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 TIME VARIATION OF FINE STRUCTURE CONSTANT AND PROTON-ELECTRON MASS RATIO WITH QUINTESSENCE

2007 ◽  
Vol 22 (25n28) ◽  
pp. 2003-2011 ◽  
Author(s):  
SEOKCHEON LEE
Keyword(s):  
Fine Structure ◽  
Scalar Field ◽  
Field Potential ◽  
Structure Constant ◽  
Coupling Constants ◽  
Fine Structure Constant ◽  
Electron Mass ◽  
Mass Ratio ◽  
History Of ◽  
The Universe

Recent astrophysical observations of quasar absorption systems indicate that the fine structure constant α and the proton-electron mass ratio μ may have evolved through the history of the universe. Motivated by these observations, we consider the cosmological evolution of a quintessence-like scalar field ϕ coupled to gauge fields and matter which leads to effective modifications of the coupling constants and particle masses over time. We show that a class of models where the scalar field potential V(ϕ) and the couplings to matter B(ϕ) admit common extremum in ϕ naturally explains constraints on variations of both the fine structure constant and the proton-electron mass ratio.

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 Strong limit on the spatial and temporal variations of the fine-structure constant

2014 ◽  
Vol 11 (S308) ◽  
pp. 628-630
Author(s):  
T. D. Le
Keyword(s):  
Fine Structure ◽  
Structure Constant ◽  
High Sensitivity ◽  
Temporal Variations ◽  
Mean Value ◽  
Spatial And Temporal Variations ◽  
Fine Structure Constant ◽  
Strong Limit ◽  
History Of ◽  
The Universe

AbstractObserved spectra of quasars provide a powerful tool to test the possible spatial and temporal variations of the fine-structure constant α = e2/ћc over the history of the Universe. It is demonstrated that high sensitivity to the variation of α can be obtained from a comparison of the spectra of quasars and laboratories. We reported a new constraint on the variation of the fine-structure constant based on the analysis of the optical spectra of the fine-structure transitions in [NeIII], [NeV], [OIII], [OI] and [SII] multiplets from 14 Seyfert 1.5 galaxies. The weighted mean value of the α-variation derived from our analysis over the redshift range 0.035 < z < 0.281 Δα/α= (4.50 ± 5.53) \times 10-5. This result presents strong limit improvements on the constraint on Δα/α compared to the published in the literature

Multiple Model of Anti-Grand Unification, The Regularization with Wilson Loop Action and Critical Coupling Constants

1997 ◽  
Vol 12 (02) ◽  
pp. 73-94 ◽  
Author(s):  
L. V. Laperashvili ◽  
H. B. Nielsen
Keyword(s):  
Fine Structure ◽  
Wilson Loop ◽  
Structure Constant ◽  
Coupling Constants ◽  
Fine Structure Constant ◽  
Multiple Point ◽  
Multiple Model ◽  
Coupling Constant ◽  
Critical Coupling ◽  
Lattice Simulation

The present work considers the phase transition between the confinement and "Coulomb" phases in U(1) gauge theory described by Wilson loop action. It was shown (using as an example the approximation of circular loops) that the critical coupling constant is rather independent of the regularization method. Taking into account the renormalization by artefact monopole contributions and the existence of strings in confinement phase assuming the maximal value of the effective fine structure constant equal to α max =π/12≈0.26, we obtain α c ≈0.204, in agreement with Monte Carlo lattice simulation result: α c ≈0.20. Such an approximate regularization independence ("universality") of the critical couplings is needed for the fine structure constant predictions claimed from "the multiple-point criticality principle".

scholarly journals EXISTENCE OF GROUND STATES OF HYDROGEN-LIKE ATOMS IN RELATIVISTIC QED I: THE SEMI-RELATIVISTIC PAULI–FIERZ OPERATOR

2011 ◽  
Vol 23 (04) ◽  
pp. 375-407 ◽  
Author(s):  
MARTIN KÖNENBERG ◽  
OLIVER MATTE ◽  
EDGARDO STOCKMEYER
Keyword(s):  
Electromagnetic Field ◽  
Fine Structure ◽  
Quadratic Form ◽  
Ground States ◽  
Structure Constant ◽  
Coupling Constants ◽  
Fine Structure Constant ◽  
Coupling Constant ◽  
Coulomb Coupling ◽  
Quantized Electromagnetic Field

We consider a hydrogen-like atom in a quantized electromagnetic field which is modeled by means of the semi-relativistic Pauli–Fierz operator and prove that the infimum of the spectrum of the latter operator is an eigenvalue. In particular, we verify that the bottom of its spectrum is strictly less than its ionization threshold. These results hold true, for arbitrary values of the fine-structure constant and the ultraviolet cut-off as long as the Coulomb coupling constant is less than 2/π. For Coulomb coupling constants larger than 2/π, we show that the quadratic form of the Hamiltonian is unbounded below.

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