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Graphene Introduces the Second Negative Fine Structure Constant, Negative Speed of Light, and the Imaginary Set of Base Planck Units

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Submitted:

02 December 2022

Posted:

02 December 2022

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Abstract
The reflectance $R$ of monolayer graphene for the normal incidence of electromagnetic radiation is known to be remarkably defined only by $\pi$ and the fine structure constant $\alpha$. It is shown in this paper that the reflectance (or the sum of transmittance and absorptance) of monolayer graphene, expressed as a quadratic equation with respect to the fine structure constant $\alpha$ must unsurprisingly introduce the \emph{2$^\text{nd}$} fine structure constant $\alpha_2$, as the root of this equation. It turns out that this 2$^\text{nd}$ fine structure constant is negative and the sum of its reciprocal with the reciprocal of the \emph{physical} fine structure constant $\alpha$ is independent of the reflectance value $R$ and remarkably equals $-\pi$. Particular algebraic definition of the fine structure constant $\alpha^{-1} = 4\pi^3 + \pi^2 + \pi$, containing the free $\pi$ term, when introduced to this sum, yields $\alpha_2^{-1} = -4\pi^3 - \pi^2 - 2\pi < 0$. Assuming universal validity of the physical definition of $\alpha$, $\alpha_2$ defines the negative speed of light in vacuum $c_n$ and introduces the imaginary set of base Planck units. The average of this speed and the speed of light in vacuum is in the range of the Fermi velocity ($10^6$ m/s).
Keywords: 
Planck units; the fine-structure constant; speed of light in vacuum
Subject: 
Physical Sciences  -   Mathematical Physics
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.

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