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Topological Vortex Space-Time Ontology (TVSTO) Bao-hua ZHANG I. Introduction Topological Vortex Space-Time Ontology (TVSTO) is a revolutionary theoretical framework for spacetime. Its core tenets can be summarized across the following three levels: 1.1 Reconstruction of Spacetime Essence: TVSTO regards spacetime not as traditional Euclidean space, but as a dynamic vortex network formed through topological phase transitions of a non-viscous, incompressible, and isotropic ideal fluid. This theory breakthrough integrates spacetime geometry with fluid dynamic properties, offering a new perspective for understanding the universe’s fundamental structure. 1.2 Vortex Dynamics Mechanism: The theory explains physical phenomena through topological invariants (such as winding numbers and genus), positing that non-local correlations like quantum entanglement originate from the geometric intrinsic properties of the vortex network. This mechanism unifies quantum mechanics and general relativity at the level of spacetime topology. 1.3 Explanation of Modern Physical Problems: TVSTO not only successfully describes classical physical phenomena but also provides a self-consistent theoretical framework for frontier issues like dark energy and macroscopic quantum phenomena. Its perspective of symmetry-dominated natural laws further challenges the paradigm of traditional particle physics. II. Theoretical Innovativeness of TVSTO Through a mathematical vortex nucleation model, TVSTO achieves a unified description spanning from microscopic quantum vortices to cosmic-scale structures, marking a paradigm shift in natural philosophy from creationism and mechanism toward topological emergence. The theoretical innovativeness of TVSTO is primarily reflected in breakthroughs in its methodology and physical interpretation: 2.1 Methodological Innovation: Unlike traditional physical models based on particles or field theories, TVSTO adopts a topological fluid dynamics framework, treating spacetime as a quantized fluid and explaining the emergence of matter and energy through topological phase transitions of vortices (e.g., winding number transitions). For instance, quantum entanglement is redefined as a non-local geometric correlation within the vortex network, rather than a probabilistic correlation in traditional quantum mechanics. 2.2 Breakthroughs in Physical Interpretation: 2.2.1 Dark Energy: The theory proposes that the universe’s accelerated expansion stems from the dynamic evolution of the topological structure of vortices in the background space, with its repulsive effect generated by a geometric repulsion mechanism between vortices. 2.2.2 Unification of Quantum Gravity: TVSTO naturally introduces a geometric description of gravity through the higher-dimensional structures formed by vortex self-organization, avoiding the issue of extra dimensions inherent in traditional string theory. 2.2.3 Nature of Symmetry: It introduces the concept of “symmetry transition,” proposing that the emergence of complex systems (e.g., superfluid vortices) results from the layering of topological symmetries, rather than symmetry breaking. These innovations give TVSTO unique advantages in explaining macroscopic quantum phenomena (such as optical skyrmions), with its mathematical framework showing significantly higher agreement with experimental observations compared to traditional theories. III. Mathematical Framework of TVSTO The mathematical framework of TVSTO is based on topological fluid dynamics, and its core equations and models can be summarized into the following key parts: 3.1 Vortex Dynamics Equation: Uses a modified form of the generalized Navier-Stokes equation to describe the generation and evolution of topological vortices in an ideal fluid: ∂v/∂t + (v·∇)v = −∇p + κ∇²v + F_topo Here, κ is the vortex topological invariant (e.g., winding number), and F_topo represents the topological interaction force between vortices. Introduces the quantization condition ∮v·dl = nℏ/m (n is an integer), linking vortex circulation quantized angular momentum. 3.2 Spacetime Topology Model: 3.2.1 Depicts the birth of spacetime through the Vortex Nucleation Model: Background space undergoes a topological phase transition under critical conditions, forming a vortex network with genus g. Its metric tensor g_{μν} is determined by the vortex density field ρ_v: ds² = ρ_v(φ)dt² − ρ_v⁻¹(φ)dφ² where φ is the topological phase of the vortex field. 3.2.2 Establishes the Conservation Law of Winding Number: W = (1/4π) ∫ v · (∇ × v) d³x = const. This equation ensures the geometric stability of vortex correlations and directly supports the non-locality interpretation of quantum entanglement. 3.3 Symmetry Transition Theory: Proposes higher-order symmetry groups G_n to describe the vortex self-organization process. System complexity is achieved through transitions in the order n of the symmetry group, rather than through traditional symmetry breaking. For example, the emergence of a superfluid vortex corresponds to a symmetry transition from G₂ to G₄. These mathematical tools, validated through experiments (e.g., optical vortex interference experiments) and theoretical self-consistency (e.g., asymptotic compatibility with general relativity), provide a solid computational foundation for TVSTO. IV. Theoretical Self-Consistency and Experimental Verification of TVSTO The experimental verification and theoretical self-consistency of TVSTO are mainly reflected in the following aspects: 4.1 Theoretical Self-Consistency: 4.1.1 Compatibility with General Relativity: TVSTO reduces to the Einstein field equations in the weak-field limit. Its vortex metric tensor coincides with the Minkowski metric under flat spacetime conditions, ensuring continuity with the classical gravity domain. 