AUTHOR=Susskind Leonard 

TITLE=Complexity and Newton's Laws

JOURNAL=Frontiers in Physics

VOLUME=8

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00262

DOI=10.3389/fphy.2020.00262

ISSN=2296-424X

ABSTRACT=<p>In a recent note [<xref ref-type="bibr" rid="B1">1</xref>], 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 [<xref ref-type="bibr" rid="B2">2</xref>] 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 [<xref ref-type="bibr" rid="B2">2</xref>], 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 et al. [<xref ref-type="bibr" rid="B3">3</xref>] constructing symmetry generators for the approximate symmetries of the SYK model.</p>