A stochastic semiclassical model for collapse-induced gravitational waves

We present a self-consistent stochastic semiclassical framework in which objective localization (collapse) of quantum states induces localized fluctuations in the stress–energy distribution that source causal gravitational wave perturbations via an Einstein–Langevin type equation. The model combines a Lindblad-averaged continuous spontaneous localization (CSL)-like dynamics with a local collapse bookkeeping field that enforces local energy–momentum conservation. Linearized analysis yields a causal wave equation for metric perturbations sourced by a stochastic tensor whose statistics are computable from collapse parameters. We derive scaling laws for expected strain statistics from a localized mass superposition, provide order-of-magnitude estimates and outline experimental strategies and model limitations. The construction avoids standard no-go objections (superluminal signaling and Page–Geilker constraints) at the ensemble level while yielding concrete, testable predictions for future high-sensitivity detectors. This model offers a phenomenological approach that can guide future experiments, assuming advancements in preparing mesoscopic superpositions and detecting subtle gravitational effects.