The Proton-Electron Mass Ratio from Icosahedral Geometry: Twist Conservation in D=3
Abstract
We derive the proton-to-electron mass ratio μ = m_p/m_e from first principles using only the dimension D=3 and icosahedral geometry. The formula μ = D!·π^(D!−1) + π/(5·D·D!) yields μ = 6π⁵ + π/90 = 1836.153015, matching the observed value 1836.152673 to 0.19 ppm. This improves upon Lenz's 1951 observation that μ ≈ 6π⁵ by a factor of 100 while providing physical interpretation: the proton and electron are not separate particles but two expressions of a single topological twist — the proton is the inward twist (bulk term 6π⁵) and the electron is the outward twist (boundary term π/90). This explains why electric charges are exactly equal (same twist, opposite directions), why the electron has no color charge (outside the color mechanism), and why pair creation always produces both particles together. The mass ratio is geometric necessity, not coincidence.
Fields of Study & Subjects
Quantum and Classical Electrodynamics
Advanced Mathematical Theories and Applications
Advanced Mathematical Theories
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 4 January 2026
- Document type
- Preprint