New relation between entanglement and geometry from M(atrix) theory

Abstract

In the context of Matrix/light-cone gauge M theory, we develop a new approach for computing quantum entanglement between a probe gravitating in the vicinity of a source mass and the source mass. We demonstrate that this entanglement is related to the gravitational potential energy between the two objects. We then show that the von Neumann entropy is a function of two derivatives of the gravitational potential. We conjecture a relation between the entropy and the local Riemann tensor sampled by the probe, establishing a general scheme to relate entropy to local geometric data. This relation connects the rate of change, rotation, and twist of a small volume element at the probe's location to the quantum entanglement of the probe with the source.