An Interpretation of the Fine-Structure Constant and Atomic Scales - Hypotheses on a Characteristic Energy of the Electron–Proton Pair 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 pair 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.