Abstract
The fine-structure constant, which determines the strength of the electromagnetic interaction, is briefly reviewed beginning with its introduction by Arnold Sommerfeld and also includes the interest of Wolfgang Pauli, Paul Dirac, Richard Feynman and others. Sommerfeld was very much a Pythagorean and sometimes compared to Johannes Kepler. The archetypal Pythagorean triangle has long been known as a hiding place for the golden ratio. More recently, the quartic polynomial has also been found as a hiding place for the golden ratio. The Kepler triangle, with its golden ratio proportions, is also a Pythagorean triangle. Combining classical harmonic proportions derived from Kepler’s triangle with quartic equations determine an approximate value for the fine-structure constant that is the same as that found in our previous work with the golden ratio geometry of the hydrogen atom. These results make further progress toward an understanding of the golden ratio as the basis for the fine-structure constant.
Highlights
Writing on the history of physics, Stephen Brush says that in 1916: Sommerfeld generalized Bohr’s model to include elliptical orbits in three dimensions
“The fine-structure constant derives its name from its origin
That ancient spiritual ‘dynamis’ of number is still active, which was formerly expressed in the ancient doctrine of the Pythagoreans that numbers are the origin of all things and as harmonies represent unity in multiplicity.” [9]. These calculations of the inverse fine-structure constant with the main parameters of the Great Pyramid have been directed toward a better understanding of the golden ratio as the basis for the fine-structure constant
Summary
Writing on the history of physics, Stephen Brush says that in 1916: Sommerfeld generalized Bohr’s model to include elliptical orbits in three dimensions He treated the problem relativistically (using Einstein’s formula for the increase of mass with velocity),. Describing Sommerfeld’s work with Felix Klein, Pauli writes: The standard treatise on the ‘theory of the top,’ which he wrote in conjunction with his teacher F Klein in his early days, while he was still a ‘Privatdozent’ in Göttingen, and in which many technical problems are discussed, possesses a significance going far beyond applied mathematics. He was a master of the technical applications of mathematics, of the partial differential equations of physics; of the formal classification of spectra; and again of wave mechanics, and in all alike he made decisive advances [9]
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