Entanglement Before Spacetime in Quantum-Gravity-Induced Interactions

TL;DR

The paper argues that gravitationally mediated entanglement, as in QGEM, can be formulated without assuming spacetime distance by using a conformally invariant twistor framework. It shows that the bilocal phase $\Phi_{AB}$, generated by a massless mediator, is well-defined and non-factorizable even absent a metric, with spacetime distance and the Newtonian $1/r$ behavior arising only after introducing an infinity twistor to break conformal invariance. The authors identify twistor-space invariants $I_{AB}$ and $\mathcal{K}_{AB}$ that govern the phase in a scale-free, conformal setting, and demonstrate how conformal breaking yields the familiar Newtonian limit via a twistor propagator $K(Z,Z') = 1/\langle Z Z' \rangle$. In the static limit, they recover $\Phi_{AB} \sim -\frac{G m_A m_B}{\hbar} \int dt \, \frac{1}{r(t)}$, linking the emergent geometry to the underlying bilocal quantum structure. Overall, the work clarifies that QGEM experiments test the existence of a non-factorizable bilocal quantum channel rather than spacetime locality itself, with spacetime locality emerging as a representational choice after conformal symmetry breaking.

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.