The Two Relativistic Rydberg Formulas of Suto and Haug: Further Comments

Abstract

In a recent paper, we [1] discussed that Suto [2] has pointed out an interesting relativistic extension of Rydberg’s formula. In that paper, we had slightly misunderstood Suto’s approach, something we will comment on further here. The relativistic Suto formula is actually derived from a theory where the standard relativistic momentum relation is changed. The relativistic Rydberg formula we presented and mistakenly thought was the same as Suto’s formula is, on the other hand, derived to be fully consistent with the standard relativistic energy-momentum relation. Here we will point out the differences between the formulas and correct some errors in our previous paper. The paper should give deeper and better intuition about the Rydberg formula and what it represents.