The connection between quantum entanglement and spacetime geometry, first articulated by Van Raamsdonk, was formalized by Jacobson through theentanglement equilibrium condition and extended by Cao and Carroll to a bulk derivation of the linearized Einstein equation from the extremizationof generalized entropy over a geodesic ball. A foundational obstruction to this programme is that local algebras in relativistic QFT are Type III1 andadmit no well-defined von Neumann entropy. We resolve this obstruction by reformulating the Cao–Carroll condition in the crossed-product algebra of Wittenand Chandrasekaran–Penington–Witten, producing a Type II∞ setting where entropy and its variation are rigorously defined. We then apply this frameworkto QCD in the confining regime, where the confinement entropy gradient acts as a localized matter perturbation sourcing curvature through the equilibriumcondition. The resulting metric perturbation amplitude is hS ≈ 5 × 10−39, parametrically set by the ratio (ΛQCD/MPl)2. All assumptions are statedexplicitly, and detectability is assessed against current experimental capabilities.The detailed algebraic proof supporting the crossed-product reformulation is presented in the companion paper.
Krock et al. (Fri,) studied this question.