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A Mathematical and Physical Analysis On the Origin of Objects (or Matters) in Space (2)

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Posted 2025-12-19 04:36:40

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2. Critique of Theories that Mystify the Origin of Matter

2.1 Characteristics of Common Mystifying Theories

1) Creation ex nihilo: Asserts that matter can arise from absolute "nothingness" (non-quantum vacuum) via divine or spiritual will, violating all known conservation laws.

2) Non-material consciousness creationism: Posits consciousness or spirit as primary, with matter as its projection or condensation, but fails to specify the coupling mechanism between consciousness and physical quantities.

3) Higher-dimensional projection theory: Claims that observed matter is merely a projection of higher-dimensional entities but cannot provide a testable mathematical mapping or physical predictions.

2.2 Refutation from the Philosophy of Science

1) Principle of Falsifiability: The aforementioned theories typically avoid falsification by constantly adding ad hoc assumptions, lacking the basic features of a scientific theory.

2) Occam's Razor: Introducing supernatural entities is superfluous given that TVT can provide a self-consistent mechanism.

3) Lack of Mathematical Consistency: Mystifying theories often lack rigorous mathematical formulation and cannot interface with established physical laws (e.g., General Relativity, Quantum Field Theory).

3. The Mathematical Mechanism of Matter Formation in TVT: Topological Phase Transitions and Vortex Excitations

3.1 Dynamical Description of the Ideal Superfluid Space

Let the macroscopic wave function of the spatial superfluid be \(\Psi(\mathbf{r},t) = \sqrt{\rho(\mathbf{r},t)} e^{i\theta(\mathbf{r},t)}\), where \(\rho\) is the superfluid density (constant and incompressible), and \(\theta\) is the phase. The dynamics are described by a Gross-Pitaevskii type equation [2]:

\[i\hbar \frac{\partial \Psi}{\partial t} = -\frac{\hbar^2}{2m} \nabla^2 \Psi + V_{\text{ext}} \Psi + g |\Psi|^2 \Psi\]

In the absence of external potential and under homogeneous, isotropic conditions, the ground state is a flow with uniform phase. However, topologically non-trivial configurations of the phase \(\theta\) can give rise to stable excitations.

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