Omnidimensional Convex Polytopes

2023

Preprint

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 $c$. The second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$ present in Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene leads to the imaginary Planck units. Furthermore, it sets $c_n \approx -3.06 \times 10^8~\text{[m/s]}$. It follows that electric charges are the same in real and imaginary dimensions. Neutron stars and white dwarfs, objects emitting perfect black-body radiation, need energy exceeding their mass-energy equivalence ratios. Complex energies are defined in terms of real and imaginary Planck units. Their imaginary parts, inaccessible for direct observation, store the excess of these energies. It follows that black holes are fundamentally uncharged, charged micro neutron stars and white dwarfs with masses lower than $5.7275 \times 10^{-10}~[\text{kg}]$ are unphysical, and the radii of white dwarfs' cores are limited to $R_{\text{WD}} < 6.7933~G M_{\text{WD}}/c^2$. It is conjectured that the maximum atomic number $Z=238$. A black-body object is in the equilibrium of complex energies of masses, charges, and wavelengths if its radius $R_\text{eq} \approx 2.7665~G M_{\text{BBO}}/c^2$, which corrects the value of the photon sphere radius $R_{\text{ps}}=3G M/c^2$, taking into account the value(s) of the fine-structure constant(s), which is otherwise neglected in general relativity.

Section: α 2 -Set Of Planck Unitsmentioning

confidence: 99%

The Imaginary Universe

2023

Preprint

“…were also derived [17] (Eqs. [29][30][31] based on the thin film model (setting n s = 1 for substrate).…”

Section: The Second Fine-structure Constantmentioning

confidence: 99%

“…and can be expressed, using the relation (31), in terms of base Planck units q P , ℓ P , m P , t P , and T P .…”

Section: α 2 -Set Of Planck Unitsmentioning

confidence: 99%

“…Base Planck units themselves admit negative values as negative square roots. By choosing complex analysis, within the framework of emergent dimensionality [5,9,11,30,31], we enter into bivalence by the very nature of this analysis. All geometric objects have both positive and negative volumes and surfaces [31] equal in moduli.…”

Section: α 2 -Set Of Planck Unitsmentioning

confidence: 99%

“…By choosing complex analysis, within the framework of emergent dimensionality [5,9,11,30,31], we enter into bivalence by the very nature of this analysis. All geometric objects have both positive and negative volumes and surfaces [31] equal in moduli. On the other hand, imaginary and negative physical quantities are the subject of research.…”

Section: α 2 -Set Of Planck Unitsmentioning

confidence: 99%

See 2 more Smart Citations

The Imaginary Universe

2023

Preprint

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 $objects$ 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 $R_{WD} < 6.7933~G M_{WD}/c^2$. A black-body object is in the equilibrium of complex energies of mass, charge, and electromagnetic radiation if its radius $R_{eq} \approx 2.7665~G M_{BBO}/c^2$.

The Imaginary Universe

2023

Preprint

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 $c$. The second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$ is present in Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene, leading to these imaginary Planck units, and it establishes $c_n \approx -3.06 \times 10^8~\text{[m/s]}$. It follows that electric charges are the same in real and imaginary dimensions. We model neutron stars and white dwarfs, emitting perfect black-body radiation, as objects having energy exceeding their mass-energy equivalence ratios. We define complex energies in terms of real and imaginary Planck units. Their imaginary parts, inaccessible for direct observation, store the excess of these energies. It follows that black holes are fundamentally uncharged, charged micro neutron stars and white dwarfs with masses lower than $5.7275 \times 10^{-10}~[\text{kg}]$ are inaccessible for direct observation, and the radii of white dwarfs' cores are limited to $R_{\text{WD}} < 6.7933~G M_{\text{WD}}/c^2$. It is conjectured that the maximum atomic number $Z=238$. A black-body object is in the equilibrium of complex energies of masses, charges, and photons if its radius $R_\text{eq} \approx 2.7665~G M_{\text{BBO}}/c^2$, which corrects the value of the photon sphere radius $R_{\text{ps}}=3G M/c^2$, by taking into account the value(s) of the fine-structure constant(s), which is otherwise neglected in general relativity. Complex Newton’s law of universal gravitation, based on complex energies, leads to the black-body object's surface gravity and the generalized Hawking radiation temperature, which includes its charge. The proposed model explains the registered (GWOSC) high masses of neutron stars' mergers without resorting to any hypothetical types of exotic stellar objects.