Quantum statistical gravity: time dilation due to local information in many-body quantum systems

TL;DR

This paper proposes a mechanism where local information and entanglement in many-body quantum systems give rise to a gravitational potential that influences classical objects, linking quantum information to gravity.

Contribution

It introduces a novel conjecture connecting mutual information and entropy reduction to emergent gravity in quantum systems, emphasizing the role of measurement and entanglement.

Findings

Measurement reduces local entropy and influences gravitational potential.

Classical motion occurs at constant probability, connecting entropic forces to gravity.

The proposed mechanism links quantum information dynamics to emergent gravity phenomena.

Abstract

We propose a generic mechanism for the emergence of a gravitational potential that acts on all classical objects in a quantum system. Our conjecture is based on the analysis of mutual information in many-body quantum systems. Since measurements in quantum systems affect the surroundings through entanglement, a measurement at one position reduces the entropy in its neighbourhood. This reduction in entropy can be described by a local temperature, that is directly related to the gravitational potential. A crucial ingredient in our argument is that ideal classical mechanical motion occurs at constant probability. This definition is motivated by the analysis of entropic forces in classical systems, which can be formally rewritten in terms of a gravitational potential.