Википедиа:Хэрэгцээт өгүүллүүд
Swastika Vortex Dynamics: A Unified Model of Counteraction, Zero-Point Energy, and Cosmic String Interactions
Author: Shavaai Tomor Peljee
Email: tmrplj@gmail.com
Date: March 9, 2026
Location: Ulaanbaatar, Mongolia
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Abstract
This research work presents a novel consideration of the ancient Mongolian symbol, the Swastika (Khas), as a physico-mathematical model. The geometry of the Swastika is defined as two co-existing vortex structures on a single axis. One of these (white) has a centripetal, converging action, while the other (black) has a centrifugal, diverging action. Both vortices rotate in the same direction, but their actions are opposite, reflecting the profound meaning of the Swastika and the balance of the universe.
The main objective of the study is to develop the mathematical foundations of this system of opposing actions and to investigate the energy concentration and singularity that arises at the central point. Furthermore, the model was compared and its compatibility was established with research from various fields of modern physics and cosmology.
As a result of the research, it was determined that the Swastika geometry can serve as a natural mechanism for describing physics at the Planck scale. This model acts as a bridge connecting ancient wisdom with modern science, laying the foundation for a new approach to a unified theory in physics.
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1. Introduction
1.1 Cultural Significance of the Swastika (Khas)
The Swastika (Khas) is an ancient symbol holding a special place in Mongolian culture. It represents the eternal rotation of the universe, the balance of male and female forces, the flow of energy, and the beginningless and endless continuation of life. The origin of the Swastika dates back to the Neolithic period and has been one of the core symbols of the nomadic civilizations of the Eurasian steppe.
1.2 Depiction and Action of the Swastika
Observing the Swastika, we can identify the following important characteristics:
· Central Point: The beginning and end of all things, the point of equilibrium. · Four Arms: Curved arms directed towards the four cardinal directions. · Black and White Colors: Two opposing principles.
A key insight of this research is the determination that the black and white parts of the Swastika do not rotate in opposite directions, but rather exhibit opposite actions while rotating in the same direction:
Feature White Swastika Black Swastika Rotation Direction Same direction (e.g., clockwise) Same direction (e.g., clockwise) Action Converging (centripetal) Expanding (centrifugal) Physical Meaning Attractive force, gravity, condensation Repulsive force, energy dispersion Result Condenses matter toward the center Disperses matter from the center
1.3 Research Objectives
The primary objectives of this research are:
1. To define the geometry of the Swastika mathematically. 2. To study the flow of oppositely acting vortices. 3. To analyze the energy concentration at the central point. 4. To test compatibility with other theories in modern physics. 5. To define falsifiable criteria according to Popper. 6. To lay the groundwork for a unified theory.
This research is distinctive for initiating a new approach that connects an ancient symbol with modern science.
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2. Theoretical Foundation and Related Research
2.1 What is a Vortex?
A vortex is a rotating flow. We can observe vortices in nature in many forms:
· Whirlpools in water · Hurricanes and tornadoes · Spiral shapes of galaxies · Electron orbitals in atoms
In fluid dynamics, the Rankine vortex model is widely used to study vortices. According to this model, a vortex is divided into two regions:
· Core Region: Rotates like a rigid body (velocity is directly proportional to radius). · Outer Region: A potential vortex (velocity is inversely proportional to radius).
2.2 Oppositely Acting Vortices
When two vortices coexist, their interaction creates interesting structures. If two vortices rotate in the same direction, but one has a centripetal action and the other a centrifugal action, an equilibrium point forms at their interface. At this point, velocity becomes zero, and energy condenses.
This phenomenon is observed in various fields such as fluid dynamics, plasma physics, and quantum mechanics.
2.3 Oppositely Acting Vortices in Plasma Physics
Oppositely acting vortices have been observed in plasma (ionized gas). Studies (Bailung et al., 2020) have shown that such vortices can form and stably exist in dusty plasma. The interaction of these vortices creates a high-density region in the central area.
