Complexity and Newton's Laws

In a recent note [1] I argued that the holographic origin of ordinary gravitational attraction is the quantum mechanical tendency for operators to grow under time evolution. In a follow-up [2] the claim was tested in the context of the SYK theory and its bulk dual—the theory of near-extremal black holes. In this paper I give an improved version of the size-momentum correspondence of [2], and show that Newton’s laws of motion are a consequence. Operator size is closely related to complexity. Therefore one may say that gravitational attraction is a manifestation of the tendency for complexity to increase. The improved version of the size-momentum correspondence can be justified by the arguments of Lin, Maldacena, and Zhao [3] constructing symmetry generators for the approximate symmetries of the SYK model.