A Proposal for Emergent Spacetime from Quantum Information Geometry - A Synthesis of Holographic Fisher Geometry, Loop Quantum Gravity, and Emergent Spacetime

Abstract

I present a framework, co-developed with artificial intelligence, in which spacetime geometry emerges from quantum information geometry. The fundamental postulate is that spatial metric components equal the Quantum Fisher Information Metric of coherent states on an underlying spin network, with temporal components constrained by the gravitational field equations and the Loop Quantum Gravity Immirzi parameter γ0\gamma_0 γ0 serving as the entanglement-geometry coupling constant. The coherence length σ(r)\sigma(r) σ(r) is derived self-consistently from the spatial QFIM combined with the vacuum Einstein Field Equations (obtained via Jacobson's thermodynamic argument), yielding the Schwarzschild metric without assuming its form *a priori*. Consistency with the Kerr metric is verified separately. The framework predicts a dark matter to baryonic matter ratio of π/(2γ0)\pi/(2\gamma_0) π/(2γ0) from boundary-bulk holographic geometry, yielding values in the range 5.4–6.6 depending on the Immirzi parameter; with de Sitter curvature corrections, the prediction narrows to 5.43, within 1.0σ\sigma σ of Planck 2018 observations (Ωc/Ωb=5.36±0.07\Omega_c/\Omega_b = 5.36 \pm 0.07 Ωc/Ωb=5.36±0.07). This emergent dark matter scales as ρ∝a−3\rho \propto a^{-3} ρ∝a−3, identical to Cold Dark Matter, under the assumption of topological defect conservation. The Lorentzian signature emerges consistently from the Kähler structure of projective Hilbert space and the unitarity of quantum evolution.

Keywords: quantum gravity, Fisher information, loop quantum gravity, emergent
spacetime, dark matter, holographic principle, black holes, Immirzi parameter,
thermodynamic gravity