Grand Relativity: A Conformal Scalar-Tensor Framework

Grand Relativity (GRL) is a conformal scalar-tensor theory in which a single dimensionless scalar field φ(xμ) governs the local values of the speed of light c, Newton’s constant G, and inertial mass m, while Planck’s constant ℏ and the fine-structure constant α remain strict global invariants. These scalings are uniquely fixed by two conservation laws: energy conservation (E = mc2 = const ) and gravitational charge conservation (Gm = const ). The invariance of α further constrains the electromagnetic sector, requiring the elementary charge to scale as e ∝ φ1/2, which renders all atomic transition frequency ratios independent of φ and guarantees compatibility with atomic clock and quasar spectroscopy constraints. The field φ takes its lowest values at high-mass-density regions and rises outward, so ∇φ always points away from mass. Gravity emerges as a thermodynamic entropic force: regions of low φ near mass support a vastly larger momentum phase space, producing an irreversible statistical drift inward that reproduces the geodesic acceleration a = −c2∇φ/φ with the correct attractive sign from first principles. The same scalar vacuum naturally generates (i) galactic flat rotation curves without dark matter, (ii) gravitational lensing identical to General Relativity ( ˆα = 4GM/c2b, PPN parameter γ = 1), (iii) accelerated cosmic expansion without a cosmological constant, (iv) thermodynamic singularity avoidance, and (v) a perpetually cyclic universe emerging from a single high-φ origin state. The scalar kinetic sector βX3/2 is demonstrated to be ghost-free and causally stable, with scalar sound speed c2 s = 1/2 in the deep-field limit. Gravitational wave propagation is shown via an eikonal analysis to satisfy vGW = c(φ) exactly at every spacetime 1 point, passing the GW170817 constraint structurally; a subleading amplitude scaling Aμν ∝ 1/φ yields a falsifiable prediction for the ratio dGW L /dEM L (z) testable with LISA and Cosmic Explorer. The framework is tested against 135 SPARC disc galaxies using zero free parameters, achieving a median fractionalerror of 10.6%