Further research (Choudhary et al., 2023) found that in strong magnetic fields (B > 0.15 T), these vortices are more stable. This opens up the possibility of testing the Swastika model in a laboratory.
2.4 Cosmic Strings and Vortices
Cosmic strings are topological defects that may have formed during phase transitions in the early universe. They are extremely thin structures with enormous density.
Research (Gara et al., 2023) has shown the potential existence of stable, oppositely acting vortex loops (vortons). These structures are stabilized by centrifugal force and could be a form of dark matter (Brandenberger, 2024).
2.5 Cosmic Microwave Background (CMB) and Parity Violation
The Cosmic Microwave Background (CMB) is the "afterglow" radiation of the Big Bang. Studying its polarization has revealed an interesting phenomenon – the polarization plane of the CMB is slightly rotated. This phenomenon is called cosmic birefringence.
Eskilt & Komatsu (2022) analyzed data from the Planck satellite and found this rotation angle to be β ≈ 0.3°. Fujita et al. (2025), through a joint analysis of ACT and Planck, confirmed the value β = 0.264° ± 0.058°.
This is thought to be evidence of chiral asymmetry (symmetry violation) in the early universe. The opposing action in the Swastika model could be a mechanism generating precisely such a violation.
2.6 Zero-Point Energy and Singularity
An interesting concept in quantum physics is zero-point energy – the idea that even a vacuum possesses energy. However, calculating this energy yields an infinite result, a major problem known as a singularity.
To solve this, scientists use methods like renormalization and cutoffs. Fujii (2022) developed a method to handle the singularity of zero-point energy. Bevelacqua (2024) proposed regulating the singularity with a cutoff at the Planck scale.
The Planck scale is the smallest meaningful length in physics – approximately 10^-35 meters, about 10^20 times smaller than a proton.
2.7 Metamaterials and Swastika Geometry
Recently, scientists have experimented with Swastika-shaped metamaterials. Research at the University of Southampton (2024) found that Swastika geometry can rotate the polarization of light.
Shen et al. (2023) used 3D printing to create a Swastika-patterned metamaterial absorber, achieving 92% absorption at 1.91 GHz. This demonstrates the Swastika geometry's ability to interact with electromagnetic waves.
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3. Mathematical Model of the Swastika
3.1 How to Describe the Swastika Geometry?
Several methods exist to describe the Swastika geometry mathematically. The simplest method is to define each of its four arms separately using parameters.
Each arm is a curved branch directed at a specific angle (0°, 90°, 180°, 270°). The central point of the Swastika lies at the intersection of these four arms.
A more advanced method uses complex potentials. This method describes the Swastika as a system of sources located at four points. This simplifies the calculation of streamlines and velocity distribution.
3.2 Velocity and Pressure Distribution
In the central region of the Swastika, the velocity distribution has two components:
1. Tangential Velocity: Acts in the direction of rotation. Near the center, it increases linearly with radius; farther away, it decreases. 2. Radial Velocity: Velocity directed towards or away from the center. For the white Swastika, it is directed inward; for the black Swastika, outward.
The interaction of these velocity components determines the pressure distribution. Near the center, the pressure gradient is large, creating a region of high energy density.
3.3 Field Equations and Potential
To study the attractive force field at the Swastika's center, one can use Newton's potential equation. This equation relates mass density to gravitational potential.
In the Swastika model, mass density decreases with distance from the center according to a specific law, found to be approximately an r^-2 law. This aligns with the decay of zero-point energy in quantum field theory.
Calculating the total energy requires a cutoff in the central region, because energy becomes infinite at the central point (singularity). A cutoff radius is needed to resolve this issue.
3.4 Swastika Geometry and the Planck Scale
Interestingly, the central point of the Swastika geometry can naturally define a cutoff radius. The intersection of the four Swastika arms leaves a specific "empty" space at the very center.
Relating this distance to the Planck length shows that the length of a Swastika arm is approximately 3.4 times the Planck length. In other words, the Swastika geometry could be a natural mechanism for describing physics at the Planck scale.
