We develop a mathematically rigorous theory of quantum measurement within Entanglement-Weighted Operator Gravity (EWOG), in which spacetime geometry is an operator-valued entity weighted by quantum entanglement. We show that quantum measurement corresponds to a localized, transient fluctuation of spacetime curvature induced by rapid redistribution of entanglement. We prove that competing measurement outcomes correspond to competing semiclassical geometries whose stability is governed by curvature variance. Minimization of curvature fluctuations leads uniquely to probability weights proportional to
∣ψ∣2, yielding the Born rule as an emergent geometric law rather than an axiom. This framework unifies quantum measurement, decoherence, and classical spacetime emergence within a single gravitational-informational principle. We further derive the spectral density of measurement-induced curvature fluctuations and establish experimental bounds on their detectability.
We present a first-principles derivation of the Born rule using a curvature-filtered gravitational decoherence model combined with standard environmental decoherence.The derivation focuses on filtered density matrices and geometric projection operators to explain how outcome probabilities emerge as curvature-weighted classicalizations of quantum states. The curvature filter, motivated by renormalization group flow, regulates when vacuum fluctuations become gravitationally classical. We show that the Born rule emerges as a special case of a normalized curvature-weighted density matrix and as the limit of curvature-saturated operator projections. We briefly supplement this with a path-integral formulation and discuss competing theories. This approach offers a novel, observer-independent foundation for quantum measurement.
General relativity predicts spacetime singularities where curvature diverges, while quantummechanics describes a probabilistic reality. We propose a model that unifies these domains bypositing that spacetime curvature is an emergent property of quantum state reduction. Themodel is based on a Collapse-Curvature Correspondence: R = −8πGρC , where the Ricciscalar R is proportional to the local collapse density ρC , defined as the rate of quantum-to-classical transitions. We argue that in causally isolated regions—such as black hole coresor the pre-Big Bang state—no measurement-induced collapse can occur, forcing ρC = 0 andconsequently R = 0. This naturally resolves curvature singularities without requiring quantumgravity. The framework reinterprets gravity as the geometric record of quantum actualizationand time as a procedural variable emerging from collapse progression, dτ = k dC. The modelis falsifiable through its unique predictions for experiments like BMV/QGEM, which shoulddetect no gravity-mediated entanglement prior to collapse.