Decoherence-Conditioned Spacetime: A Framework for Classical Geometry

We propose a modification of the coupling between classical spacetime geometry and quantum matter in which the spacetime metric at each event is sourced by the stress-energy tensor evaluated on a locally decohered density matrix constructed from the causal past of that event. This replaces the usual semiclassical expectation value with a coarse-grained stress tensor derived from a decoherence channel acting on the quantum state restricted to the causal past. In this framework, decoherence determines which sector of the quantum state can influence classical spacetime geometry: coherent phase correlations remain present in the quantum state but do not source classical spacetime geometry. The resulting effective stress tensor is formulated to be covariant and compatible with the Bianchi identities under branchwise conservation. The framework avoids macroscopic-superposition paradoxes of the traditional semiclassical approach and predicts the absence of gravitationally mediated entanglement in the Bose–Marletto–Vedral protocol. Observation of such entanglement would therefore falsify the proposal.