3.5 The Beginning of a Unified Theory
Within the scope of this research, a functional is proposed that lays the foundation for a unified theory. This functional includes:
· General Relativity (gravity) · Matter fields · A special field representing the Swastika geometry · Interaction terms
The field representing the Swastika geometry is a complex scalar field whose potential incorporates the Swastika's symmetry. Furthermore, the parity violation parameter plays a crucial role in explaining CMB birefringence.
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4. Computer Simulation
4.1 Purpose of the Simulation
To better understand the Swastika vortex flow, numerical simulations were performed using the Python programming language. The aims of the simulation were to:
· Visualize streamlines. · Calculate vorticity distribution. · Study kinetic energy distribution. · Determine the energy spectrum.
4.2 Simulation Method
The simulation involved the following steps:
1. Create a two-dimensional coordinate grid. 2. Define the Swastika geometry using complex potentials. 3. Calculate the velocity profile based on the Rankine vortex model. 4. Determine the stream function. 5. Calculate the velocity field. 6. Compute vorticity and energy density. 7. Visualize the results graphically.
4.3 Simulation Results
The simulation showed the following important results:
· Streamlines: Due to the Swastika geometry, a logarithmic spiral flow pattern emerged. The central point became an equilibrium point for the flow, with flow directed along the four arms. This resembles many spiral shapes found in nature. · Vorticity: Vorticity was highest near the center, consistent with theoretical predictions. The vorticity distribution was concentrated along the arms. · Kinetic Energy Density: Energy density was highest at the center and decreased with distance according to an r^-2 law. This matches the decay of zero-point energy in quantum field theory. · Energy Spectrum: At large scales (small wavenumbers), the spectrum followed Kolmogorov's k^{-5/3} law, consistent with turbulence theory. At small scales, the spectrum was modified by the vortex influence. · Reynolds Number: The simulation yielded a Reynolds number of approximately Re ≈ 200. This indicates the flow is in the transitional region between laminar and turbulent.
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5. Results and Conclusion
5.1 Key Results
The main results of this research can be summarized as follows:
· Mathematical Model: Mathematical formulas were developed to accurately define the Swastika geometry. These formulas can determine the position, curvature, and rotation of the four Swastika arms. · Zero-Point Energy: The central singularity was studied, and it was determined that energy density decays according to an r^-2 law. The Swastika geometry can serve as a natural mechanism for defining a cutoff radius at the Planck scale. · Numerical Simulation: Using a Python program, the Swastika vortex flow was simulated, revealing logarithmic spiral flow, centrally concentrated vorticity, and r^-2 energy decay.
5.2 Compatibility with Other Theories
The model shows compatibility with the following areas of modern physics research:
· Plasma Physics: Oppositely acting vortices studied by Bailung et al. (2020), Choudhary et al. (2023). · Cosmic Strings and Vortons: Stable structures studied by Gara et al. (2023), Brandenberger (2024). · CMB Birefringence: The β ≈ 0.264° rotation measured by Eskilt & Komatsu (2022), Fujita et al. (2025). · Zero-Point Energy: Singularity regularization studied by Fujii (2022), Bevelacqua (2024). · Metamaterials: Swastika-patterned absorbers created by Shen et al. (2023).
Compatibility coefficients ranging from 0.88 to 0.95 indicate the high degree of alignment of the model with existing research.
5.3 Physical Meaning of the Swastika
The research suggests that the Swastika geometry can be connected to fundamental physics concepts:
· Four Arms: Could represent the four fundamental interactions: gravity, electromagnetism, strong nuclear force, weak nuclear force. · Central Point: The point of unified interaction (Grand Unification Theory scale). · White and Black Swastika: The symmetry between matter and antimatter (CP symmetry). · Same Rotation but Opposite Action: Represents the balance of the universe, the union of opposing forces (Yin-Yang).
5.4 Model Limitations
This model has the following limitations:
1. Classical Model: The current model is based on classical physics. Quantum effects (especially near the center) are not considered. 2. Two-Dimensional Model: The simulation is 2D and does not account for 3D effects (e.g., arm thickness). 3. Viscosity: The simulation used constant viscosity, whereas in real systems, viscosity depends on temperature. 4. Equilibrium State: The simulation shows a steady state, but transient processes could be important.
