Interpretation of FSC-Experiments Deviation

The Fine Structure Constant (FSC) discussion started 1916 with the definition of alpha by Sommerfeld ( α =e 2 /(2 * h * c * ε o )) which must be a constant number in so far as the elementary charge (e) is a constant. Morel et al. ( 2020) and Parker et al. (2018) presented the most accurate FSC from similar atomic (Rb and Cs) interferometric experiments recently. Surprisingly there is a „tension“ between their two values from an experimental point of view manifesting a theoretical problem due to a „running“ alpha-number indicating a „running“ elementary charge-value which should not be the case in Standard Physics. Here is our interpretation from the General Relativity (GR) point of view to come up with a constant alpha(0) within both experiments.


I. Introduction
"The Standard-Model (SM) reveals that the Fine-Structure-Constant (FSC) characterises the strength of the electromagnetic interaction between elementary charged particles and therefore is ubiquitous in physics." [1] "The greatest triumphs of Quantum Electrodynamics (QED) is revealing the magnetic moment of the electron depending on alpha. The magnetic moment of an electron is subtly larger than that expected for a charged, point-like particle by a factor (a e ) of roughly a e( α ) =1 + α/(2π).+. " [1] .
The corresponding magnetic moment "(g e( m µ) -2) anomaly" of the magnetic moment (m µ ) has been verified to ever-increasing accuracy by "infinite" number of Feynman-Integrals calculation. Nevertheless there is a 2.5 σ deviation between measurements of a e (mµ) =(g e (mµ) − 2)/2 from experiment and the Standard Model prediction of a e ( α ) using various statistical methods from theory. [1,2] "Atom interferometers measure α is based on measuring the recoil kinetic energy transferred. First, a laser beam makes an atom absorb and emit multiple photons and, in doing so, recoil. The mass of the atom m(A) is deduced by measuring the kinetic energy of this recoil. After measuring k, the photon wavenumber, this recoil kinetic energy is given by ︎ ω r , where ω r =h*k/(4pi*m(A)) is the recoil frequency of the Atom." [1] The Atom to electron mass ratio (m(A)/m eE (A) is known to accuracy better than 0.1 ppb for many species [3] . Second, the electron's mass m eE (A) is calculated using the precisely known ratio of the atom's mass m(A) to the mass of an electron m eE (A) from experiment (Morel and Parker). At least, α is determined from the data: electron's mass m eE (A), atom mass m(A), and the binding energy E B (R y ) of a hydrogen atom due to R y (m eCodata ) (Rydberg constant), which is known from spectroscopy representing also the H-ionisation energy. [3] Here is the formula used to calculate alpha(A) [4] 1 R y (=R ∞ proportional to m e* e 4 ) the Rydberg-Constant (in units 1/m) from Codata [4] 2 R y , direct measurement from spectroscopy with high accuracy, theoretically depends on the (SR-invariant) electron restmass m e from Codata (formula 2). BUT this restmass m e must be different to mass m eE (A) of the electron released in the process due to the "recoil velocity". Otherwise we can not explain a constant alpha(0) value. So we have to give up the "SR-invariant meE" if the SR relativistic effect does not make such a significant difference between the relativistic mass m eE (v,A) and its restmass m eE (A) at zero velocity because of a tiny recoil velocity estimated and therefore not discussed within the two papers. So m eE (Cs) must be measured significantly different from m eE (Rb) to come up with a constant alpha(0) value measured within both experiments. (This fact is not discussed in both papers.) Morel et al. have improved the accuracy of alpha to 81 p.p.t. [3] Although there is only a smaller tension between each of the determinations of α (Rb) (1/137.035999206(11)) and α (Cs) (137.035999046 (27)) to the standard-model prediction of α (g s ) (1/137.035999174 (35)), from the anomalous magnetic moment [3,4] , there is a strong tension between Morel [3] (Rb:137.035999206(11)) and Parker [4] (Cs: 137.035999046 (27)

II. Hypothesis:
The mass m eE (Rb) (from experiment) of the electron escaping the rubidium atom m(Rb) with ratio m(Rb)/m eE (Rb) (from literature) or mass m eE (Cs) (from experiment) escaping the Caesium Atom with ratio m(Cs)/m eE (Cs) (from literature), involved in the process, must be different in value due to the ionisation energy respectively is our new way of thinking.

II.1 Conclusion from Hypothesis:
If the electrons rest-mass m eE (A) increases depending on the process of ionisation then alpha decreases (so 1/alpha increases) while using formula 1. Notice the irregular jumps between the ionisation energies in eV!

II.2 Hypothesis applied
The restmass of the electron m eE (x A ) -measured within 5-experimental processes -are different and depend on the ionisation energy x (x: normalised number, x=E(A)/Eo and E 0 =1eV used as a reference)! So does alpha(x)! 4 The change of the released mass m eA (x A ) escaping the atom produces running alpha(x A ) numbers.

III.1 Explanation of the "tension" between alpha(A)-experiments
The hypothesis (influence of the ionisation energy on restmass meA(x A )) is quite well fulfilled. See linear fit while using Morel and Parker high accuracy numbers only.
So alpha(0) as fundamental constant can be used for calculation of the elementary charge (e) value to be compared with that from Codata.