dorsal/arxiv
View SchemaFine-structure Constant, Anomalous Magnetic Moment, Relativity Factor and the Golden Ratio that Divides the Bohr Radius
| Authors | R. Heyrovska, S. Narayan |
|---|---|
| Categories | |
| ArXiv ID | physics/0509207 |
| URL | https://arxiv.org/abs/physics/0509207 |
Abstract
Sommerfeld introduced the fine-structure constant into physics, while he was taking into account the relativistic effects in the theory of the hydrogen atom. Ever since, it has puzzled many scientists like Eddington, Dirac, Feynman and others. Here the mysterious fine-structure constant, alpha = (Compton wavelength/de Broglie wavelength) = 1/137.036 = 2.627/360 is interpreted based on the finding that it is close to 2.618/360 = 1/137.508, where the Compton wavelength for hydrogen is a distance equivalent to an arc length on the circumference (given by the de Broglie wavelength) of a circle with the Bohr radius and 2.618 is the square of the Golden ratio, which was recently shown to divide the Bohr radius into two Golden sections at the point of electrical neutrality. From the data for the electron (e) and proton (p) g-factors, it is found that (137.508 - 137.036)= 0.472 = [g(p) - g(e)]/[g(p) + g(e)] (= 2/cube of the Golden ratio), and that (2.627 - 2.618)/360 = (small part of the Compton wavelength corresponding to the intrinsic radii of e and p/de Broglie wavelength) = 0.009/360 = (1- gamma)/gamma, the factor for the advance of perihilion in Sommerfeld's theory of the hydrogen atom, where gamma is the relativity factor.
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"abstract": "Sommerfeld introduced the fine-structure constant into physics, while he was\ntaking into account the relativistic effects in the theory of the hydrogen\natom. Ever since, it has puzzled many scientists like Eddington, Dirac, Feynman\nand others. Here the mysterious fine-structure constant, alpha = (Compton\nwavelength/de Broglie wavelength) = 1/137.036 = 2.627/360 is interpreted based\non the finding that it is close to 2.618/360 = 1/137.508, where the Compton\nwavelength for hydrogen is a distance equivalent to an arc length on the\ncircumference (given by the de Broglie wavelength) of a circle with the Bohr\nradius and 2.618 is the square of the Golden ratio, which was recently shown to\ndivide the Bohr radius into two Golden sections at the point of electrical\nneutrality. From the data for the electron (e) and proton (p) g-factors, it is\nfound that (137.508 - 137.036)= 0.472 = [g(p) - g(e)]/[g(p) + g(e)] (= 2/cube\nof the Golden ratio), and that (2.627 - 2.618)/360 = (small part of the Compton\nwavelength corresponding to the intrinsic radii of e and p/de Broglie\nwavelength) = 0.009/360 = (1- gamma)/gamma, the factor for the advance of\nperihilion in Sommerfeld\u0027s theory of the hydrogen atom, where gamma is the\nrelativity factor.",
"arxiv_id": "physics/0509207",
"authors": [
"R. Heyrovska",
"S. Narayan"
],
"categories": [
"physics.gen-ph"
],
"title": "Fine-structure Constant, Anomalous Magnetic Moment, Relativity Factor and the Golden Ratio that Divides the Bohr Radius",
"url": "https://arxiv.org/abs/physics/0509207"
},
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