Calculation of the Fine Structure Constant derived from Principle Theory.

Recently we have presented in a paper that the combination of two Principle Theories, General Relativity (GR) and Thermodynamics (TD), is able to derive the restmass (m) of an electron which (surprisingly) depends on the Sommerfeld Fine Structure Constant (FSC). In this paper we present a completed calculation of the FSC number (1/ α =137.035999024(9)) from a GR+TD point of view. Since the introduction of the Higgs mechanism, the Standard Model (SM) presents an explanation of (inertial) mass contribution from interaction with the Higgs-Field [1] but the FSC is not involved. In our two preprints [2] we showed independently form the Higgs-Model that elementary particles restmass depends on the FSC number [2.1] . Nevertheless we have to take into account a Higgs contribution on restmass due to permanent interaction with sub-quantized W-Bosons, Z-Boson, and Higgs-Boson as the (SM) requires. The electron self-energy is based on an interaction not only with “itself” due to 5 inertial (“ internal ”) forces [2.1] but also interacts with the Higgs-Field [1] and with an electro-weak-field [1] . Let us assume an absent external electromagnetic field and its possible interaction with photons [3] .

Nevertheless we have to take into account a Higgs contribution on restmass due to permanent interaction with sub-quantized W-Bosons, Z-Boson, and Higgs-Boson as the (SM) requires. The electron self-energy is based on an interaction not only with "itself" due to 5 inertial ("internal") forces [2.1] but also interacts with the Higgs-Field [1] and with an electroweak-field [1] . Let us assume an absent external electromagnetic field and its possible interaction with photons [3] .
From GR+TD basics [2] , Einstein's equation of motion [3] , and the following differential equation 1.1 gives m(t) [2.1] while introducing r(t) [2.1] (mass generating function). In so far as GR+TD must include permanent interaction with Quantum-Fields as there are: Gravity-, Higgs-and Weak-em-Field then we must have a focus on alpha while including both SM [1] and GR+TD [2] theoretical and experimental facts [1,2,3] . (We leave out here the discussion about the second parameter N, initial Quantum-Number, explaining the quantisation of elementary particles mass [2.1] .) The GR+TD result of the FSC is [2] : Beta and g44 are two (formally well know) free SR and GR parameters. Let us first assume the most simple aspects g44=beta=1 to come up with a first zero approximation of alpha The next step is a hypothesis that the inertial restmass (GR+TD based 5-force [2.1] action) is accompanied by a limiting velocity v 0 =α 0 *c < c because we are discussing non zero restmass.
Notice: Sommerfeld mentioned v e =α*c is the orbit velocity of the "point-like" electron in a Hydrogen atom first orbit. In our approach v e =α*c might be the initial action velocity of a non-point like Electron with centre at rest. Our hypothesis respects that initial and orbit action of an electron matches in so far if both internal and external periodic action is completed at the same time.
Now assume still g44=1 and we have a next absolute and constant (Einstein SR based) alpha number while introducing the hypothesis beta0=sqrt(1-(v 0 /c) 2 ) from above.
This alpha-value 2.1.3 can be completed by g44 from theory. Then alpha might be compared with the experimental values given from Parker [4] and Morel [5] . Both experiments present a high precision alpha-number from different experiments. If g44 would be different in number the tension between Parker (137.035999046) and Morel (137.035999206) might be understood from a general theoretical point of view. From the SM point of view alpha must be a constant. In so far the two experiments reveal a problem pointing beyond the SM.
To come up with a "running" alpha from GR+TD, we accept the following internal and external action contribution on the metric number g44. These contributions are: -"Internal" Yukawa and the W, Z, Higgs-Boson contributions.
-"External" Gravity Field contributions from earth and sun on earth.
Definition: external: "convex GR-Schwarzschild metric contribution (negative sign)" internal: "concave GR+SM-action contribution (positive sign)". In so far as the experiments are executed on earth surface we discuss the earth metric influence. We start with the Schwarzschild metric contribution φ E (earth mass M E and earth Radius RE). Here in the form of "potential energy divided by potential self-energy of the electron" (energy based definition).
The next contribution is the external Schwarzschild sun contribution φ SE at earth (R E ) surface while introducing the sun-mass (M S ) and mean-distance (R SE =1.496*10 11 m) value from experiment (1.471*10 11 m (January) up to 1.521*10 11 m (July)).

= 1.97478*10 -8
As we can see, the sun on earth contribution is one order more in size than the earth contribution on the metric number itself. The main contribution is from 2.2.4 (uncertainty 12 th figure) and from 2.2.3 (uncertainty 14 th figure) less influence.
The external Schwarzschild moon contribution φ M at the moon-surface while introducing the mass and distance values respectively is given in the next formula.

=6.28022*10 -11
The Schwarzschild sun on moon contribution φ SM is not much different to the sun on earth contribution because of the nearly same distance.
2.2.6 = 1.97472*10 -8 Conclusion: The alpha number must be different on earth and on moon. The last word has the experiment: In 2026 NASA and ESA are planning atomic interferometry experiments on space lab (private information).
The g44-metric (on earth experiments) includes three constant contributions (Yukawa, QED and Earth) and one non constant contribution due to parameter R SE (the sun-earth distance in January and July differs significantly). The change in alpha is shown in table 1. It is useful to repeat the Parker and Morel experiments in January and July at the same time. Experiment meets Theory The calculation of 1/alpha=137.035999024(9) from GR+TD (table 1) and the estimation of 1/alpha(0eV)=137.035999020(27) (figure 1) [2.2] are very close.  [4,5] repeated on earth at July and January at the same time should show a significant difference to prove or disprove our theoretical point of view concerning the FSC depends on g44 metric number.