The Rydberg Constant Interpreted as the Gaussian Curvature, Gauss-Bohr-de Broglie Model – Two Shadow Projections of the Helix, Unlocking of the Fixed Constant c of the Speed of Light – New Tests for Old Physics

We have newly interpreted the Rydberg constant R∞ as the Gaussian curvature – the ratio of the 4π electron spin rotation to the area on the Gauss – Bohr sphere travelled by that electron. Rydberg constant for hydrogen RH was newly derived and can be experimentally tested and compared with the value RH derived from the reduced mass. The de Broglie electron on the helical path embedded on the Gauss – Bohr sphere was projected as two shadows: the real shadow Re [cos(t)] and the imaginary shadow Im [i sin(t)]. This model differs from the Schrödinger famous quantum wave description in the physical interpretation. The wave amplitude is here interpreted as the distance of the shadow from the Gauss – Bohr sphere. Moreover, we have newly inserted into the wave equation curvature and torsion of that de Broglie helix. One very interesting result of this model is the estimation of the constant c of the speed of light with three additional significant figures. We have divided the very precise CODATA 2018 value for R∞ expressed in frequency and the CODATA 1986 value for R∞ expressed in wavenumber unit. Based on these precise spectroscopic data we might increase the accuracy of the constant c of the speed of light to twelve significant figures.

Bohr’s Derivation of the Rydberg Formula

Atoms evolved from hypothetical entities into the objects of detailed laboratory study. The discovery of the negatively charged electron by Thomson in 1897 implied that atoms, indivisible for more than 2000 years, now had to be recognized as having some kind of internal structure. In 1911 Rutherford interpreted the latest experimental results in terms of a ‘nuclear atom’, in which most of the atom’s mass is concentrated in a small central nucleus, surrounded by electrons which account for much of the volume. In 1913, Bohr presented a theory of atomic structure which combined a model of classical mechanical ‘orbits’ and transitions between these orbits governed by quantum rules. Although he made some unjustified (and incorrect) assuptions regarding the quantization of orbital angular momentum, he successfully predicted the Rydberg formula and showed that the Rydberg constant is a composite of fundamental physical constants.

The Rydberg constant and proton size from atomic hydrogen

At the core of the “proton radius puzzle” is a four–standard deviation discrepancy between the proton root-mean-square charge radii (rp) determined from the regular hydrogen (H) and the muonic hydrogen (µp) atoms. Using a cryogenic beam of H atoms, we measured the 2S-4P transition frequency in H, yielding the values of the Rydberg constantR∞= 10973731.568076(96) per meterandrp= 0.8335(95) femtometer. Ourrpvalue is 3.3 combined standard deviations smaller than the previous H world data, but in good agreement with the µp value. We motivate an asymmetric fit function, which eliminates line shifts from quantum interference of neighboring atomic resonances.