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Journal Articles APL Quantum Year : 2024

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

Gilbert Reinisch

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 = e^2/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 spacetime invariance.
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Year Month Jours
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Sunday, September 1, 2024
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Sunday, September 1, 2024
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Dates and versions

hal-04518676 , version 1 (24-03-2024)

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Gilbert Reinisch. Mathematical definition of the fine-structure constant: A clue for fundamental couplings in astrophysics. APL Quantum, 2024, 1 (1), ⟨10.1063/5.0200259⟩. ⟨hal-04518676⟩
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