Quantifying Existence: Energy, Relational Measurement, and the ∆E Field in the Theory of Relative Cosmic Equilibrium (RCE)

This paper, titled "Quantifying Existence: Energy, Relational Measurement, and the ∆E Field in the Theory of Relative Cosmic Equilibrium (RCE)", represents the second stage (RCE–II) in the development of the Theory of Relative Cosmic Equilibrium. Building upon the foundational work [Ennabati, 2025, Zenodo DOI:10.5281/zenodo.16397460], this study introduces the Relational Equation of Reality (RER)—a unified formalism linking time, gravity, light, and matter through a single energetic field ΔE. The work provides empirical calibration of the three relational coefficients (b, ξ, κ) using experimental and cosmological data:– b from gravitational time dilation (GPS/NIST),– ξ from strong gravitational lenses (SLACS/DES/HSC),– κ from CMB and BAO diffusion scales. These calibrations confirm that energy, time, and geometry are not independent entities but relational manifestations of the same equilibrium dynamics. The RCE framework resolves key inconsistencies between general relativity and quantum mechanics, eliminates the need for dark energy or spacetime expansion, and redefines reality as a continuous energetic equilibrium seeking ΔE → 0. This paper completes the empirical and theoretical validation of the RCE framework and establishes a new energetic-relational paradigm for understanding the universe.