The Origin of Fundamental Constants: Constants as Local Manifestations of Global Gradients

Here, we present a derivation of fundamental constants from first principles within Unified Quantum Gravity (UQG), a theory where Planck's constant (h-bar) and Newton's constant G emerge as dynamical fields h-bar(Pi) and G(Pi) from an underlying resolution field Pi(x). Our central result is the discovery that the central charge c = 1875 of the holographic conformal field theory at black hole horizons satisfies the relation sqrt(c) is approximately N = 43, where N is the effective number of quantum degrees of freedom. This remarkable relation c is approximately N squared provides the missing link between holography and the Standard Model, allowing us to derive the fine structure constant alpha is approximately 1/137 from purely geometric considerations. We predict unique observational signatures: spatial variations Delta alpha / alpha is circa 3 x 10^-5 correlated with CMB fluctuations, temporal evolution d alpha / dt is circa 10^-12 yr^-1, and a universal correlation Delta alpha / alpha = -1.5 x Delta G / G between electromagnetic and gravitational coupling variations. These predictions are testable with current quasar spectroscopy and atomic clock experiments, providing a smoking gun signature for the emergent nature of physical constants.