Emergent Gravity and Gauge Fields from the Mixed-State Quantum Geometric Tensor: The Relational-Informational Model

I present the Relational-Informational Model (RIM), a framework in which the spacetime metric and gauge elds emerge, in the semiclassical regime, from the mixed-state Quantum Geometric Tensor (msQGT) of an observer's reduced density matrix ρObs = TrSys |Ψ⟩⟨Ψ|, dened within a globally static universe satisfying the ˆ WheelerDeWitt constraint Htot |Ψ⟩= 0. The observer's conguration is parametrised by relational observablespartial observables in the Rovelli sense that acquire denite values through correlations with the system, not by imposing external spacetime coordinates on the WheelerDeWitt wave functional. The real part of the msQGTthe Quantum Fisher Information Matrix (QFIM)denes the emergent spacetime metric via the Bures distance; a modular-ow criterion justies the Riemannian truncation. The Einstein eld equations follow from the First Law of Entanglement Entropy applied on every local causal horizon constituted by the modular Hamiltonian K=−log ρObs, with the QFIM explicitly providing the metric in the Raychaudhuri equationa logical connection absent in Jacobson's thermodynamic derivation. The imaginary partthe Uhlmann curvatureproduces gauge elds. I clarify that the physically relevant gauge structure arises not from the full right-action redundancy of the purication bundle, but from the eective gauge freedom within eigenvalue-degenerate subspaces under the Uhlmann parallel-transport condition. The Uhlmann holonomy is experimentally observable and its physical reality is grounded in mixed-state interferometry, by analogy with the AharonovBohm eect. Non-degenerate spectra yield U(1); two-fold degeneracy yields SU(2); three-fold degeneracy yields SU(3). If the spectral structure of ρObs exhibits these degeneracy patterns, the resulting eective gauge group is Ggauge = U(1) ×SU(2) ×SU(3). RIM derives both geometry and gauge elds from a single quantum-informational object without requiring holographic duality or extra dimensions.