A Relational Reinterpretation of the Speed of Light and the Fine-Structure Constant

This paper proposes a relational reinterpretation of the speed of light c and the fine-structure constant α using a spatial quantum ℓ₀ and a temporal quantum τ₀ emerging from pregeometric connectivity. The spatial quantum is defined as a fundamental spatial measure generated when interaction endows a connection with measure, whereas the temporal quantum is defined as the interval corresponding to one fundamental update of a connection state. The quantity c₀ ≡ ℓ₀/τ₀ is then defined as a pregeometric fundamental speed; the identification c₀ = c remains a physical hypothesis at the present stage. In addition, the phase motion previously written as α = rω/c is reconsidered in terms of synchronized updates of C₂ and C₃. The angular frequency ω is reinterpreted not as an absolute internal rotation of a single structure but as the relative angular frequency ωrel = ω₂ − ω₃. If, during one common update τ₀, C₂ advances by π and C₃ by 2π/3, the relative phase advance is Δφrel = π/3. Under the hypothesis c₀ = c, this gives α = (rrel/ℓ₀)Δφrel = (π/3)(rrel/ℓ₀). Here rrel is introduced not as a literal radius of the electron but as a spatial scale characterizing the relation between the two phase structures. The central claim is not a derivation of the numerical values of c or α, but the possibility that both constants can be organized as quantities expressing relations among space, time, and relative phase.