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, for emergent spacetime 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. By applying Heisenberg Uncertainty Principle considerations to the Hamiltonian constraint of LQG, I motivate the coherence length $\sigma(r)$ and show consistency with the Schwarzschild and Kerr metrics. I demonstrate that the Einstein Field Equations arise naturally from thermodynamic variation of the master equation, establishing General Relativity as the equilibrium state of quantum geometry. The framework predicts a dark matter to baryonic matter ratio of $\pi/(2\gamma_0) \approx 5.73$, consistent with Planck 2018 observations ($5.36 \pm 0.3$). I prove this emergent dark matter scales as $\rho \propto a^{-3}$, identical to Cold Dark Matter. Numerical verification confirms mathematical consistency, conservation law preservation, and correct classical limits.

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