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Mathematical definition of the fine-structure constant: A clue for fundamental couplings in astrophysics

Authors :
Gilbert Reinisch
Source :
APL Quantum, Vol 1, Iss 1, Pp 016111-016111-5 (2024)
Publication Year :
2024
Publisher :
AIP Publishing LLC, 2024.

Abstract

Astrophysical tests of the stability—or not—of fundamental couplings (e.g., can the numerical value ∼1/137 of the fine-structure constant α = e2/ℏc vary with astronomical time?) are a very active area of observational research. Using a specific α-free non-relativistic and nonlinear isotropic quantum model compatible with its quantum electrodynamics (QED) counterpart yields the 99% accurate solution α = 7.364 × 10−3 vs its experimental value 7.297 × 10−3. The ∼1% error is due to the deliberate use of mean-field Hartree approximation involving lowest-order QED in the calculations. The present theory has been checked by changing the geometry of the model. Moreover, it fits the mathematical solution of the original nonlinear integro-differential Hartree system by use of a rapidly convergent series of nonlinear eigenstates [G. Reinisch, Phys. Lett. A 498, 129347 (2024)]. These results strongly suggest the mathematical transcendental nature—e.g., like for π or e—of α’s numerical value of ∼1/137 and, hence, its astrophysical as well as its cosmological stability.

Details

Language :
English
ISSN :
28350103
Volume :
1
Issue :
1
Database :
Directory of Open Access Journals
Journal :
APL Quantum
Publication Type :
Academic Journal
Accession number :
edsdoj.f234219828e451dbff9c7d87b41b856
Document Type :
article
Full Text :
https://doi.org/10.1063/5.0200259