Uhlmann Gauge Gravity: Spacetime from Purification Gauge Symmetry and Quantum Fisher Geometry

Keywords: AI, Quantum gravity

TL;DR: Spacetime geometry emerges from quantum Fisher information and purification gauge symmetry, yielding a falsifiable, information-geometric theory of quantum gravity.

Abstract: We propose a new candidate theory of quantum gravity, Uhlmann Gauge Gravity (UGG), in which spacetime geometry emerges from the information geometry of local quantum states and a novel gauge principle associated with purification redundancy. For a density matrix ρ(x) at each spacetime point, we identify the metric g_{μν}(x) with the quantum Fisher (Bures) metric of ρ(x), and introduce a non-Abelian gauge field A_μ(x) given by the Uhlmann connection on purifications w(x) with w(x)w†(x) = ρ(x). We construct a diffeomorphism- and gauge-invariant action coupling (i) the Einstein–Hilbert term for g_{μν}, (ii) a Yang–Mills term for the Uhlmann curvature F_{μν}, and (iii) Fisher-gradient terms for ρ(x). The theory reduces to general relativity in the long-wavelength limit but predicts distinctive, falsifiable corrections: (i) dispersion-suppressed gravitational waves with fixed positive sign, (ii) polarization-dependent phase shifts sourced by Tr(F∧F), and (iii) Fisher-curvature corrections to black hole entropy. These effects are testable with upcoming gravitational-wave and black-hole spectroscopy experiments. All derivations are reproducible from released code computing Fisher metrics and Uhlmann curvatures for lattice-discretized quantum states.

Submission Number: 99