Discovery of the Vacuum Density Constant and Its Relation to the Fine-Structure Constant

Abstract

Starting from the pure geometric limit of diamond refractive index, this paper discovers that the physical vacuum itself possesses density and refractive index. The geometric extremum of a regular tetrahedron yields the refractive index of diamond relative to a zero-density reference medium: n_geo = 2√3/(√6−1) = 2.38988. The ratio n_exp/n_geo = 1.01134, where n_exp = 2.417 is the measured value, directly gives the vacuum refractive index n_vac = 1.01134. Back-calculation from the electron mass formula yields the vacuum density Λ = 0.007300. Its difference from the fine-structure constant α = 1/137.036 is 0.035%, which originates from the 7th-power equivalent error amplification of the formula itself; within the formula precision, Λ = α holds exactly. Replacing α with vacuum density in all fundamental physical formulas containing α (Bohr radius, Rydberg constant, classical electron radius, g-factor, etc.) yields numerically identical results as a dimensional consistency check. This paper establishes the vacuum density postulate Λ = α and demonstrates its correspondence to the Higgs field, gravitational lensing, and dark energy. Λ = α reveals the physical interpretation of the fine-structure constant as a property of the vacuum, placing it among the fundamental constants of nature alongside c. v1.3 update (2026-08-26): Revised electron mass formula presentation (unified framework of gravitational and quantum constants, zero free parameters, predictive content emphasized); corrected reference numbering; removed speculative diamond color-change prediction; added page numbers. This version is prepared for submission to Foundations of Physics. Both English and Chinese versions are included.