Curvature modifies the quantum vacuum in ways that can enhance or suppress entanglement harvesting by Unruh–DeWitt detectors. We prove a general theorem showing that the leading-order correction to harvested negativity scales as δN=O (R⋅I) = O (R I) δN=O (R⋅I), with the sign and magnitude controlled by spacetime geometry. For static, bridge-like “nacelle” geometries, we derive Theorem 2: the detector response functional specializes to Iϕ=Lϕ⋅F (Ω, T, rAB) I = L F (, T, r₀₁) Iϕ=Lϕ⋅F (Ω, T, rAB), where Lϕ=∫ (ϕ′′ (x) ) 2 dx L = ('' (x) ) ²\, dx Lϕ=∫ (ϕ′′ (x) ) 2dx is the curvature localization functional. This establishes that nacelle curvature enhances vacuum entanglement, in direct contrast to FRW expansion (which suppresses it). The unifying geometric principle is the Synge world function σ σ: nacelle curvature compresses σ σ (enhancement), while cosmological expansion stretches it (suppression). We also propose KxNi4S2 KₓNi₄S₂ KxNi4S2 as a condensed-matter analogue, predicting a measurable phonon-vacuum concurrence scaling C∝ℓCDW−3/2 C ₂₃ₖ^-3/2 C∝ℓCDW−3/2. A log-log plot of concurrence versus CDW wavelength must yield a straight line of slope exactly −1. 5 — the smoking-gun signature of the nacelle mechanism. All derivations (including the explicit transverse collapse, integration-by-parts chain, and coupling constant η=1/ (12π2) = 1/ (12²) η=1/ (12π2) ) are given in full detail in Appendix B. The results are fully falsifiable and provide a concrete experimental target in a solid-state system.
Francis Procaccia (2026) studied this question.