The Speed of Light as a Vacuum Medium Property in Topological Soliton Theory

Abstract The speed of light c = 1/√ (μ₀ε₀) is universally treated as a fundamental constant of spacetime geometry. We argue that this perspective inverts the logical order. Maxwell's equations derive c from two electromagnetic properties of the medium: permittivity ε and permeability μ. In every material, cₘedium = 1/√ (με) varies continuously. The vacuum is no exception — its specific values ε₀ and μ₀ are properties of the vacuum as a medium, not axioms of geometry. Key arguments and connections developed: Maxwell's original derivation: c was computed from measured ε₀ and μ₀ (1865), not postulated; Einstein elevated this derived quantity to a geometric axiom (1905) (§2) Historical inversion traced: Michelson-Morley → crisis → Einstein's radical move to abandon ether — cost: a derived electromagnetic quantity became a spacetime postulate (§3) Experimental evidence that vacuum behaves as a medium: vacuum birefringence (Δn ~ 4×10⁻²⁴ at 2. 5 T), Casimir effect, Scharnhorst effect (c > c₀ between plates, predicted Δc/c ~ 10⁻³⁶) (§4) Vacuum impedance identity: Z₀ = √ (μ₀/ε₀) ≈ 377 Ω; the fine structure constant α = Z₀/ (2RK) is a dimensionless ratio of vacuum electromagnetic properties (§7) Soliton framework connection: the H = 0 sector of the Faddeev-Niemi field IS the vacuum; Paper X's KK compactification relates μ₀ to R₅; ε₀ and μ₀ are in principle computable from the soliton condensate (§8) Reframing: "constancy of c" = statement about vacuum spatial/temporal uniformity; the question is not "why c? " but "why these values of ε₀ and μ₀? " (§5) Einstein's postulate reinterpreted: not a statement about geometry, but about vacuum homogeneity and isotropy — a physical property of the electromagnetic medium (§6) This is a conceptual/interpretive paper — it reframes, does not derive or predict new experimental effects. The distinguishing prediction would be ε₀ = f (R₅, α, mₑ) computed from the Kaluza-Klein framework; until this computation is performed, the reframing is empirically equivalent to the standard postulate.