Derivation of the fine structure constant

Derivation of the fine structure constant

The Sommerfeld fine structure constant as coupling constant describes the strength of the electromagnetic force between

two elementary charges. The formula of the fine structure constant is:

(3-44)

With the CODATA-value:

0,00729735253594845000 or .

The fine structure constant can also be shown with the quantized quantities. The first term is replaced with c² from the

Maxwell Formula:

Having we use for the elementary charge and obtain:

(3-45)

By transforming, we will obtain:

(3-46)

And since it is given , we at least obtain:

(3-47)

Accordingly, it is seen that the fine structure constant instead on the elementary charge only depends on the natural

constants c and and has the dimensional value of

or .

The absolute deviation from the CODATA value is only:

0,00000308104262349701.

According to the new world model, the electromagnetic force (a) between electrons and protons is caused by the inverse

ratio of the Planck mass and the geometric generic component.

(3-48)

With the quantized charge, we also can formulate the fine structure constant as follows:

(3-49)

With the quantized charge and the electron mass, we obtain the following relationship:

(3-50)

This relationship is quite similar to the derived formula

(3-16) for the classical electron radius from the last Chapter, with the only change in masses:

In the above formula (3-50) it can also been seen similarities in the fine structure constant with the gravitational force. At

the end of this Chapter we will derive the gravitational constant, and a comparison of the two forces shows that the fine

structure constant describes a kind of "gravitational force" in the atoms. The strength of the electromagnetic force between

protons and electrons is based on quantized loads just like the gravitational force.

I have found the following relations in analyses I made:

(3-51)

With the electron mass in eV: