Fine Structure Constant derived from Principle Theory.

Derivation of mass (m), charge (e) and fine structure constant (FSC) from theory are unsolved problems in physics up to now. Neither the Standard Model (SM) nor the General theory of Relativity (GR) has provided a complete explanation for the existence of the rest mass, i.e. restmass of the electron. The question “ of what is rest mass ” is therefore still essentially unanswered. We will show that the combination of two Principle Theories, General Relativity and Thermodynamics (TD), is able to derive the restmass of an electron (m), which surprisingly depends on the (Sommerfeld) FSC (same for the charge (e)).


Introduction
Since the introduction of the Higgs mechanism, the Standard Model (SM) presents an explanation of mass in the following way: "mass is built up by exchange-particles", so-called Higgs particles [1] .
The mass of the Higgs mechanism is greater, the stronger the field is coupled to the elementary particle. The Higgs field is a free hypothesis given a priori in order to be able to justify non-zero mass by interaction with the field generating inertial force transferred. However, this free "invention" has become a physical reality because there must be a Higgs boson from theory with a certain mass -theoretically predicted by Peter Higgs -and confirmed experimentally in the meantime [1] .
If the moving electron interacts with the Higgs field, then the mass of the electron must be greater. The conclusion based on this argument is now that the Higgs-Mass-value should be smaller if the electron is at rest. If so the main part of restmass must come up from another "action" explaining inertial mass of an electron with center of mass assumed at rest.
There is an alternative to the SM for deriving the (missing) rest energy of the electron independently of the Higgs-Hypothesis. This alternative is well known as Einstein's theory of relativity [2] . Mass and its gravity are the basis of theoretical considerations there.
"… insofern, dass man von Punktteilchen (mit Masse) ausgehen darf, ist die Thermodynamik eine vollständige Theorie." (A.E) Thus, we have to give up first the point particle hypothesis and second we need to combine GR and Thermo-Dynamics (TD) because each alone cannot predict the existence of the electron mass. This is exactly the path that Einstein practically set in his wordings, but did not cover it himself "A theory that sets mass and charge a priori is incomplete." (A.E)

Newton
Momentum P G-Field Acceleration g Velocity

Derivation of mass
The general theory of relativity (GR) in connection with the principles of thermodynamics (TD) together makes it possible to answer the question of the rest mass differences of elementary particles if the following two hypotheses are taken into account.

Hypothesis:
The restmass of the elementary particle is not that invariant.

Hypothesis:
The main laws of thermodynamics and principles of GR are taken into account when solving the "equation of motion of an elementary particle at rest".
Let us first look at Newton's equation of motion (F = dP / dt) or Einstein's equation of moments of pre-relativistic time in the vector representation (1.0) as a basis for further discussion. In a special case, Newton and Einstein discuss the interaction of two masses with respect to their gravitational force (space time curvature instead of force within Einstein's approach).
In purely formal terms, the G-field is a "free invention" like the Higgs field is. The physical reality of a G-Field arises from the fact that an apple is attracted and accelerated by the earth's mass. In this case, it is assumed that both the apple and the earth have a (rest) "mass-reality", namely before the apple is accelerated by earth. This is standard in physics and not that way of thinking we are going to proceed next.
The following common equation of momentum assumes that all quantities are time-dependent, i.e. mass m(t), distance r(t), and unit vector u(t). 2.0 In 2.0 f μ describes the existence of internal forces. So "f µ due to a G-Field" is a free invention. The physical reality of internal force of an "internal G-Field" arises from the fact that we have experimental reality of an electrons restmass. The same argument holds true for the external Higgs-Field because we have the experimental reality of the mass of the Higgs-Boson. Additionally to the Higgs-Field we assume a G-Quantum-Field.
We neglect an external interaction with the environment (F = 0), for example no interaction with the external Higgs field or with the external G field. (Of course this external action must be possible.) Then we carry out the mathematical operations (left side 2.0). Formally by the product rule we get five "internal" force components f1, f2, f3, f4, f5 of a particle m(t): ("point" means partial derivation) is the mass in question in kilograms. r (t) is a distance function in meters due to internal action assumed to come up with restmass m(t) and u (t) is a unit vector allowed to rotate.
We have to define a "math-structure" of each f µ if we want to complete physically the momentum equation due to internal action of one particle with center at rest. With f 2 (the second force of five from 2.1) we define an internal force combined with inertial acceleration (-r''). Thus presenting the following differential equation 2.1.1 in a general time dependent form: A solution r(t), (let us say a mass generating function) gives first m (t) and second allows to calculate the "effective mass value" (m), i.e. rest mass from a time average. The time average is from a mean square giving the effective value of mass (2.1.7 and 2.1.8) to be compared with the experimental value.
Notice: Furthermore the invention of a similar f1 (Coulomb-Contribution) leads to the reality of the elementary charge of the electron. f4 leads to the magnetic moment of the electron. f3 is due to a Coriolis contribution. f5 seems to be an unknown force up to now. (No further discussion here.) Since the speed of light is an invariant within the theory of relativity, we can get the following equation if we multiply by c 2 (invariant GR-value) and introduce the Einstein kappa instead of Newton's G value.

2.1.2
We see immediately that now m (t), the mass of the particle, can no longer be an invariant. In order to be able to reconcile the equation with the conservation of energy, we allow a non-adiabatic change of state of mass included into the energy conservation concept, while applying the Second Law of Thermodynamics for that with respect to the mass generating function r(t).

E=m(t)*c 2 +Q(t)=const
2a Generating function r(t) Ψ has to be imagined as a periodic wave-function. However, the "loss energy dQ <0" (frequency-loss), executed by exponential decay while including the electron life-span τ, must be taken into account for each periodic process (II-Law applied). Here we only deal with rest mass non zero, based on action with less than speed of light, and dQ<0 for that. The electron therefore necessarily loses energy i.e. mass (dark matter candidate). The loss is unimaginably little, hence the very long lifespan is the consequence.

2b Important Prediction
This concept, "lifespan" τ (due to non-adiabatic "internal" action) leads to the derivation of the FSC (revealed from a principle theory, as Pauli required, see 2.1.11, 2.1.12, 2.1.13).    Table 3 The Higgs-Field mass contribution might explain the difference between GR+TD results and experimental ratio.

End of excurse
In so far as the Fermion-Quantum-Number N cannot be explained completely by physical arguments at this moment, we accept that N remains an unsolved problem in equation E3.

Conclusion:
So the FSC is depending on GR(g44) and SR(β) parameters, now derived from a principle theory. This new results predict new experiments.

Application and a new Experiment
3.1 The FSC on white dwarfs are different due to the metric influence g44 [3] . 3.2 The same to the moon (private investigation, suggested experiment 2020).