Relational Entropy Gravity Theory: A Framework for Gravitational Emergence

The Relational Entropy Gravity Theory (REGT) presents a novel framework positing that gravity emerges from a pre-spacetime relational coherence lattice composed of abstract states \(\mathcal{R}_{ij}\), optimized through a coherence entropy metric \(\mathcal{S}\) inspired by quantum information theory and entropic principles. Drawing from relational quantum mechanics and lattice models, REGT derives Newtonian gravity and Einstein's field equations in the classical limit while forecasting verifiable deviations, including asymmetric gravitational wave chirp patterns (\(\Delta h \approx 10^{-23}\)), quantum entanglement correlation shifts (\(\Delta C / C_{\text{GR}} \approx 10^{-5}\)), scale-dependent redshift oscillations (\(\Delta z \approx 10^{-6}\)), and lattice defect-induced gauge fields observable at high energies. Supported by detailed derivations, numerical simulations, and experimental protocols utilizing instruments such as LIGO/Virgo, LHCb, and JWST/DESI, this discrete approach addresses quantum gravity infinities and offers implications for cosmology, such as resolving Hubble tension, pending empirical validation.