The Electron as a Bridge Between Gravity

The fine-structure constant α is one of the most pervasive dimensionless quantities in physics. Its effects are described with extraordinary precision across atomic, quantum-electrodynamic, spectroscopic, chemical, and astrophysical phenomena, yet its numerical value remains an empirical input and the reason for its unusually broad physical role remains unresolved. This work approaches the problem relationally: rather than asking only why α⁻¹ ≈ 137.036, it examines the position of α within a dimensional system formed by the five constants {e, mₑ, h, c, G}, where e is the elementary charge.In esu-CGS units this five-constant family has dimensional rank three and therefore exactly two independent dimensionless degrees of freedom. An exhaustive analysis of its three-constant subsets identifies the fine-structure constant α = 2πe²/(hc) and the electron–gravity constant αₑG = e/(mₑ√G) as natural complementary invariants; αₑG² is the ratio of electrostatic to gravitational interaction between two electrons. Since G forms a dimensionless group only together with e and mₑ, the electron, through its charge and mass, is the element through which gravitation and α meet. This concerns their structural position, not a relation between their values.Adding an independent frequency introduces a third dimensionless invariant, ηⱼ = hνⱼ/(mₑc²). Dimensional analysis alone imposes no relation among these three quantities. A separate search, restricted to lowest-order reciprocal products with positive unit exponents, identifies αₑGηⱼ = 1 as the unique two-member candidate whose underlying constants span the complete six-quantity system, selecting the characteristic frequency νⱼ = mₑ²c²√G/(he) = 0.06053898(67) s⁻¹. This closure is a physical conjecture, not a consequence of the Vaschy–Buckingham theorem, and requires independent experimental validation.The resulting structure places α within a wider relational network of fundamental constants rather than treating it as an isolated dimensionless number. The analysis also distinguishes dimensional representation from dimensionless physical information and provides a concrete experimental target through which the proposed closure can be tested independently. The work originated in the author’s study of Anton Bopp’s unpublished manuscripts but develops the dimensional and relational structure independently in contemporary terms. Experimental realization of the predicted frequency is addressed in a companion metrology paper.