The U-cell model demonstrates emergent special relativity and gravity from a discrete elastic substrate, suggesting a new framework for fundamental physics.
We present the U-cell model, in which matter fields are coupled to and carried by a discrete, non-relativistic elastic substrate, and Special Relativity emerges as the dynamically stable infrared fixed point of the renormalization group flow. We prove that a unique covariant coupling drives all field velocities exponentially toward the substrate wave speed c0 with a positive Lyapunov function — global, self-consistent, and quantum-stable. Gravity emerges from the longitudinal substrate flow via the Gullstrand-Painlevé metric; Einstein's field equations and the exact prefactor 8piG/c^4 are derived from substrate compressibility. The Lorentz contraction of U-cells screens lattice granularity from high-energy probes, giving c_TZ ~ 10⁻⁴⁹ for LHC electrons — consistent with all bounds. The model makes a single falsifiable prediction: a Lorentz-violating asymmetry c_TZ ~ (v_in/c)(E_kin/E_Lambda)^2 in photoelectron emission, with annual modulation ~9% at a predicted galactic phase, accessible to a precision experiment with slow electrons.
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Norbert Prebeck (2026) studied this question.