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 proposal, co-developed with artificial intelligence, in which spacetime geometry emerges from quantum information geometry. The fundamental postulate is that the spacetime metric tensor equals the Quantum Fisher Information Metric of an underlying entanglement network, with the Loop Quantum Gravity Immirzi parameter as the coupling constant. The coherence length σ (r) is derived from the spatial Quantum Fisher Information Metric combined with the vacuum Einstein Field Equations, yielding a non-circular derivation of the Schwarzschild metric. Consistency with the Kerr metric is verified separately. The Einstein Field Equations arise naturally from thermodynamic variation, establishing General Relativity as the equilibrium state of quantum geometry. The framework predicts a dark matter to baryonic matter ratio of π/ (2γ₀), yielding values in the range 5. 4–6. 6 depending on the Immirzi parameter value adopted, broadly consistent with Planck 2018 observations (Ωc/Ωb = 5. 36 ± 0. 05), and shows that this emergent dark matter scales as ρ ∝ a⁻³, identical to Cold Dark Matter, under the assumption of topological defect conservation. The Lorentzian signature is shown to emerge from the unitarity of quantum evolution via the Kähler structure of projective Hilbert space. Keywords: quantum gravity, Fisher information, loop quantum gravity, emergent spacetime, dark matter, holographic principle, black holes, Immirzi parameter, thermodynamic gravity