4.1.2 Consistency with Quantum Mechanics: Quantum entanglement explained via the winding number conservation law shows no contradiction with Bell’s inequality experimental results and can circumvent the measurement paradox in traditional quantum theory. 4.1.3 Completeness of the Mathematical Framework: The vortex nucleation model is compatible with the mathematical structure of topological field theories (e.g., Chern-Simons theory), and its symmetry transition theory also conforms to group theory constraints. 4.2 Experimental Verification: 4.2.1 Observation of Optical Skyrmions: The topological structures of optical vortices observed experimentally (e.g., vortex phase singularities) highly coincide with the geometric characteristics of the vortex network predicted by TVSTO. Measurements of their winding numbers support the theory’s non-local correlation model. 4.2.2 Superfluid Vortex Experiments: The quantized vortex circulation behavior observed in ultra-cold superfluids is consistent with TVSTO’s quantization condition ∮v·dl = nℏ/m, verifying the applicability of the vortex dynamics equation. 4.2.3 Macroscopic Quantum Phenomena: Topological phase transitions in certain condensed matter systems (e.g., topological insulator edge states) exhibit symmetry evolution patterns similar to those described by TVSTO’s symmetry transition theory. These verifications indicate that TVSTO can not only explain existing experimental phenomena but also provides a testable predictive framework for future research (e.g., dark energy detection, quantum gravity experiments). V. Conclusion By redefining the nature of spacetime, TVSTO provides a theoretical framework for modern physics that combines innovativeness with explanatory power. Its core contributions lie in: 5.1 Paradigm Innovation: Replacing traditional particle or field-based models with topological fluid dynamics, it treats spacetime as a dynamic vortex network, unifying the geometric descriptions of quantum mechanics and general relativity. 5.2 Problem-Solving Capability: It successfully explains frontier issues like dark energy and quantum entanglement, and breaks through the limitations of traditional symmetry breaking via its symmetry transition theory. 5.3 Experimental and Mathematical Verification: Experimental observations in optical vortices and superfluids show high agreement with theoretical predictions, and the mathematical framework possesses both self-consistency and extensibility. Topological Vortex Space-Time Ontology (TVSTO) not only advances the deep understanding of natural laws but also opens new pathways for future research, such as the unification of quantum gravity.
Topological Vortex Space-Time Ontology (TVSTO)
Bao-hua ZHANG
I. Introduction
Topological Vortex Space-Time Ontology (TVSTO) is a revolutionary theoretical framework for spacetime. Its core tenets can be summarized across the following three levels:
1.1 Reconstruction of Spacetime Essence:
TVSTO regards spacetime not as traditional Euclidean space, but as a dynamic vortex network formed through topological phase transitions of a non-viscous, incompressible, and isotropic ideal fluid. This theory breakthrough integrates spacetime geometry with fluid dynamic properties, offering a new perspective for understanding the universe’s fundamental structure.
1.2 Vortex Dynamics Mechanism:
The theory explains physical phenomena through topological invariants (such as winding numbers and genus), positing that non-local correlations like quantum entanglement originate from the geometric intrinsic properties of the vortex network. This mechanism unifies quantum mechanics and general relativity at the level of spacetime topology.
1.3 Explanation of Modern Physical Problems:
TVSTO not only successfully describes classical physical phenomena but also provides a self-consistent theoretical framework for frontier issues like dark energy and macroscopic quantum phenomena. Its perspective of symmetry-dominated natural laws further challenges the paradigm of traditional particle physics.
II. Theoretical Innovativeness of TVSTO
Through a mathematical vortex nucleation model, TVSTO achieves a unified description spanning from microscopic quantum vortices to cosmic-scale structures, marking a paradigm shift in natural philosophy from creationism and mechanism toward topological emergence. The theoretical innovativeness of TVSTO is primarily reflected in breakthroughs in its methodology and physical interpretation:
2.1 Methodological Innovation:
Unlike traditional physical models based on particles or field theories, TVSTO adopts a topological fluid dynamics framework, treating spacetime as a quantized fluid and explaining the emergence of matter and energy through topological phase transitions of vortices (e.g., winding number transitions). For instance, quantum entanglement is redefined as a non-local geometric correlation within the vortex network, rather than a probabilistic correlation in traditional quantum mechanics.
2.2 Breakthroughs in Physical Interpretation:
2.2.1 Dark Energy: The theory proposes that the universe’s accelerated expansion stems from the dynamic evolution of the topological structure of vortices in the background space, with its repulsive effect generated by a geometric repulsion mechanism between vortices.
2.2.2 Unification of Quantum Gravity: TVSTO naturally introduces a geometric description of gravity through the higher-dimensional structures formed by vortex self-organization, avoiding the issue of extra dimensions inherent in traditional string theory.
