Authors: Jesús Sánchez
The fine-structure constant α  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 . 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.
Comments: 10 Pages. Published on: Journal of High Energy Physics, Gravitation and Cosmology, 2018, 4, 510-518
[v1] 2019-05-19 12:15:20
Unique-IP document downloads: 32 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.