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The Structure of Space and its Impact on Interplanetary Travel and Answers to Fundamental Cosmological Questions
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Shape of the hypersurface ℵ
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Journal of Advances in Physics Vol 20 (2022) ISSN: 2347-3487 https://rajpub.com/index.php/japDOI: https://doi.org/10.24297/jap.v20i.9215
The Structure of Space and its Impact on Interplanetary Travel and Answers to Fundamental
Cosmological Questions
*Natalia Julia Sobolewska1, *Joanna Paulina Sobolewska2, *Marek Juliusz Sobolewski3, *Michał Amadeusz
Sobolewski4, *Dariusz Stanisław Sobolewski5
1,2,3,4,5
Physics department, Theoretical physics, HTS High Technology Solutions, Poland
Abstract
The article presents the far-reaching implications of the theory entitled "Theory of Space" (Sobolewski D. S.,
Theory of Space, 2016) (Sobolewski D. S., Theory of Space, 2017) (Sobolewski D. S., Theory of Space, 2022 - new
unpublished edition) and of the publication "New Generations of Rocket Engines" (Sobolewska, Sobolewska,
Sobolewski, Sobolewski, & Sobolewski, 2021). Among others, it presents the shape of curved space in 𝐸 4 for
𝛽
selected planets of the solar system and the Sun, taking into account boundary hypersurfaces 𝛼ℵ𝛼 and ℵ𝛽 and
gravitational interactions. The existence of space tunnels was analysed and the perspective of new technologies
enabling interplanetary travel was outlined. Furthermore, due to the revealed structure of space, cosmological
issues including the existence of other Universes and possible effects of their interactions are addressed. The
constant Gdańsk was also introduced 𝐺𝐺𝑑𝑎ń𝑠𝑘 which, together with the introduced equation, makes it possible
to determine the maximum immersion depth of an astronomical object of mass 𝑀.
(All co-authors of this article made the same contribution under the direction of D.S. Sobolewski.)
Keywords: Interstellar Travel, Gravitational interactions, Curvature of the space, Cosmology, Theory of Space,
Radius of the universe, Curvature of the hypersurface alpha, Curvature of the hypersurface beta, Universes,
Poznań constant, Gdańsk constant
Introduction
The theory entitled "Theory of Space" (Sobolewski D. S., Theory of Space, 2016) (Sobolewski D. S., Theory of Space, 2017)
derives fundamental concepts of physics such as the passage of time, matter and energy from the concept of space, which is
a four-dimensional differential manifold 𝑅𝑒 𝑀 immersed in a four-dimensional Euclidean space.
Matter, according to the cited theory, appears to us in the form of space swirls, of which elementary particles are built, and the
velocity of time flow in a given region of space characterizes its properties. Therefore, one may say that the currently applied
concept of space-time is nothing else but a far-reaching simplification of description of physical phenomena by reducing
properties of four-dimensional space to three-dimensional space and lapse of time, which depends on properties of space,
𝛽
including distances between four-dimensional boundary hypersurfaces ℵ𝛽 , 𝛼ℵ𝛼 , which is shown in Fig. 1 (Sobolewski D. S.,
Theory of Space, 2016) (Sobolewski D. S., Theory of Space, 2017).
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, Journal of Advances in Physics Vol 20 (2022) ISSN: 2347-3487 https://rajpub.com/index.php/jap
𝛽 𝛽
⬚ℵ
̆𝑝
𝑈 ෭𝑞
𝑈
𝛼 𝛼
⬚ℵ
𝛽 𝛽
Fig. 1 Area of space 𝑈 ⊂ 𝑅𝑒 𝑀 bounded by four-dimensional boundary hypersurfaces ℵ , 𝛼ℵ𝛼 (Sobolewski D.
S., Theory of Space, 2017).
𝛽
In this paper, we will focus on the differentiated properties of boundary hypersurfaces 𝛼ℵ𝛼 and ℵ𝛽 using for
̆𝑝 and
this purpose the analysis of their deformations under the influence of matter (space channels of the type 𝑈
𝑈̆𝑞 ), which is consistent with the revealed deformations revealed in the
"Theory of Space" (Sobolewski D. S., Theory of Space, 2016).
𝛽
We shall also determine the shape of boundary hypersurfaces 𝛼ℵ𝛼 and ℵ𝛽 for a single astronomical object of
mass 𝑀 including black holes.
In addition, we will present the cosmological consequences of the results obtained including the formation of
four-dimensional space tunnels and present the emerging possibility of using the gravitational field to orient
the space channels of the rocket as mentioned in "New Generations of Rocket Engines" (Sobolewski D. S.,
Sobolewski, Sobolewski, Sobolewska, & Sobolewska, 2020).
