Ontological Law Integrating Variance, Entanglement, and Reality: Time as Quantum Information Geometry and Observational Prospects

I propose a reformulation of temporal emergence in loop quantum cosmology (LQC) through quantum information geometry. Time is defined as the Fisher–Rao geodesic length in the space of quantum density operators, parameterized by spectral complexity (A). The choice of (A) is rigorously linked to the micro-canonical partition function of the gravitational degrees of freedom in Loop Quantum Gravity (LQG, analogous to the Bekenstein–Hawking entropy). This framework dissolves the circularity between “time” and “change” by grounding temporal flow in the changing information content of the discrete LQG volume spectrum. In Part II, I derive the informational correction term to the effective Friedmann equation from a modified LQC Hamiltonian potential. The model predicts enhanced suppression of the CMB power spectrum at large angular scales (ℓ < 30), offering a specific, testable explanation for the observed Planck quadrupole anomaly. While preliminary estimates suggest a deficit of O(5–10%) for ℓ < 5, the paper emphasizes the need for immediate numerical computation and Bayesian analysis to constrain the free parameter α and validate these claims.