An Interpretation of the Fine-Structure Constant and Atomic Scales - Hypotheses on a Characteristic Energy of the Electron–Proton Couple and a Minimum Energy

We examine the hypothesis that certain physical quantities have a minimum of nonzero magnitude. Identifying the present expansion rate H0 with a minimum frequency gives an energy Emin = hH0. We assign to the electron–proton couple a characteristic energy Eep = √(me mp)c², and then identify Eep and Emin with the corresponding electric and gravitational energy scales to which the interaction ratio β applies. These hypotheses lead to α = 2πG(me mp)3/2c/(H0h²). An extension to a minimum length and a minimum speed then yields α = πβ³/Σ. Several standard atomic scales can thus be rewritten using these parameters. Conversely, the measured constants give H0 ≈ 72.0128 km s⁻¹ Mpc⁻¹, a value consistent with the local SH0ES determination considered here. The physical significance of these results remains conditional on the proposed identifications. This version clarifies the electron–proton couple hypothesis, adds two diagrams of the relations, improves equation typography, and includes a link to the latest version. English translation of the French preprint: https://doi.org/10.5281/zenodo.22646818.