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

Szymon Łukaszyk

doi:10.20944/preprints202212.0045.v5

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preprints.org > physical sciences > mathematical physics > doi: 10.20944/preprints202212.0045.v5

Preprint Article Version 5 Preserved in Portico This version is not peer-reviewed

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

Szymon Łukaszyk

Version 1 : Received: 2 December 2022 / Approved: 2 December 2022 / Online: 2 December 2022 (09:58:36 CET)
Version 2 : Received: 7 December 2022 / Approved: 8 December 2022 / Online: 8 December 2022 (07:43:33 CET)
Version 3 : Received: 11 December 2022 / Approved: 12 December 2022 / Online: 12 December 2022 (03:39:27 CET)
Version 4 : Received: 18 December 2022 / Approved: 19 December 2022 / Online: 19 December 2022 (10:52:31 CET)
Version 5 : Received: 24 December 2022 / Approved: 26 December 2022 / Online: 26 December 2022 (11:07:39 CET)
Version 6 : Received: 20 January 2023 / Approved: 23 January 2023 / Online: 23 January 2023 (09:31:48 CET)
Version 7 : Received: 10 March 2023 / Approved: 13 March 2023 / Online: 13 March 2023 (09:45:17 CET)
Version 8 : Received: 17 March 2023 / Approved: 20 March 2023 / Online: 20 March 2023 (09:55:20 CET)
Version 9 : Received: 24 March 2023 / Approved: 27 March 2023 / Online: 27 March 2023 (15:46:32 CEST)
Version 10 : Received: 2 April 2023 / Approved: 3 April 2023 / Online: 3 April 2023 (11:08:11 CEST)
Version 11 : Received: 6 April 2023 / Approved: 10 April 2023 / Online: 10 April 2023 (05:17:51 CEST)
Version 12 : Received: 14 April 2023 / Approved: 17 April 2023 / Online: 17 April 2023 (03:09:25 CEST)
Version 13 : Received: 5 May 2023 / Approved: 8 May 2023 / Online: 8 May 2023 (10:45:18 CEST)
Version 14 : Received: 29 May 2023 / Approved: 2 June 2023 / Online: 2 June 2023 (08:15:16 CEST)
Version 15 : Received: 18 August 2023 / Approved: 21 August 2023 / Online: 21 August 2023 (11:39:16 CEST)
Version 16 : Received: 1 October 2023 / Approved: 2 October 2023 / Online: 3 October 2023 (11:53:49 CEST)
Version 17 : Received: 19 October 2023 / Approved: 20 October 2023 / Online: 20 October 2023 (04:33:33 CEST)

How to cite: Łukaszyk, S. Graphene Introduces the Second Negative Fine Structure Constant and the Imaginary Set of Base Planck Units. Preprints 2022, 2022120045. https://doi.org/10.20944/preprints202212.0045.v5 Łukaszyk, S. Graphene Introduces the Second Negative Fine Structure Constant and the Imaginary Set of Base Planck Units. Preprints 2022, 2022120045. https://doi.org/10.20944/preprints202212.0045.v5

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MDPI and ACS Style

Łukaszyk, S. Graphene Introduces the Second Negative Fine Structure Constant and the Imaginary Set of Base Planck Units. Preprints 2022, 2022120045. https://doi.org/10.20944/preprints202212.0045.v5

APA Style

Łukaszyk, S. (2022). Graphene Introduces the Second Negative Fine Structure Constant and the Imaginary Set of Base Planck Units. Preprints. https://doi.org/10.20944/preprints202212.0045.v5

Chicago/Turabian Style

Łukaszyk, S. 2022 "Graphene Introduces the Second Negative Fine Structure Constant and the Imaginary Set of Base Planck Units" Preprints. https://doi.org/10.20944/preprints202212.0045.v5

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 2$^\text{nd}$ fine-structure constant $\alpha_2$, as the 2$^\text{nd}$ root of this equation, as well as two $\pi$-like constants for a convex and a saddle surface. It turns out that this 2$^\text{nd}$ fine-structure constant is negative, and the sum of its reciprocal with the reciprocal of the fine-structure constant $\alpha$ is independent of the reflectance value $R$ and remarkably equals $-\pi$. Particular algebraic definition of the fine-structure constant $\alpha^{-1} = 4\pi^3 + \pi^2 + \pi \approx 137.036$, containing the free $\pi$ term and agreeing with the physical definition of this dimensionless constant to the 5$^\text{th}$ significant digit, when introduced to this sum, yields $\alpha_2^{-1} = -4\pi^3 - \pi^2 - 2\pi \approx -140.178$. Assuming universal validity of the physical definition of $\alpha$, $\alpha_2$ defines the negative speed of light in vacuum $c_n$. The average of this speed $c_n$ and the speed of light in vacuum $c$ is in the range of the Fermi velocity ($10^6$ m/s). Furthermore, the 2$^\text{nd}$ negative fine-structure constant $\alpha_2$ alone introduces the imaginary set of base Planck units.

Keywords

Planck units; the fine-structure constant; speed of light in vacuum; emergent dimensionality

Subject

Physical Sciences, Mathematical Physics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Comments (1)

Comment 1

Received: 26 December 2022
Commenter: Szymon Łukaszyk
Commenter's Conflict of Interests: Author

Comment: A novel form of relation (26).
New reference [13].
Clarity and grammar corrections.

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