This work develops a geometric interpretation of the fine-structure constant as a phase accumulation arising from directed traversal through a structured spatial medium. Rather than treating as an empirical coupling parameter, it is modeled as a dimensionless ratio that emerges from the interaction between a one-dimensional propagation path and an underlying distributed geometry. A physically realizable system is introduced in the form of an exponentially tapered helical conductor (the "trumpet coil"), defined by a radius profile (z) = r₀ e^-k z. geometry produces a constant logarithmic gradient, dz r = -k, enables uniform phase-slip accumulation along the length of the structure. A first-order geometric phase law is derived: = \, d, represents a geometric ratio constructed from the balance of expansive and torsional contributions. Under minimal scaling assumptions, this reduces to\ = 2 (rwrₙ), rw and rₙ are the wide and narrow radii of the tapered structure. This phase contribution is distinct from conventional transmission-line phase accumulation, which is given by\ₓ₋ = ₀L (z) \, dz, (z) = L' (z) C' (z), scales primarily with frequency and length. In contrast, the geometric phase term depends only on the logarithmic taper ratio and is predicted to be frequency-invariant to first order. The total observed phase is therefore decomposed as\₎₁ₒ = ₓ₋ + ₆₄₎₌ + ₀ₑ₀ₒ₈ₓ₈₂, the geometric contribution is isolated experimentally by subtracting the best-fit transmission-line baseline across multiple taper geometries. A key experimental prediction is a linear relationship: d (rw/rₙ) = 2, a slope on the order of 10^-2 radians. This magnitude is within the resolution of modern vector network analyzers, enabling a practical validation pathway. A distinguished configuration occurs atwrₙ = e^/2, which the one-pass phase is and the symmetric round-trip phase is 2, suggesting a geometric closure condition. The results provide a testable framework in which electromagnetic coupling is interpreted as a geometric phase phenomenon. The proposed experiment offers a direct method to determine whether a logarithmic, frequency-independent phase contribution exists beyond conventional distributed electromagnetic behavior.
David Thomson (Thu,) studied this question.