Quantum Gravity and String Theory

   

From Information to Geometry: A Relational Framework for Emergent Spacetime via Quantum Fisher Information

Authors: Lee Jin Woo

I present a rigorous formulation of the Relational-Informational Model (RIM), proposingthat spacetime geometry is not a fundamental background but an emergent property arisingfrom the entanglement structure between an observer and the universe. By defining theobserver as a quantum reference frame within a globally static universe (Htot|Ψ⟩= 0), I de-rive the spatial metric directly from the distinguishability of quantum states. Utilizing the Taylor expansion of the Bures distance, I prove that the physical metric corresponds to the Quantum Fisher Information Matrix (QFIM) of the observer’s reduced density matrix. Furthermore, addressing the critique regarding zero net flux in static Rindler frames, I employthe First Law of Entanglement Entropy involving the Modular Hamiltonian to demonstratethat the thermodynamic evolution of this informational geometry naturally obeys the Ein-stein field equations. This framework provides a concrete mathematical pathway unifyingQuantum Information Theory with General Relativity.

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[v1] 2026-02-02 20:52:43

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