Fine structure constant has geometrical nature

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The discussion centers on the relationship between tangential energy and dipole speed in atomic ring oscillators, asserting that tangential energy is proportional to the square of the dipoles' speed. Mathematical simulations indicate that the radiation emitted by these oscillators consists almost entirely of tangential energy. The calculated results align with experimental data from the spectra of various ionized atoms, reinforcing the validity of the findings. A specific number, 1.08612, emerges from calculations related to resonance energy in a fixed-length ring and is proposed to enhance the accuracy of predicting radiated frequencies in ionized atoms. This number, along with a coefficient K and amplitude order of resonance, is suggested to function similarly to Rydberg's constant in atomic spectral formulas.
vlamir
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In the previous theme I spoke, that tangential energy of the dipole of speed is proportional to its square. Accordingly, tangential energy of radial resonance oscillations of the energy ring is proportional to the total square of all dipoles of speed in the ring. See file "dipole of speed.pdf" in thread "New interpretation of gravitational constant".
At mathematical simulation of atomic ring oscillators it was revealed, that the radiation of the oscillator consists of tangential energy practically 100 %.
The matching of the calculated outcomes with experimental data in spectrums of ionized atoms of hydrogen, helium, lithium, beryllium, boron, carbon, nitrogen and oxygen has confirmed this legitimacy.
...
Math see in attached zip-file (5Kb)
 

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what does the number 1.08612 represent?
 
Originally posted by loop quantum gravity
what does the number 1.08612 represent?
At calculation of resonance energy in a ring (this energy has 6 variable components) main condition is the condition of constant value of length of a ring (piD). All 6 formulas contain composite integrals, which cannot be solved by standard methods. Therefore I have exchanged integrals by more simple algebraic expressions. In outcome, for tangential energy the number 1.08612 was obtained.
Then I have applied the formula to spectrums of ionized atoms.
Number 1.08612, coefficient K and amplitude order of resonance allow to calculate the radiated frequency of ionized atoms with more accuracy.
I consider, that these three numbers fulfill the same function, as Rydberg's constant in the formula by Balmer.
 

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