Special and General Relativity from the Finite-QEC Substrate: The Propagation Clock, the Equivalence Principle, and the Horizon Ledger

Abstract

The relativity companion to the series: special and general relativity recovered as emergent properties of the finite-QEC substrate. Special relativity is the universal reversible propagation clock — the invariant speed c is one lattice step per service tick, and internal observers built from the same reversible walk/QEC clock infer Lorentz symmetry even though the microscopic update has a preferred order. General relativity is the coarse-grained covariance of that clock under substrate strain and record load: the metric encodes how local clocks, causal cones, and rulers renormalise, and matter follows geodesics because its propagation phase is extremised in the distorted clock field. The matter sector is an exactly isotropic massless Weyl cone whose three spatial hops form an anticommuting Clifford triple, forcing the relativistic dispersion at leading order; straining the cone yields the metric perturbation directly — the metric perturbation is the strain field — and the linearised Bianchi identity and the substrate's strain-ledger conservation become one statement, making G_μν = 8πG T_μν a consistent field equation rather than an imposed one. The equivalence principle follows once gravity couples to the full energy (kinetic plus confinement/Yukawa mass), not the bare hopping. Finally, the program's four horizon objects — the Bekenstein area law, the Hawking ladder, the firewall isometry, and the gravitational source — are shown to be one register-syndrome read four ways. Explicit about tiers: the kinematic spine is computed and machine-verified; three steps rest on flagged standard imports (Nielsen–Ninomiya IR restoration, Sakharov induced gravity, Weinberg's soft-graviton theorem).

Keywords

How to cite

Elliman, D. (2026). Special and General Relativity from the Finite-QEC Substrate: The Propagation Clock, the Equivalence Principle, and the Horizon Ledger. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.20876717

@techreport{elliman2026relativity,
  author      = {Elliman, David},
  title       = {Special and General Relativity from the Finite-QEC Substrate: The Propagation Clock, the Equivalence Principle, and the Horizon Ledger},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.20876717},
  url         = {https://neusym.ai/papers/relativity}
}