Matter-Mediated Entanglement in Classical Gravity: Suppression by Binding Potentials and Localization

TL;DR

The paper challenges the claim that a classical gravitational field can generate entanglement between distant masses via a quantum-field-theoretic, matter-exchange mechanism. It reframes the essential channel as a quantum tunneling/evanescent propagation process, not a fundamentally field-theoretic effect, and shows that realistic binding/localization in solids introduces a large energy scale that suppresses this channel exponentially with distance. Using a WKB-based argument, the authors derive an evanescent length $\ell = \hbar / \sqrt{2 m E_b}$ and show that the resulting amplitude decays as $A(d) \propto e^{-d/\ell}$, making the entanglement mechanism effectively negligible at macroscopic separations relevant to experiments. Consequently, the entanglement highlighted by AH signals a matter-exchange channel rather than the nonclassicality of gravity, preserving the validity of LOCC-based gravitational-witness tests in realistic bound-matter platforms.

Abstract

Aziz and Howl [Nature 646 (2025)] argue that two spatially separated masses can become entangled even when gravity is treated as a classical field, by invoking higher-order "virtual-matter" processes in a QFT description of matter, which is non-LOCC (local operations and classical communication). We point out that the relevant mechanism is not intrinsically field-theoretic, but is essentially a quantum tunneling/evanescent matter channel, which is already captured within ordinary quantum mechanics. More importantly, the microscopic constituents of realistic macroscopic objects are bound and localized by strong potentials, introducing a large internal energy scale that suppresses coherent propagation between distant bodies. Including such binding/localization generically yields an exponential suppression, rendering the matter-mediated contribution negligible at the macroscopic separations relevant to gravitational-entanglement proposals. Consequently, the entanglement identified by AH diagnoses the presence of a coherent matter-exchange channel rather than the classical or quantum nature of gravity, and it does not undermine LOCC-based witness arguments in realistic bound-matter platforms.

Figures (1)

• Figure 1: This figure describes AH's channel generating quantum entanglement between two objects. In the middle of this figure is the Feynman diagram of particle tunneling (Fig. 2 in AH's paper). They assume all particles are free, but in a solid, atoms can propagate only if they are excited by a virtual energy $E_b$, which leads to an exponential-decay factor.