Materials and Methods
The grounds of presented results refer to the theory from the field of theoretical physics entitled: "Theory of
space" (Sobolewski D. S., Theory of Space, 2016) (Sobolewski D. S., Theory of Space, 2017) (Sobolewski D. S.,
Theory of Space, 2022 - new unpublished edition), which gave us, among others, the essence of the gravitational
interactions and equations describing the curvature of the space.
Summing up, in this work method of analysis and logical structure have been applied based on notions, models
and equations introduced by the "Theory of Space", along with "New Generations of Rocket Engines"
(Sobolewska, Sobolewska, Sobolewski, Sobolewski, & Sobolewski, 2021).
Results and Discussion
Shape of the hypersurface 𝛼ℵ𝛼
Using numerical calculations, a solution to the nonlinear differential equation (1) describing the boundary
hypersurface 𝛼ℵ𝛼 (Fig. 1) outside the astronomical object presented in the "Theory of Space" (Sobolewski D. S.,
Theory of Space, 2016) (Sobolewski D. S., Theory of Space, 2017) (Sobolewski D. S., Theory of Space, 2022 - new
unpublished edition) for single astronomical objects.
The differential equation (2) describing a boundary hypersurface 𝛼ℵ𝛼 (Fig. 1) inside the astronomical object was
introduced and solved numerically.
√𝜒′(𝑥)2 +1−1 1 1
− ) {𝜒′(𝑥): 0 ≤ 𝜒′(𝑥) ≤ 𝜒′(𝑥𝑅 )}
𝐺𝑀 𝐺𝑀
𝑥= (−𝐿𝑜𝑔 ( ) + 𝐿𝑜𝑔 ( )+ (1)
𝑐2 𝑐2𝑅 3
√𝜒′(𝑥)2 +1 √𝜒′(𝑥)2 +1−1
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, Journal of Advances in Physics Vol 20 (2022) ISSN: 2347-3487 https://rajpub.com/index.php/jap
2𝑐 2 𝑅(√𝜒′ (𝑥)2 +1−1) 𝑅(2√𝜒′ (𝑥)2 +1+1) 𝐺𝑀
𝑥 = √3 − ( − ) {𝜒′(𝑥): 𝜒′(0) ≤ 𝜒′(𝑥) ≤ 𝜒′(𝑥𝑅 )} (2)
𝑐2
𝐺𝑀 √𝜒′ (𝑥)2 +1 3√𝜒′ (𝑥)2 +1
The results are presented as two- and three-dimensional diagrams in the Euclidean space coordinate system 𝐸 4
with the origin of the coordinate system located at the center of the astronomical object
- Fig. 2, Fig. 3.
Fig. 2 Shape of the boundary hypersurface 𝛼ℵ𝛼 near the Earth. By 𝜕𝑂 denotes the edge of the Earth.
Fig. 3 Shape of the boundary hypersurface 𝛼ℵ𝛼 near the Earth.
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, Journal of Advances in Physics Vol 20 (2022) ISSN: 2347-3487 https://rajpub.com/index.php/jap
𝛽
Shape of the hypersurface ℵ𝛽
𝛽
A differential equation describing the boundary hypersurface is introduced ℵ𝛽 (Fig. 1) in the interior of a single
astronomical object in the curvilinear coordinate system associated with the hypersurface 𝛼ℵ𝛼 which has been
solved (4) and presented in the form of a diagram together with the solution disclosed outside the astronomical
object (3) in the theory entitled "Theory of Space" (Sobolewski D. S., Theory of Space, 2016) (Sobolewski D. S.,
Theory of Space, 2017) (Sobolewski D. S., Theory of Space, 2022 - new unpublished edition).
𝐺𝑀 1 𝐺𝑀
𝐹 ( cos−1 (
𝛽
𝜒(𝑟) = √ )|2) + 𝐶1 {𝑟: 𝑅 ≤ 𝑟} (3)
𝑐𝑘 2 𝑐𝑘𝑟 2
𝐺 2 𝑀2𝑟 2
𝑐 𝑘 𝑅3 √1 −
𝛽 𝑐 2 𝑘 2𝑅6 {𝑟: 0 ≤ 𝑟 ≤ 𝑅}
(4)
𝜒(𝑟) = − + 𝐶2
𝐺𝑀
𝛽
The diagram of relations 𝜒(𝑟) in the curvilinear system for single astronomical objects, including the Earth -
Fig. 4, Fig. 5.
𝛽
Fig. 4. Dependence diagram 𝜒(𝑟) for 𝑟 ≥ 𝑅𝐸 for the Earth.
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