After a brief review of the golden ratio in history and our previous exposition of the fine-structure constant and equations with the exponential function, the fine-structure constant is studied in the context of other research calculating the fine-structure constant from the golden ratio geometry of the hydrogen atom. This research is extended and the fine-structure constant is then calculated in powers of the golden ratio to an accuracy consistent with the most recent publications. The mathematical constants associated with the golden ratio are also involved in both the calculation of the fine-structure constant and the proton-electron mass ratio. These constants are included in symbolic geometry of historical relevance in the science of the ancients.
α is the fine-structure constant, φ is the Golden Ratio, A is the Golden Apex of the Great Pyramid and K is the polygon circumscribing constant. 2016 CODATA: 137.035 999 160 (33).
From the exponential function of Euler’s equation to the geometry of a fundamental form, a calculation of the fine-structure constant and its relationship to the proton-electron mass ratio is given. Equations are found for the fundamental constants of the four forces of nature: electromagnetism, the weak force, the strong force and the force of gravitation. Symmetry principles are then associated with traditional physical measures.
“All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei.”
― Arnold Sommerfeld, Atombau Und Spektrallinien
Fundamental Nature of the Fine-Structure Constant by Michael A. Sherbon 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. International Journal of Physical Research, Vol. 2, No. 1 (2014). Available at: http://www.sciencepubco.com/index.php/IJPR/article/view/1817 SSRN: 2380218 . .
Wolfgang Pauli and the Fine-Structure Constant by: Michael A. Sherbon
Wolfgang Pauli was influenced by Carl Jung and the Platonism of Arnold Sommerfeld, who introduced the fine-structure constant. Pauli’s vision of a World Clock is related to the symbolic form of the Emerald Tablet of Hermes and Plato’s geometric allegory otherwise known as the Cosmological Circle attributed to ancient tradition. With this vision Pauli revealed geometric clues to the mystery of the fine-structure constant that determines the strength of the electromagnetic interaction. A Platonic interpretation of the World Clock and the Cosmological Circle provides an explanation that includes the geometric structure of the pineal gland described by the golden ratio. In his experience of archetypal images Pauli encounters the synchronicity of events that contribute to his quest for physical symmetry relevant to the development of quantum electrodynamics.