Does Gravity Render Probability Quasilocal?

Abstract

We propose that probability in quantum theory, like energy in general relativity, acquires a fundamentally quasilocal character in curved spacetime. Interpreting Hermiticity as the symmetry associated with inner-product conservation, we show that gravitational boundaries and horizons convert global probability conservation into a flux balance law. The resulting quasilocal probability naturally induces effective non-Hermiticity for restricted observers while preserving global unitarity. We demonstrate this explicitly in Schwarzschild, Kerr and FLRW spacetimes and after this, we identify observational imprints in black hole ringdowns. Our results suggest that in quantum field theory on curved backgrounds, probability conservation is as geometrically conditioned as energy itself.