In this work, I develop a covariant effective field theory (EFT) in which a minimal Abelian information-gauge sector, (U (1) ), couples to a coarse-grained local entropy/nonequilibrium potential ( (x) ) and to a conserved source current (Jⁱnfo). The formulation is explicitly local, gauge invariant, and power-counting consistent in four dimensions, with gravity treated strictly at the infrared/EFT level via the Einstein–Hilbert action. The main contributions of the manuscript are as follows: Gauge-consistent formulation of an information sector. The information-gauge field (_) is introduced as an Abelian connection with Maxwell-type dynamics. Conservation of the information current (_ J^₈₍₅₎=0) follows as a Noether identity of the local (U (1) _) symmetry. The gauge-field stress tensor is manifestly gauge invariant, and energy–momentum exchange with matter is treated consistently. Controlled nonrelativistic limit and quantum observables. A systematic reduction of the covariant dynamics yields the Schrödinger equation with information-gauge potentials. Canonical commutation relations remain unchanged, while gauge-invariant curvature effects lead to a controlled noncommutativity of kinetic momenta, providing a clear alternative to ad hoc generalized uncertainty principles. Environment-dependent scaling near criticality. The manuscript introduces a thermodynamic scaling factor (ₓ₇ () ), interpreted as a regime-dependent, near-critical parameter arising from anomalous scaling, not as a universal modification of vacuum Lorentz invariance. Its role in effective dispersion and damping laws is explicitly framed within EFT validity. Falsifiable phenomenology and precision benchmarks. I provide explicit, transparent benchmark relations for entropy-gradient-induced frequency shifts and for curvature-controlled quantum broadening. These are designed to be directly testable in precision-metrology platforms (e. g. , clocks or interferometry) once a concrete experimental proxy for ( (x) ) is specified. Throughout the manuscript, care is taken to clearly distinguish motivational input from entanglement entropy from the local dynamical variables of the EFT, avoiding any claim of a UV-complete quantum theory of gravity. All predictions are explicitly stated within their domain of validity, and all plotted results are generated from equations given in the text, with corresponding code made publicly available.
Ju Hyung Lee (Wed,) studied this question.