What question did this study set out to answer?

This research aims to explore the relationship of the inverse fine-structure constant with a perturbative series for mp/me.

February 21, 2026Open Access

A Numerical Observation on the Inverse Fine-Structure Constant: Connections with a perturbative series for mp/me

Key Points

This research aims to explore the relationship of the inverse fine-structure constant with a perturbative series for mp/me.
Numerical observation of the inverse fine-structure constant relation.
Comparison with CODATA 2018 experimental uncertainty.
Analysis of coefficients and structural elements.
Identified a relation: 9/α + (35/2π)α³ = 236 × ln(6π³).
Residual error was measured at 1.3 × 10⁻⁹.
Observed coefficients and arguments align with previous perturbative series.

Abstract

We report a numerical observation concerning the inverse fine-structure constant 1/α. We find that the following relation holds to within the experimental uncertainty of CODATA 2018: 9/α + (35/2π)α³ = 236 × ln(6π³). The residual error is 1.3 × 10⁻⁹, within the CODATA 2018 experimental uncertainty on α. The coefficients 236, 9, 35, and the arguments 6 and π³ share structural elements with a previously reported perturbative series for mp/me. No theoretical derivation is offered. Is related to : https://doi.org/10.5281/zenodo.18693489

A Numerical Observation on the Inverse Fine-Structure Constant: Connections with a perturbative series for mp/me

Key Points

Abstract

Cite This Study