Reflections on the topic atom - explanations for the Pauli principle, the magneto-mechanical anomaly (spin), the Heisenberg uncertainty principle, the wave-particle-duality the light as well as for the problem of the universal physical constant

If we consider this equation and the adjoining equation, we will find an exceptionally close relationship. In each of the equations one can find on the right-hand side the square of the elementary charge, multiplied by a magnitude of the dimension cm^-l and the square of a speed. Apparently we are on a path which seems to make sense of the two theorems specified above.
Indeed, we have got an interesting result from the requirement that rest mass and self-induction coefficient be directly proportional:
It is well-known that the self-induction coefficient is entirely independent of the electrical current and only depends on the geometry of the current flow. Consequently, the rest masses of proton and neutron, for example, should be more or less identical (if we disregard the slight orbit deformation caused by the Coulomb forces)!

More is not admissible at this point, although, e.g. equating the two equations and, thus, further speculations appear to be tempting. This is forbidden because the left “classical equation” contains L11 that has not yet been characterized. If we use the standard formula to calculate the self-induction of one single charge travelling along any space curve, we will fail in the same way as with the use of the Biot-Savart law, because this formula has been derived from the perspective of external interaction. Thus, we have to try to rewrite this equation again for one single charge, while considering the knowledge obtained above, particularly that of the magnetic field theorem.

But first, let us take down a formula to calculate an induction coefficient of the external interaction between two circuit loops:

Again we discover an exeptionally valuable indication: namely, it is “common” that the integration directions of the two integrals are selected such that L12 becomes positive. Now we expect the formula of the self-induction coefficient of a single charge on an orbit of self-interaction to be a similar double integral. However, from our perspective we still do not see any argument for necessarily integrating such that L11 becomes positive! But as we already see from far the self-induction coefficient to be related to a mass, at this point we may introduce a negative mass, namely antimatter!