scholarly journals Fine-Structure Constant from Golden Ratio Geometry

2018 ◽  
Author(s):  
Michael A. Sherbon
Keyword(s):  
Fine Structure ◽  
Golden Ratio ◽  
Structure Constant ◽  
Fine Structure Constant

scholarly journals Mysticism and the Fine Structure Constant

2020 ◽  
Vol 34 (3) ◽  
pp. 455-492
Author(s):  
Philip Robert Brown
Keyword(s):  
Fine Structure ◽  
Golden Ratio ◽  
Structure Constant ◽  
Fibonacci Sequence ◽  
Fine Structure Constant ◽  
Werner Heisenberg ◽  
Empirical Discovery ◽  
The 1950S ◽  
Range Of Variation

The number $\pi/(2\cdot6^3)$, suggested as the value of the fine structure constant $\alpha$ by Werner Heisenberg in 1935, is modified by "quantizing" $\pi$. This obtains, by empirical discovery, a new number which is much closer to the current measured value of the fine structure constant and within the range of variation of the fine structure constant reported by astronomers from their observation of the spectra of distant quasars. The expression of the reciprocal of this number in base 6 arithmetic yields further evidence for the surprising connection between the number 137 and Kabbalah first noted by Gershom Scholem in the 1950s. The results are interpreted in the hermeneutic tradition of the Pauli-Jung collaboration (relating, in particular, tothe World Clock dream) and Pythagorean mysticism. Some connections of the number $137$ to the golden ratio and the Fibonacci sequence are also explored.

scholarly journals Fine-Structure Constant from Golden Ratio Geometry

2018 ◽  
Author(s):  
Michael A. Sherbon
Keyword(s):  
Fine Structure ◽  
Hydrogen Atom ◽  
Exponential Function ◽  
Golden Ratio ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Electron Mass ◽  
Mass Ratio ◽  
Mathematical Constants

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.

scholarly journals Physical Mathematics and the Fine-Structure Constant

2018 ◽  
Author(s):  
Michael A. Sherbon
Keyword(s):  
Fine Structure ◽  
Golden Ratio ◽  
History Of Mathematics ◽  
Structure Constant ◽  
Early History ◽  
Coupling Constants ◽  
Fine Structure Constant ◽  
Hyperbolic Function ◽  
History Of ◽  
And Mathematics

Research into ancient physical structures, some having been known as the seven wonders of the ancient world, inspired new developments in the early history of mathematics. At the other end of this spectrum of inquiry the research is concerned with the minimum of observations from physical data as exemplified by Eddington's Principle. Current discussions of the interplay between physics and mathematics revive some of this early history of mathematics and offer insight into the fine-structure constant. Arthur Eddington's work leads to a new calculation of the inverse fine-structure constant giving the same approximate value as ancient geometry combined with the golden ratio structure of the hydrogen atom. The hyperbolic function suggested by Alfred Landé leads to another result, involving the Laplace limit of Kepler's equation, with the same approximate value and related to the aforementioned results. The accuracy of these results are consistent with the standard reference. Relationships between the four fundamental coupling constants are also found.

scholarly journals Physical Mathematics and The Fine-Structure Constant

2018 ◽  
Vol 14 (3) ◽  
pp. 5758-5764 ◽  
Author(s):  
Michael A. Sherbon
Keyword(s):  
Fine Structure ◽  
Golden Ratio ◽  
History Of Mathematics ◽  
Structure Constant ◽  
Early History ◽  
Coupling Constants ◽  
Fine Structure Constant ◽  
Hyperbolic Function ◽  
History Of ◽  
And Mathematics

Research into ancient physical structures, some having been known as the seven wonders of the ancient world, inspired new developments in the early history of mathematics. At the other end of this spectrum of inquiry the research is concerned with the minimum of observations from physical data as exemplified by Eddington's Principle. Current discussions of the interplay between physics and mathematics revive some of this early history of mathematics and offer insight into the fine-structure constant. Arthur Eddington's work leads to a new calculation of the inverse fine-structure constant giving the same approximate value as ancient geometry combined with the golden ratio structure of the hydrogen atom. The hyperbolic function suggested by Alfred Landé leads to another result, involving the Laplace limit of Kepler's equation, with the same approximate value and related to the aforementioned results. The accuracy of these results are consistent with the standard reference. Relationships between the four fundamental coupling constants are also found.

scholarly journals Golden Ratio Geometry and the Fine-Structure Constant

2019 ◽  
Vol 16 (1) ◽  
pp. 362-368
Author(s):  
Michael A. Sherbon
Keyword(s):  
Fine Structure ◽  
Hydrogen Atom ◽  
Electromagnetic Interaction ◽  
Golden Ratio ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Weak Force ◽  
Strong Force ◽  
Harmonic Proportions ◽  
Fundamental Forces

The golden ratio is found to be related to the fine-structure constant, which determines the strength of the electromagnetic interaction. The golden ratio and classical harmonic proportions with quartic equations give an approximate value for the inverse fine-structure constant the same as that discovered previously in the geometry of the hydrogen atom. With the former golden ratio results, relationships are also shown between the four fundamental forces of nature: electromagnetism, the weak force, the strong force, and the force of gravitation.

scholarly journals Fine-structure constant from Sommerfeld to Feynman

2019 ◽  
Vol 16 (1) ◽  
pp. 335-343 ◽  
Author(s):  
Michael A. Sherbon
Keyword(s):  
Fine Structure ◽  
Golden Ratio ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Arnold Sommerfeld ◽  
Wolfgang Pauli ◽  
Johannes Kepler ◽  
Hiding Place ◽  
Quartic Polynomial ◽  
Richard Feynman

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.

scholarly journals New Limit on Space-Time Variations in the Proton-to-Electron Mass Ratio from Analysis of Quasar J110325-264515 Spectra

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 344
Author(s):  
T. D. Le
Keyword(s):  
Fine Structure ◽  
Structure Constant ◽  
Space Time ◽  
Fine Structure Constant ◽  
Electron Mass ◽  
Mass Ratio ◽  
Quasar Spectra ◽  
Time Variations ◽  
Using Data ◽  
The Universe

Astrophysical tests of current values for dimensionless constants known on Earth, such as the fine-structure constant, α , and proton-to-electron mass ratio, μ = m p / m e , are communicated using data from high-resolution quasar spectra in different regions or epochs of the universe. The symmetry wavelengths of [Fe II] lines from redshifted quasar spectra of J110325-264515 and their corresponding values in the laboratory were combined to find a new limit on space-time variations in the proton-to-electron mass ratio, ∆ μ / μ = ( 0.096 ± 0.182 ) × 10 − 7 . The results show how the indicated astrophysical observations can further improve the accuracy and space-time variations of physics constants.

scholarly journals Measurement of the running of the fine structure constant below 1 GeV with the KLOE detector

2019 ◽  
Vol 218 ◽  
pp. 02012
Author(s):  
Graziano Venanzoni
Keyword(s):  
Fine Structure ◽  
Energy Region ◽  
Direct Evidence ◽  
Branching Ratio ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Recent Measurement ◽  
Single Measurement ◽  
Lepton Universality ◽  
Hadronic Contribution

I will report on the recent measurement of the fine structure constant below 1 GeV with the KLOE detector. It represents the first measurement of the running of α(s) in this energy region. Our results show a more than 5σ significance of the hadronic contribution to the running of α(s), which is the strongest direct evidence both in time-and space-like regions achieved in a single measurement. From a fit of the real part of Δα(s) and assuming the lepton universality the branching ratio BR(ω → µ+µ−) = (6.6 ± 1.4stat ± 1.7syst) · 10−5 has been determined

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