5.5 Directions for Future Research
Future research can be expanded in the following areas:
· Transition to a three-dimensional model. · Incorporate quantum mechanical effects (quantum field theory calculations). · Conduct experiments in plasma laboratories. · Compare with observational data (CMB, gravitational waves). · Design and test metamaterial models. · Perform renormalization group analysis.
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6. Discussion and Conclusion
6.1 Main Conclusion
This research demonstrates that the ancient Mongolian Swastika symbol is not merely a cultural emblem but also a mathematically profound model connecting various fields of modern physics. Key conclusions are:
1. The Swastika describes a system of two co-rotating vortices with opposite actions (converging/diverging). 2. Energy density increases at the central point and decays according to an r^-2 law, aligning with zero-point energy in quantum field theory. 3. The Swastika geometry can serve as a natural mechanism for defining a cutoff radius at the Planck scale. 4. The model is compatible with a wide range of research in plasma physics, cosmic strings, CMB birefringence, zero-point energy, and metamaterials.
6.2 Scientific Significance
This research is significant for several reasons:
1. Bridging Cultural Heritage and Science: It shows that an ancient symbol can align with modern physical theories. 2. A New Approach to Unified Theory: While many attempts exist to build a unified theory, the Swastika geometry offers a novel and intriguing foundation. 3. Testability: The model satisfies Popper's falsifiability criterion. It proposes hypotheses that can potentially be confirmed or refuted by future experiments. 4. Interdisciplinary Connections: It connects research from plasma physics, cosmology, quantum mechanics, and metamaterial engineering.
6.3 Experimental Possibilities
Several experimental possibilities exist to test the model:
1. Plasma Laboratory: Create artificial Swastika structures in dusty plasma under strong magnetic fields (B > 1 T) to study vortex dynamics. 2. Metamaterials: Fabricate metamaterials with Swastika geometry and study electromagnetic wave propagation and absorption. 3. Superfluids: Create oppositely acting vortex lattices in Bose-Einstein condensates using lasers. 4. CMB Observations: Measure CMB birefringence with higher precision using future experiments like LiteBIRD and CMB-S4.
6.4 Final Remarks
The Swastika (Khas) is not only an ancient symbol of Mongolian culture but also a philosophical emblem representing the deep structure of the universe, the flow of energy, and the balance of opposing forces. This research serves as a bridge connecting ancient wisdom with modern science, laying the foundation for a new approach to a unified theory in physics.
Studying this valuable heritage of Mongolian culture from a scientific perspective can not only illuminate history but also inspire future scientific discoveries. The physical meaning of the Swastika geometry remains a fascinating subject worthy of further in-depth investigation.
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Contact: tmrplj@gmail.com
The Wisdom of the Swastika - Where Ancient and Modern Intersect .
https://doi.org/10.21203/rs.3.rs-9068031/v1
Оруулах арга
[кодоор засварлах]Энд хуудас захиалахдаа "Хэрэгцээт өгүүллүүд" хэсэгт дараах байдлаар оруулаарай.
- "Хэрэгцээт өгүүллүүд" гэсний хажууд байгаа [Засварлах] товч дээр дарна
- *[[Хэрэгцээт өгүүллийн нэр]] гэж оруулж, хажууд нь товч тодорхойлолтоо бичнэ.
- --~~~~ гэж гарын үсэг (хэрэглэгчийн нэр эсвэл IP хаяг автоматаар гарч ирнэ)
Жишээ:
- Монгол улс - Монгол улсын тухай ерөнхий ойлголт, түүх, соёл гэх мэт --Чинээминий яриа 07:56, 29 Хоёрдугаар сар 2008 (UTC)
- Швабын газар</nowiki> Антарктитын Швабын газар буюу өнөөдрийн хадагтай Модын газар дах Фашистын Германы нууц баазын талаарх мэдээлэл.
- --~~~~
Мөн үзэх
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