Reconstructing Relativistic Gravity from 1905–1911 Einstein: Equivalence, Lorentz Symmetry, and Self-Consistency

We reconstruct the weak-field metric structure of relativistic gravity using only theconceptual ingredients available in Einstein’s 1905–1911 work together with minimal modernconsistency language. The starting set consists of local Lorentz symmetry, universality offree fall, the equivalence principle, gravitational redshift, and recovery of the Newtonianweak-field limit for slowly moving matter. These ingredients already fix the temporal sectorof the metric tog00 = −(1 + 2Φc2)to leading order. The spatial sector is less constrained at this stage and may be written, inisotropic weak-field form, asgij =(1 − 2γ Φc2)δij ,where γ measures the spatial response per unit Newtonian potential.We then show how the standard weak-field observables for null propagation depend onthis residual ambiguity. Light bending and Shapiro delay both scale with 1 + γ, so the 1911Einstein value corresponds to γ = 0, whereas the general-relativistic completion gives γ = 1.For a solar-limb ray, these two cases yield 0.875′′ and 1.750′′, respectively. The paper’s centralconclusion is therefore precise: Einstein’s pre-1911 principles already push gravity toward ametric description, but a full relativistic closure requires a nontrivial spatial response. In theminimal pure spin-2 completion class with universal coupling and no additional long-rangescalar degree of freedom, that closure selects γ = 1.