Preprint Article Version 7 Preserved in Portico This version is not peer-reviewed

# The Imaginary Universe

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)

How to cite: Łukaszyk, S. The Imaginary Universe. Preprints 2022, 2022120045. https://doi.org/10.20944/preprints202212.0045.v7. Łukaszyk, S. The Imaginary Universe. Preprints 2022, 2022120045. https://doi.org/10.20944/preprints202212.0045.v7.

## Abstract

Imaginary dimensions in physics require an imaginary set of base Planck units and some negative parameter $c_n$ corresponding to the speed of light in vacuum $c$. Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene introduce the second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$ as a fundamental constant of nature and this constant introduces these imaginary base Planck units along with this negative parameter $c_n \approx -3.06 \times 10^8~\text{[m/s]}$. Neutron stars and white dwarfs, considered as \emph{objects} emitting perfect black-body radiation, are conjectured to possess energy exceeding their mass-energy equivalence ratios, wherein the imaginary parts of two complex energies inaccessible for direct observation make storing excess of these energies possible. With this assumption, black holes are fundamentally uncharged; charged micro neutron stars and white dwarfs with masses lower than $5.7275 \times 10^{-10}~[\text{kg}]$ cannot be observed; and the radii of white dwarfs' cores are limited to $R_{WD} < 6.7933~G M_{WD}/c^2$, where $M_{WD}$ is a white dwarf mass. This sets the bounds on charged blackbody objects' minimum masses and maximum radii.

## Keywords

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

## Subject

PHYSICAL SCIENCES, Mathematical Physics

Comment 1
Commenter: Szymon Łukaszyk
Commenter's Conflict of Interests: Author
Comment: 1. Improved introduction with mathematical mode, physical vision, and motivation.
2. Novel conjectures concerning energies, charges, and radii of perfect black-body objects (black holes, neutron stars, white dwarfs).
3. Two forms of complex energies employing in real and imaginary dimensions.
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