Why emergence of gravity in matrix theories is entropic

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 11-dimensional supergravity.