When does entanglement through gravity imply gravitons?

TL;DR

The paper scrutinizes whether entanglement generated by gravity implies gravitons by analyzing scalar-field toy-models that separate retarded causal phases from quantum fluctuations encoded in the Hadamard function. It shows that two common approximations—neglecting quantum fluctuations either by zeroing the Hadamard function or via a stationary-phase treatment—lead to distinct, inconsistent outcomes (violation of complementarity or no-signalling, respectively) while entanglement remains locally generated through retarded propagation. The work clarifies that Newtonian (instantaneous) entanglement does not certify gravitons and that true epistemological leverage arises only when retardation in entanglement generation is observed and combined with preserved no-signalling. Consequently, detecting spacetime-local entanglement through gravity with retardation would bolster the case for gravitons, whereas Newtonian entanglement alone remains inconclusive.

Abstract

Detection of entanglement through the Newtonian potential has been claimed to support the existence of gravitons, by extrapolating to a thought experiment which demonstrates that complementarity and causality would be in conflict unless quantum fluctuations exist. We critically assess this consistency argument using scalar field models. We show that whether complementarity or no-signalling is violated when quantum fluctuations are neglected, depends on how this approximation is taken, while in both cases entanglement is generated locally in spacetime. We clarify that the correct reading of the paradox requires making a clear distinction between two notions of causality violation: Newtonian action-at-a-distance and the quantum mechanical no-signalling; the latter is pertinent while the former is not. We conclude that the thought experiment (a) does not add to the epistemological relevance of entanglement through Newtonian potentials (b) lends support for the existence of gravitons, if retardation effects are detected in entanglement through gravity.

Figures (1)

• Figure 1: The set--up of the paradox 2016mariExperimentsTestingMacroscopic2018belenchiaQuantumSuperpositionMassive2019belenchiaInformationContentGravitational2022danielsonGravitationallyMediatedEntanglement. Mass A is in a path--superposition in the distant past $t_i$. Then, it undergoes a recombination process at $t_r$. The recombination of mass A is spatially separated from the splitting and recombination of mass B. The dashed lines indicate null rays. $\Sigma$ is a hypersurface for which A has recombined but B has not started the protocol. Which-path information propagates causally according to the arrows, and is encoded in the pure phases $\varphi^{\textsc{b}}_{\textsc{a}s_\textsc{a}}$. Radiation that causes decoherence also propagates causally (wriggly lines) and is produced locally to A and B. The amount of this radiation is encoded in the exponentially suppressing exponents $\Gamma_\textsc{a}$ and $\Gamma_\textsc{b}$.