Information-Geometry Equivalence (IGE): A Unified Framework for Reconciling General Relativity and Quantum Mechanics Through Quantum Fisher Information

Information-Geometry Equivalence IGE: A Unified Framework for Reconciling General Relativity and Quantum Mechanics Through Quantum Fisher Information David Khalifa Independent Researcher Email: david.kkhalifa@gmail.com ORCID: 0009-0005-0757-8934 Date: May 2026 Correspondence: david.kkhalifa@gmail.com Abstract This paper presents a comprehensive structural synthesis of the Information-Geometry Equivalence framework, an architectural mapping that reconciles General Relativity and Quantum Mechanics. By motivating a structural identification between the metric tensor of spacetime (gμν ) and the Quantum Fisher Information Metric (Iμν ), we argue that these historically isolated domains may be manifestations of a single informational substrate. Beginning with the century-old Einstein-Bohr debate over determinism and probability, we trace the intellectual lineage through the ER = EPR conjecture 6, holographic error-correcting codes 14, and thermodynamic derivations of gravity 4 to arrive at the central postulate: gμν =ℓp2 Iμν We do not claim origination of the underlying equations; rather, we provide a systematic, step-by-step mathematical bridge (a synthesized derivation) showing how Einstein's Field Equations and the time-independent Schrödinger Equation are structurally connected through Fisher Information, following the established work of Frieden 7, Caticha 8, and Swingle 9. Crucially, we resolve prior tensor-trace inconsistencies in deriving quantum mechanics by introducing a Biometric Framework, projecting the highly curved internal geometry of a quantum particle onto the flat background measuring grid of a macroscopic observer. We address critical structural issues including the Lorentzian signature problem — the QFIM is positive semi-definite while spacetime requires indefinite signature — noting that the ADM 3+1 decomposition provides a spatial/kinematic bridge while the full 4D Lorentzian identification remains an open mathematical problem. We analyze the proportionality prefactor through dimensional analysis and Beckenstein-Hawking consistency. Heuristic extensions toward relativistic wave equations are sketched, suggesting compatibility of the postulate with both the Klein-Gordon and Dirac equations under EPI assumptions, as a heuristic consistency check with Lorentz symmetries. We critically examine the limitations of Jacobson's thermodynamic approach (1995) 4, demonstrating that while it is valid as a macroscopic equation of state, it is incomplete at microscopic scales, as evidenced by the Colella-Overhauser-Werner (COW) experiment 25. The Information-Geometry framework proposes to address this incompleteness by operating consistently across all scales. The framework is applied across ten distinct physical and biological scenarios ranging from black hole singularity resolution to neural plasticity and urban infrastructure. We propose falsifiable experimental tests, including the Holographic Noise experiment at Fermilab 26 and the Bose-Marletto-Vedral (BMV) entanglement-gravity experiment 27. Cosmological implications for dark energy, dark matter, and the black hole information paradox are examined. Speculative applications in quantum-resonant medicine, information-gradient propulsion, and spacetime bandwidth manipulation are explored as logical extrapolations. The primary contribution of this work is the pedagogical integration of disparate strands of theoretical physics into a single, continuous, and falsifiable narrative, providing a unified notation currently missing from the fragmented physics literature. Keywords: Quantum Fisher Information, Information Geometry, Biometric Framework, ER = EPR, Holographic Principle, Einstein Field Equations, Schrödinger Equation, Dirac Equation, Beckenstein-Hawking Entropy, Planck Star, Entropic Dynamics, Extreme Physical Information