Emergent space time from Quantum information geometry, Dark matter as entanglement geometry
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 the spatial 3-metric emerges from the Quantum Fisher Information Metric of coherent states on an underlying spin network, with the lapse function (encoding temporal geometry) determined by the gravitational Hamiltonian constraint — a structure formalized via the ADM (3+1) decomposition — and the Loop Quantum Gravity Immirzi parameter γ₀ serving as the entanglement-geometry coupling constant. The coherence length 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) 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 5.44, within 1.1σ of Planck 2018 observations (Ω_c/Ω_b = 5.36 ± 0.07). A self-consistency equation coupling Ω_b, Ω_c, and Ω_Λ through the single parameter γ₀ predicts the full cosmic energy budget (Ω_m ≈ 0.317, Ω_Λ ≈ 0.683) from two inputs alone. This emergent dark matter scales as 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. The master equation admits a natural interpretation as a linearized Hassan-Rosen bimetric theory, with the QFIM of de Sitter coherent states forming a hyperbolic information space H³. Key limitations include unmeasurably small quantum corrections for astrophysical objects (~10⁻⁷⁰), a 10¹²² coefficient gap in the forward derivation of galactic rotation curves analogous to the cosmological constant problem, and theoretical uncertainty in the Immirzi parameter.
Keywords: quantum gravity, quantum Fisher information metric, loop quantum gravity, emergent spacetime, dark matter, holographic principle, black holes, Immirzi parameter, thermodynamic gravity, ADM formalism, bimetric gravity, entanglement entropyQuantum gravity Simulator
Research paper
https://zenodo.org/records/18722162
Quantum gravity physics simulator