[Physics] Calculation of the fine structure constant

[Jesus Sanchez]

Dear members of Physics list,

I attach you a paper I have published in the journal of High Energy Physics
Gravitation and Cosmology.

http://www.scirp.org/Journal/PaperInformation.aspx?PaperID=85840

It is regarding an equation to calculate the fine structure constant. Of
course, any comment, would be welcome.

Thanks a lot,
Best Regards,
Jesús Sánchez

Abstract:

The fine-structure constant α [1] is a constant in physics that plays a
fundamental role in the electromagnetic interaction. It is a dimensionless
constant, defined as: α=q^2/(2ε_0 hc)=0.0072973525664 (1) Being q the
elementary charge, εo the vacuum permittivity, h the Planck constant and c
the speed of light in vacuum. The value shown in (1) is according CODATA
2014 [2]. In this paper, it will be explained that the fine-structure
constant is one of the roots of the following equation: cos⁡(α^(-1)
)=e^(-1) (2) being e the mathematical constant e (the base of the natural
logarithm). One of the solutions of this equation is: α=0.0072973520977 (3)
This means that it is equal to the CODATA value in nine decimal digits (or
the seven most significant ones if you prefer). And therefore, the
difference between both values is:
Difference=(α(1)-α(3))/(α(1))·100=0.00000642% (4) This coincidence is
higher in orders of magnitude than the commonly accepted necessary to
validate a theory towards experimentation. As the cosine function is
periodical, the equation (2) has infinite roots and could seem the
coincidence is just by chance. But as it will be shown in the paper, the
separation among the different solutions is sufficiently high to disregard
this possibility. It will also be shown that another elegant way to show
equation (2) is the following (being i the imaginary unit):
e^(i/α)-e^(-1)=-e^(-i/α)+e^(-1) (5) Having of course the same root (3). The
possible meaning of this other representation (5) will be explained.
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