Entanglement Before Spacetime in Quantum-Gravity-Induced Interactions

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.

💡 Research Summary

The paper revisits the widely discussed quantum‑gravity‑induced entanglement of massive systems (QGEM) and asks a subtle but profound question: does the generation of entanglement truly require a spacetime notion of distance, or can it be understood as a more primitive quantum interaction that exists independently of any metric structure? To answer this, the authors reformulate the interaction phase that underlies QGEM protocols within the language of twistor theory, a framework that naturally encodes conformal geometry but contains no built‑in notion of length or time.

Starting from the standard effective‑field‑theory description, the gravitational (or more generally, massless) mediator is integrated out, yielding a bilocal action
(S_{\rm int}= \frac12\int d\tau d\tau’ , m_A m_B , G(x_A(\tau),x_B(\tau’))),
where (G) is the Green’s function of a massless field. The associated phase (\Phi_{AB}=S_{\rm int}/\hbar) is non‑factorizable and therefore capable of generating entanglement whenever the two worldlines are distinct. In the non‑relativistic static limit one recovers the familiar Newtonian phase (\Phi\sim G m_A m_B T/(\hbar r)), but this step already assumes a spatial separation (r).

The authors then replace the spacetime Green’s function by a twistor‑space kernel (K(Z,Z’)). A single twistor encodes a null ray; massive particles are described by a pair of twistors (a bitwistor) subject to the constraint (X^{\alpha\beta}=Z^{