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## Mar. 9th, 2018

### Fine-Structure Constant from Golden Ratio Geometry

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.

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## Sep. 16th, 2017

### Fundamental Physics and the Fine-Structure Constant

Fundamental Physics and the Fine-Structure Constant  Michael A. Sherbon

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.

## Sep. 16th, 2015

### What is the fine-structure constant?

The fine-structure constant determines the strength of the electromagnetic interaction:

1/α ≈ 157 − 337ρ/7 ≈ 137.035 999 168, with the prime constant ρ ≈ 0.414 682 509 851 111.

Sherbon, M.A. "Wolfgang Pauli and the Fine-Structure Constant," Journal of Science, Vol. 2, No. 3, pp.148-154 (2012).

Sherbon, M.A. "Fundamental Nature of the Fine-Structure Constant," International Journal of Physical Research, 3, 2(1):1-9 (2014).

Sherbon, M.A. "Quintessential Nature of the Fine-Structure Constant" GJSFR 15, 4: 23-26 (2015).

Latest experimental-QED determination of the fine structure constant: Aoyama, T., Hayakawa, M., Kinoshita, T. & Nio, M. "Tenth-Order Electron Anomalous Magnetic Moment - Contribution of Diagrams without Closed Lepton Loops," Physical Review D, 91, 3, 033006 (2015).

The improved value of the fine-structure constant 1/α = 137.035 999 157 (41)....

## Dec. 8th, 2012

### Wolfgang Pauli and the Fine-Structure Constant | Sherbon | Journal of Science

Wolfgang Pauli and the Fine-Structure Constant | Sherbon | Journal of Science

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.

Journal of Science, Vol. 2, No. 3, pp.148-154 (2012)   SSRN: abstract=2147980

## Apr. 19th, 2011

### Nature’s Information and Harmonic Proportion « Quintessentia

Nature’s Information and Harmonic Proportion

by Michael A. Sherbon

Abstract: The history of science is polarized by debates over Plato and Aristotle’s holism versus the atomism of Democritus and others. This includes the complementarity of continuous and discrete, one and the many, waves and particles, and analog or digital views of reality. The three-fold method of the Pythagorean paradigm of unity, duality, and harmony enables the calculation of fundamental physical constants required by the forces of nature in the formation of matter; thereby demonstrating Plato’s archetypal viewpoint.

papers.ssrn.com/abstract=1766049

SSRN Classics: Journal of Philosophical & Scientific Texts
Nature’s Information and Harmonic Proportion « Quintessentia

## Apr. 2nd, 2011

### Goodreads | The Philosopher's Stone: A Quest for the Secrets of Alchemy by Peter Marshall - Reviews,

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The Philosopher's Stone: A Quest for the Secrets of Alchemy
by Peter Marshall

"The Philosopher's Stone is the Holy Grail of alchemy, the ancient art of turning base metal into gold. Its magical and elemental power has fixated explorers, occultists and scientists for centuries. For the Philosopher's Stone, it is said, holds the key, not only to making gold but also to deciphering the riddle of existence and unlocking the secret of eternal life." Following such luminaries as Newton, Jung, St. Thomas Aquinas and Zosimus, who devoted most of their lives to searching for it, Peter Marshall set out to unearth the secrets of alchemy in the lands where it was traditionally practised. The result is a piece of historical, scientific and philosophical detection, as well as an exciting physical and spiritual adventure. Exploring the beliefs and practices, the myths and the symbols of the alchemists, Peter Marshall takes us on a journey into this arcane world."

Goodreads | The Philosopher's Stone: A Quest for the Secrets of Alchemy by Peter Marshall - Reviews, Discussion, Bookclubs, Lists

# Division Algebras and Quantum Theory

(29 Jan 2011)  Key: citeulike:8736513

Abstract

Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the "three-fold way". It is perhaps easiest to see it in the study of irreducible unitary representations of groups on complex Hilbert spaces. These representations come in three kinds: those that are not isomorphic to their own dual (the truly "complex" representations), those that are self-dual thanks to a symmetric bilinear pairing (which are "real", in that they are the complexifications of representations on real Hilbert spaces), and those that are self-dual thanks to an antisymmetric bilinear pairing (which are "quaternionic", in that they are the underlying complex representations of representations on quaternionic Hilbert spaces). This three-fold classification sheds light on the physics of time reversal symmetry, and it already plays an important role in particle physics. More generally, Hilbert spaces of any one of the three kinds - real, complex and quaternionic - can be seen as Hilbert spaces of the other kinds, equipped with extra structure.
CiteULike: Division Algebras and Quantum Theory