Unified GR–QM Information–Geometric Field Theory

Abstract 

Quantum mechanics and general relativity remain conceptually incompatible despite a century of
effort to reconcile them. Motivated by recent work in information geometry, quantum foundations,
and gravitational theory, this article develops a unified geometric framework in which both QM
and GR emerge from a deeper informational manifold. Quantum states are modeled as points on
a curved statistical manifold endowed with Fisher metric, symplectic form, and complex structure.
Spacetime is modeled as a Lorentzian manifold whose curvature encodes gravitational dynamics.
By embedding the quantum manifold as fibers over spacetime and introducing a curvature-coupling
connection, we show that entanglement corresponds to fiber curvature and that gravitational dy-
namics emerge from informational constraints. Schr¨odinger evolution appears as geodesic flow on
the quantum manifold, while Einstein’s equations arise from curvature evolution on the spacetime
base. In appropriate limits, the unified theory reduces to classical GR and standard QM. This
information-geometric framework provides a mathematically natural and conceptually coherent
bridge between quantum mechanics and general relativity, and suggests experimentally testable
mixed-curvature effects in quantum systems subject to gravitational fields.