The Born Rule from Spacetime: Unifying Decoherence and Gravity

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. Please contact me at [email protected] for questions or collaborations.