. I also demonstrate that the posited regime corresponds to distances being super-Planckian in the dual eleven dimensional supergravity.