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 for emergent spacetime in which geometry arises directly from the quantum information structure of the vacuum. The fundamental postulate is that the spacetime metric tensor equals the Quantum Fisher Information Metric of an underlying entanglement network, scaled by the Loop Quantum Gravity Immirzi parameter.

The vacuum coherence length is derived from the Tolman-Ehrenfest thermodynamic equilibrium condition, demonstrating that the Schwarzschild and Kerr metrics are necessary consequences of a thermalized quantum vacuum. I show that the Einstein Field Equations arise naturally from thermodynamic variation of this information geometry, establishing General Relativity as the equilibrium state.

The framework yields two falsifiable predictions without fine-tuning: (1) A dark matter to baryonic matter mass ratio of approximately 5.73, derived from holographic integral geometry, which is consistent with Planck 2018 observations (5.36 ± 0.3); and (2) A cosmological scaling for emergent dark matter of rho ~ a^-3, indistinguishable from Cold Dark Matter. Numerical verification confirms that quantum corrections are negligible for astrophysical black holes (~10^-70) but become significant at the Planck scale, resolving the Big Bang singularity via a quantum bounce.

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