Quantum Gravity and String Theory

   

The Geometry of Information: Unifying Gravity and Gauge Fields via the Mixed-State Quantum Geometric Tensor

Authors: Lee Jin Woo

Building upon the Relational-Informational Model (RIM), where spacetime geometry emerges from the Quantum Fisher Information of an observer’s reduced density matrix, I extend the framework to derive all four fundamental interactions from a single information-geometric object: the mixed-state Quantum Geometric Tensor (msQGT).The observer, defined as a subsystem within a globally static universe (Hˆtot|Ψ⟩ = 0), is generically described by a mixed state ρObs = TrSys|Ψ⟩⟨Ψ|. The real symmetric part of the msQGT—the Quantum Fisher Information Metric—reproduces the spacetime metric and gravitational dynamics as established in the companion paper. The imaginary antisymmetric part—the Uhlmann curvature—encodes gauge field strengths. Crucially, the gauge group is determined by the degeneracy structure of ρObs: non-degenerate spectra yield U(1) electromagnetism, two-fold degeneracies produce SU(2) weak interactions, and three-fold degeneracies generate SU(3) color symmetry. I derive the Einstein—Hilbert and Yang—Mills actions from a unified information-theoretic variational principle, interpret coupling constants as geometric rigidities tied to the eigenvalue structure of ρObs, and present explicit toy-model calculations. The frame-work identifies open problems including fermion generations, mass hierarchy, and the cosmological constant. These results suggest that all fundamental interactions arecomplementary manifestations of one underlying quantum information geometry.

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[v1] 2026-02-21 20:07:17

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