The M\"obius Game: A Quantum-Inspired Test of General Relativity

TL;DR

This paper introduces a new inequality inspired by quantum mechanics to test the dynamical nature of spacetime, using a multi-agent game on a M"obius graph to detect changes in curvature as a signature of general relativity.

Contribution

It presents a novel inequality derived from a generalized Bell setup to certify the dynamical character of spacetime in a game-theoretic context.

Findings

The inequality can detect spacetime curvature changes.

Violation of the inequality certifies dynamical spacetime.

The approach links quantum-inspired tests to general relativity.

Abstract

We present a tight inequality to test the dynamical nature of spacetime. A general-relativistic violation of that inequality certifies change of curvature, in the same sense as a quantum-mechanical violation of a Bell inequality certifies a source of entanglement. The inequality arises from a minimal generalization of the Bell setup. It represents a limit on the winning chance of a collaborative multi-agent game played on the M\"obius graph. A long version of this Letter including other games and how these games certify the dynamical character of the celebrated quantum switch is accessible as arXiv:2309.15752 [gr-qc].