This preprint presents a logarithmic coordinate system for the positive scalar isotropic electromagnetic constitutive pair (ε, μ). The variables χ and ζ separate the propagation product εμ from the impedance ratio μ/ε, giving c = c₀e⁻χ and Z = Z₀eζ. In these coordinates, logarithmic permittivity and permeability become null coordinates of an auxiliary log-constitutive plane with quadratic form dσ² = dχ² − dζ² = dξε dξμ. The paper uses this structure to classify scalar propagation and impedance regimes, identify pure propagation and pure fixed-cone impedance sectors, relate the impedance coordinate to normal-incidence reflection through r = tanh(Δζ/2), and locate the reduced quantum impedance Zℏ = ℏ/e² on the fixed-cone impedance axis. The construction is structural only: it does not propose new Maxwell equations, a spacetime metric, a varying fine-structure constant, or a superluminal signalling mechanism.
Zbigniew Misztela (Mon,) studied this question.