Entanglement Before Spacetime in Quantum-Gravity-Induced Interactions

TL;DR

This paper reformulates quantum-gravity-induced entanglement in a twistor framework without assuming spacetime, revealing that entanglement can exist independently of spacetime geometry and clarifying the quantum nature of such protocols.

Contribution

It introduces a conformally invariant twistor approach to analyze gravitational entanglement, showing that entanglement persists without spacetime geometry and identifying how spacetime emerges.

Findings

Entanglement remains well-defined without spacetime geometry.

The Newtonian $1/r$ phase emerges after breaking conformal invariance.

Spacetime geometry is not essential for entanglement generation.

Abstract

Quantum-gravity-induced entanglement of massive systems (QGEM) is commonly approximated in the nonrelativistic static limit by a Newtonian interaction between spatially separated masses. In this work, we reformulate the gravitationally mediated interaction phase in a conformally invariant twistor framework in which no notion of spacetime distance is assumed. We show that the bilocal phase responsible for entanglement generation remains well-defined and non-factorizable even in the absence of spacetime geometry. The familiar Newtonian $1/r$ phase, relevant for QGEM protocols, arises only after the conformal invariance is broken by introducing the infinity twistor, which selects a particular spacetime representation of the underlying bilocal quantum interaction. Our results isolate the genuinely quantum content of QGEM protocols and clarify the contingent role played by spacetime geometry in mediating entanglement.