Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 2 December 2022 / Approved: 2 December 2022 / Online: 2 December 2022 (09:58:36 CET)
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How to cite: Łukaszyk, S. Graphene Introduces the Second Negative Fine Structure Constant, Negative Speed of Light, and the Imaginary Set of Base Planck Units. Preprints 2022, 2022120045. https://doi.org/10.20944/preprints202212.0045.v1 Łukaszyk, S. Graphene Introduces the Second Negative Fine Structure Constant, Negative Speed of Light, and the Imaginary Set of Base Planck Units. Preprints 2022, 2022120045. https://doi.org/10.20944/preprints202212.0045.v1

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

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