Why Emergence of Gravity in Matrix Theories is Entropic

TL;DR

The paper investigates how gravity and spacetime can emerge from Matrix theory by positing a two-timescale hierarchy: very slow diagonal (D) modes and fast off-diagonal (R) modes. It develops a density-matrix framework where slow measurements are complemented by a thermally excited fast sector, yielding an entropic force $F = T \nabla S$ that reproduces the gravitational interaction observed in Matrix-theory calculations, with the regime $\tau_D \gg \tau_R$ mapping to $r \gg \ell_P$. The work provides a gauge-consistent operator-algebra approach and introduces effective couplings $G_{\mathrm{eff}}^2$ and $g_{\mathrm{eff}}^2$ to characterize the emergent dynamics, linking to the DLCQ/11D M-theory picture. It argues that gravity emerges as an entropic force from fast-mode entropy, offering a concrete realization of Verlinde-type ideas within a controlled Matrix-theory setting and outlining clear avenues for extension to supersymmetry and large-$N$ limits.

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.