Unified Field Dynamics from Non-Linear Spacetime Transformations (Photons, Mass and Gravity from a Single Geometric Principle)

We show that a single, globally-invertible diffeomorphism 12 July 2025 Φ : xμ 7−→ Xμ(x) (μ = 0,1,2,3) encodes both electromagnetic and gravitational physics. Splitting its Jacobian,μ ∂Xμ μ μ Jν=∂xν =Sν+Aν, Fμν≡2Aμν,the antisymmetric part Aμν is the electromagnetic two-form, while the symmetric part Sμν deforms the metric and sources curvature. Coupled to a Born–Infeld (BI) action, this non-linear mapreduces to Maxwell’s equations in the weak-field limit; cures the classical point-charge divergence; produces topologically protected “wrappings” whose energies define a discrete mass spectrum—the electron (|N| = 1) and proton (|N| = 3) masses emerge without a Higgs sector; predicts only a 1.0 × 10−14 % upward shift in the Schwinger pair-production threshold—negligible at current laser intensities—for a BI scale b ≃ 8.3 TeV, testable at petawatt laser facilities. We present full field equations, a confinement-energy derivation Econf ∝ |N|4/3ΛQCD, a one-loop proof that the BI scale is renormalization-group invariant (β(b) = 0), and experimental signatures from atomic spectroscopy to magnetar light-bending.