Temporal Bubbles and Photon Propagation in Fractal-Spectral Spacetime: Local Constancy of c, Apparent Superluminality, and the Horizon Problem

The speed of light is both constant and variable — at different levels of description. Locally, in every temporal bubble, c is exactly c. Across bubbles with different temporal flow rates, coordinate velocities differ. This is not new physics — it is standard GR reformulated in the language of fractal-spectral spacetime. The new content is the fractal structure. We formalize temporal bubbles as connected spacetime regions where the temporal flow rate τ (x) is approximately constant, with boundaries defined by τ-gradients. The fractal texture of matter creates a natural hierarchy of bubbles at scales from Planck (Δτ/τ ~ 1) through nuclear (~10⁻³⁹), atomic (~10⁻⁴⁴), Earth surface (~10⁻⁹), galactic (~10⁻⁶), to cosmic voids (~10⁻⁵). At every scale, c is locally constant — the framework preserves local Lorentz invariance exactly. Modified Maxwell equations in fractal-spectral spacetime are derived from the covariant form in the metric ds² = −c²τ²dt² + gᵢj dxⁱ dxʲ, producing additional cross-product terms (B × g_τ and E × g_τ) analogous to gravitomagnetic corrections in GR. These vanish within bubbles and activate only at boundaries. The dispersion relation ω² = k²c²τ²1 + O (|∇τ|²/k²) introduces frequency-dependent propagation — high-frequency photons are less affected than low-frequency ones — a new prediction absent from standard GR, at the ~10⁻¹⁸ level in Earth's field. Temporal refraction at bubble boundaries follows a Snell-like law: sinθ₁/sinθ₂ = τ₂/τ₁, recovering gravitational lensing with fractal log-periodic corrections. The photon is reinterpreted as a resonant perturbation of the electromagnetic field — a soliton-like structure transportable through synchronization with the local spacetime texture. The enlarged effective causal structure provides a candidate resolution of the cosmological horizon problem: coordinate velocities exceeding c across temporal bubbles allow causal contact over regions that appear disconnected in the naive light cone. This is presented as a candidate mechanism, not a proven solution — whether it produces sufficient e-foldings depends on the desynchronization dynamics (see the companion inflation paper). Predictions include frequency-dependent propagation corrections (~10⁻¹⁸), log-periodic signatures in pulsar timing residuals, and temporal refraction at gravitational boundaries. All predictions preserve local Lorentz invariance and causality.