The Speed of Light Is Not Fundamental

Topological Soliton Theory — Paper XII The Speed of Light Is Not Fundamental Alexander Novickis · [email protected] Abstract The speed of light c = 1/√(μ₀ε₀) is universally treated as a fundamental constant of nature. We show it is not fundamental: it is derived from the topology of the vacuum. Within the topological soliton framework, the vacuum is a concrete field configuration whose electromagnetic response functions are computed from the Kaluza-Klein compactification geometry. We derive c itself from the mass hierarchy formula to 0.015% accuracy. The theory has no free parameters. Key results: c derived from first principles (§8.6): c = m_e² G / (ℏ α^(21−15α/2)) = 299,838 km/s (0.015% error). Of the inputs: α is derived from S⁷ geometry (Paper XLVI), the exponent from trace anomaly (Paper X), and c, m_e, G form a system where measuring any one determines the other two. ℏ is the sole independent measured input μ₀ and ε₀ derived from KK geometry (§8.4): Explicit closed-form expressions — μ₀ = 16πℏ²G/(c⁴e²R₅²), ε₀ = c²e²R₅²/(16πℏ²G) — reproducing measured values exactly Acoustic metric on the H=1 soliton (§8.4): Numerical evaluation gives birefringence ratio 1.27, anisotropy 1.40, with the rank problem resolved via F₂ (rank 3) and S³ KK fiber (rank 3) Vacuum impedance: Z₀ = 4πℏα/e² = 376.73 Ω derived without c; α = Z₀/(2R_K) connects vacuum EM properties to the quantum of resistance (§7) Historical analysis: Maxwell derived c from ε₀ and μ₀ (1865); Einstein elevated this to a spacetime postulate (1905); the soliton programme restores the original logic and goes further by deriving all vacuum EM constants (§2–3) Emergent Lorentz invariance: The FN vacuum produces an exactly Lorentz-invariant wave equation; violations appear only at the soliton core (δc/c ~ α² ~ 50 ppm) (§6) Metric signature derived (§9.2): The Lorentzian signature diag(−1,+1,+1,+1) is the unique choice compatible with both stable topological solitons and propagating perturbations; Euclidean and ultrahyperbolic signatures are excluded Zero free parameters (§8.6): α is derived from S⁷ geometry; c, m_e, G form a system of 2 equations in 3 unknowns. ℏ converts topological integers to SI units, not physics to numbers — in Planck units, no external inputs are required The theory has no free parameters — ℏ converts topological integers to SI units, not physics to numbers. Every vacuum electromagnetic constant — c, μ₀, ε₀, Z₀ — is determined by the compactification topology. The speed of light is not fundamental. Keywords speed of light vacuum permittivity vacuum permeability electromagnetic medium vacuum impedance topological soliton Hopf fibration Kaluza-Klein mass hierarchy acoustic metric fine structure constant Maxwell equations Faddeev-Niemi model electromagnetic constants metric signature emergent Lorentz invariance Planck constant Type Preprint License CC BY 4.0 Date 2026-04-03 Subject Theoretical Physics Paper Series: Topological Soliton Theory The Toroidal Electron (Paper I) Fine Structure Constant as Soliton Aspect Ratio (Paper II) Quarks and Confinement from Multi-Sector Hopf Solitons (Paper III) Neutrinos as SU(2) Skyrmions (Paper IV) Entanglement as Topology (Paper V) Dark Matter as Topological EM Structures (Paper VI) Topological Solitons vs. the Standard Model (Paper VII) Strong CP Problem Dissolved (Paper VIII) Topological Baryogenesis (Paper IX) From the Hopf Bundle to the Standard Model (Paper X) Dark Energy from Topological Vacuum Constraints (Paper XI) Speed of Light from Vacuum Topology (Paper XII) Antenna Impedance and Topological Mode Conversion (Paper XIII) Two Roads to 137 (Paper XIV) Quantum Foam from Hopf-Linked Fluctuations (Paper XV) Detecting Electron Topology via Precision Spectroscopy (Paper XVI) © 2026 Alexander Novickis. Licensed under Creative Commons Attribution 4.0 International.