Fine-structure Constant, Anomalous Magnetic Moment, Relativity Factor and the Golden Ratio that Divides the Bohr Radius

R. Heyrovska; S. Narayan

Home/Archive/arXiv

arXiv · physics/0509207

Fine-structure Constant, Anomalous Magnetic Moment, Relativity Factor and the Golden Ratio that Divides the Bohr Radius

R. Heyrovska·S. Narayan

View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

physics.gen-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

R. Heyrovska, S. Narayan. 2005-09-24. Fine-structure Constant, Anomalous Magnetic Moment, Relativity Factor and the Golden Ratio that Divides the Bohr Radius. https://arxiv.org/abs/physics/0509207

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Constraining $f(R)$ gravity and evolving dark energy via large-scale structure and phase-space trajectories

We present a joint observational analysis confronting viable $f(R)$ modified gravity theories, specifically the Hu \& Sawicki and Starobinsky models, with background and large-scale structure (LSS) data. Utilizing Monte-Carlo Markov chain (MCMC) sampling across datasets including baryon acoustic oscillations (BAO), type Ia supernovae (SNeIa), cosmic microwave background (CMB) distance priors, and linear growth measurements ($f\sigma_8$, $f$, $\sigma_8$), we place tight constraints on the model parameters governing deviations from General Relativity. For the full dataset combination, we obtain $\log_{10} b_\mathrm{HS} = -6.325_{-1.138}^{+1.216}$ for the Hu \& Sawicki model and $b_\mathrm{S} = (0.8\pm61.0)\times10^{-4}$ for the Starobinsky model. Model comparison based on the Akaike Information Criterion indicates that these $f(R)$ extensions are statistically favored over flat $\Lambda\text{CDM}$ ($|\Delta\text{AIC}| \ge 3.99$) for the combined data. However, when considering the Bayesian Information Criterion, the evidence for support is significantly reduced. Furthermore, we construct two-dimensional phase-space diagrams in the $(\mu, \gamma)$ and $(\mu, \Sigma)$ planes across several redshifts, establishing a novel diagnostic null-test allowing us to probe for deviations from $\Lambda\text{CDM}$, corresponding to the fixed point $(1,1)$ in both planes, using LSS observables. Should future weak-lensing and galaxy surveys provide data points with $\mu-1<0$ and $\gamma-1>1$ or $\Sigma-1 < 0 $, then the aforementioned models could be directly ruled out.

physics.gen-ph↗

arXiv2026

Bound states in the continuum of gravitational waves

Bound states in the continuum (BICs) are ubiquitous wave phenomena, but have not yet been demonstrated for gravitational waves (GWs). Here, in-plane periodic perturbations, exponentially localized at the plane $z = 0$, are shown to lead to distributional surface energy tensors at this plane and to be regular vacuum solutions ($T_{\mu \nu} = 0$) of the linearized Einstein field equations outside of it. These are achieved by explicitly calculating the Ricci tensor components and the Ricci scalar from the metric perturbation tensor. To fulfill each vacuum solution ($R_{{\sigma \nu}_{(+, \times)}} = 0$ and $R_{{}_{(+, \times)}} = 0$), different surface polariton-like dispersions are required. These bound perturbations decay exponentially to a flat metric ($h_{{BIC}_{(+,\times)}} \propto e^{- k_z |z|}$), and each localized metric has a correspondence to a different planar GW polarization ($+,\times$). The Lorenz gauge-fulfilling solutions exist at the $\Gamma$ point in momentum space, dwelling within the continuum of wavevectors of propagating GWs. The strains in the unit cell of the periodic perturbations have opposite parities relative to the corresponding planar GWs under a $C_2$ in-plane rotation, making them incompatible by symmetry with their propagating counterpart, indicating localization via symmetry protection.

physics.gen-ph↗

arXiv2026

Sector-Resolved Bayesian Model Averaging for DESI-Era Cosmology

We present a quotient-space Bayesian formulation for DESI-era anomaly interpretation. Given a pattern-labeled catalog with map $i\mapsto \Act(i)$, the induced posterior $p(\Act\mid D)$, sector inclusion probabilities $P_\alpha$, co-activation probabilities $P_{\alpha\beta}$, and grouped Bayes factors $B_\alpha(D)$ are exact summaries over predeclared physical activation events. Pairwise comparisons such as $\lcdm$ versus $\wacdm$ remain ordinary Bayes-factor tests between specified families; the quotient construction addresses the coarser question of which physical sector carries posterior support when different sectors are represented by unequal numbers of catalog elements. We derive a sector-resolved DESI-CMB-SN likelihood specification for late-time background, early-time ruler, supernova calibration, perturbation, and gravitational-wave propagation sectors. The construction includes an Alcock-Paczynski/isotropic-scale BAO decomposition, a pure-ruler projection, analytic marginalization of low-rank supernova calibration modes, Fisher-normalized sector priors, inactive-sector leakage tests, log-evidence uncertainty propagation, and prior/sector-partition diagnostics. The result is a quantitative procedure for reporting model-comparison support at the level of physically interpretable sectors.

physics.gen-ph↗