2.2.3 Nature of Symmetry: It introduces the concept of “symmetry transition,” proposing that the emergence of complex systems (e.g., superfluid vortices) results from the layering of topological symmetries, rather than symmetry breaking.
These innovations give TVSTO unique advantages in explaining macroscopic quantum phenomena (such as optical skyrmions), with its mathematical framework showing significantly higher agreement with experimental observations compared to traditional theories.
III. Mathematical Framework of TVSTO
The mathematical framework of TVSTO is based on topological fluid dynamics, and its core equations and models can be summarized into the following key parts:
3.1 Vortex Dynamics Equation:
Uses a modified form of the generalized Navier-Stokes equation to describe the generation and evolution of topological vortices in an ideal fluid:
∂v/∂t + (v·∇)v = −∇p + κ∇²v + F_topo
Here, κ is the vortex topological invariant (e.g., winding number), and F_topo represents the topological interaction force between vortices.
Introduces the quantization condition ∮v·dl = nℏ/m (n is an integer), linking vortex circulation quantized angular momentum.
3.2 Spacetime Topology Model:
3.2.1 Depicts the birth of spacetime through the Vortex Nucleation Model: Background space undergoes a topological phase transition under critical conditions, forming a vortex network with genus g. Its metric tensor g_{μν} is determined by the vortex density field ρ_v:
ds² = ρ_v(φ)dt² − ρ_v⁻¹(φ)dφ²
where φ is the topological phase of the vortex field.
3.2.2 Establishes the Conservation Law of Winding Number:
W = (1/4π) ∫ v · (∇ × v) d³x = const.
This equation ensures the geometric stability of vortex correlations and directly supports the non-locality interpretation of quantum entanglement.
3.3 Symmetry Transition Theory:
Proposes higher-order symmetry groups G_n to describe the vortex self-organization process. System complexity is achieved through transitions in the order n of the symmetry group, rather than through traditional symmetry breaking. For example, the emergence of a superfluid vortex corresponds to a symmetry transition from G₂ to G₄.
These mathematical tools, validated through experiments (e.g., optical vortex interference experiments) and theoretical self-consistency (e.g., asymptotic compatibility with general relativity), provide a solid computational foundation for TVSTO.
IV. Theoretical Self-Consistency and Experimental Verification of TVSTO
The experimental verification and theoretical self-consistency of TVSTO are mainly reflected in the following aspects:
4.1 Theoretical Self-Consistency:
4.1.1 Compatibility with General Relativity: TVSTO reduces to the Einstein field equations in the weak-field limit. Its vortex metric tensor coincides with the Minkowski metric under flat spacetime conditions, ensuring continuity with the classical gravity domain.
4.1.2 Consistency with Quantum Mechanics: Quantum entanglement explained via the winding number conservation law shows no contradiction with Bell’s inequality experimental results and can circumvent the measurement paradox in traditional quantum theory.
4.1.3 Completeness of the Mathematical Framework: The vortex nucleation model is compatible with the mathematical structure of topological field theories (e.g., Chern-Simons theory), and its symmetry transition theory also conforms to group theory constraints.
4.2 Experimental Verification:
4.2.1 Observation of Optical Skyrmions: The topological structures of optical vortices observed experimentally (e.g., vortex phase singularities) highly coincide with the geometric characteristics of the vortex network predicted by TVSTO. Measurements of their winding numbers support the theory’s non-local correlation model.
4.2.2 Superfluid Vortex Experiments: The quantized vortex circulation behavior observed in ultra-cold superfluids is consistent with TVSTO’s quantization condition ∮v·dl = nℏ/m, verifying the applicability of the vortex dynamics equation.
4.2.3 Macroscopic Quantum Phenomena: Topological phase transitions in certain condensed matter systems (e.g., topological insulator edge states) exhibit symmetry evolution patterns similar to those described by TVSTO’s symmetry transition theory.
These verifications indicate that TVSTO can not only explain existing experimental phenomena but also provides a testable predictive framework for future research (e.g., dark energy detection, quantum gravity experiments).
V. Conclusion
By redefining the nature of spacetime, TVSTO provides a theoretical framework for modern physics that combines innovativeness with explanatory power. Its core contributions lie in:
5.1 Paradigm Innovation:
Replacing traditional particle or field-based models with topological fluid dynamics, it treats spacetime as a dynamic vortex network, unifying the geometric descriptions of quantum mechanics and general relativity.
5.2 Problem-Solving Capability:
It successfully explains frontier issues like dark energy and quantum entanglement, and breaks through the limitations of traditional symmetry breaking via its symmetry transition theory.
5.3 Experimental and Mathematical Verification:
Experimental observations in optical vortices and superfluids show high agreement with theoretical predictions, and the mathematical framework possesses both self-consistency and extensibility.
Topological Vortex Space-Time Ontology (TVSTO) not only advances the deep understanding of natural laws but also opens new pathways for future research, such as the unification of quantum gravity.