Fundamental Nature of the Fine-Structure Constant

Michael Sherbon

doi:10.14419/ijpr.v2i1.1817

Abstract

Arnold Sommerfeld introduced the fine-structure constant that determines the strength of the electromagnetic interaction. Following Sommerfeld, Wolfgang Pauli left several clues to calculating the fine-structure constant with his research on Johannes Kepler's view of nature and Pythagorean geometry. The Laplace limit of Kepler's equation in classical mechanics, the Bohr-Sommerfeld model of the hydrogen atom and Julian Schwinger's research enable a calculation of the electron magnetic moment anomaly. Considerations of fundamental lengths such as the charge radius of the proton and mass ratios suggest some further foundational interpretations of quantum electrodynamics.

Highlights

In addition to introducing the fine-structure constant [1]-[5], Arnold Sommerfeld added elliptic orbits to Bohr’s atomic model deriving the Bohr-Sommerfeld model [6, 7]
The fine-structure constant is viewed in this work from both a mathematical and a physical perspective, as Hemmo and Hagar maintain that “... in current spacetime physics there can be no dynamical derivation of primitive geometrical notions such as length.”
With an extension of the Keplerian intuition regarding the fundamental geometry of basic polygons, conic sections and Platonic polyhedra included in Wolfgang Pauli’s World Clock geometry; the mathematical and physical model for the calculations is an alternative to accounting for individual contributions of the interactions between field quanta and begins to address some of the questions raised by Richard Feynman, Freeman Dyson, Paul Dirac and others about quantum electrodynamics [70]

Summary

Introduction

In addition to introducing the fine-structure constant [1]-[5], Arnold Sommerfeld added elliptic orbits to Bohr’s atomic model deriving the Bohr-Sommerfeld model [6, 7]. The “primacy of geometry” is a mathematical assumption made in the work that follows, with the aim of progress toward additional physical understanding of the fine-structure constant [21]-[23]. Wolfgang Pauli’s World Clock involved basic geometric constructions depicting the cycles of time. His World Clock was likened to Kepler’s first geometrical ordering of the solar system found in ancient geometry [8] and related to geometric constructions involving the Pythagorean right triangle [24]

Calculating the fine-structure constant

Euler’s constant and Kepler’s equation

Electron magnetic moment anomaly

Ratios of fundamental physics

Conclusion