Key Papers

On mobile, "landscape view" is recommended due to formula.

📢 Announcement

Publications on Complex Oscillator Dynamics

The following papers will be sequentially published based on the Theory of Oscillator Dynamics: 4/20-

1.General Theory of Complex Oscillator Dynamics

1) Phase Resonance of Oscillators: Essential Answers to the 7 Millennium Problems (2025.04.21)
2) Epistemological Declaration on Solving the Seven Great Problems of Mathematics(2025.04.22)
3) Declaration of the Completion of Ontology(2025.04.26)
4) Singularity Axiom(2025.05.01)
5) Declaration of Integration and Completion of Classical Mechanics (2025.05.03)
6)Complex oscillators theory with Integration of quantum mechanics(2025.05.04)
7)Intermediate Summary - The Essentialist Turn in Scientific Methodology(2025.05.04)
8)Essentialistic Shift in Scientific Method (2025.05.09)
9) Complex Gravitational Black Hole Theory: A Non-Singularity Model(2025.05.26)
10) Unified Interpretation of Cosmological Phenomena via Complex Gravity System (2025.05.30)

11) Unified Theory of Gravity as Spatial Energy Flow (2025.06.23)
12)Scientific Historical Evaluation of Complex Phase Natural Dynamics(2025.07.02)
13)Timeless Mathematical Reconstruction of the 7 Millennium Problems(2025.07.05)
14)Unified Complex Oscillator Dynamics (COD)(2025.07.10)
15)The Quantum Dynamics of Awakening :
A Natural Oscillator Interpretation of the Mahāyāna One Mind I
- As a Note on the Awakening of Mahayana Faith in the Quantum Theory(2025.07.22>
16)Verification of Imaginary Energy (+Gravity) in Complex Phase Space(2025.08.01)
17)Declaration of the Dismantling of the Time Axis(2025.08.02)
18)Heidegger’s Being and Time Interpreted by COD Theory(2025.08.03)

19) Solving three-body and many-body problems based on COD and Riemannian geometry (2025.08.06)
20) COD vs. Kepler + JPL Verification Report (2025.08.15)
21) A Theory Of Cosmology and TOE based on COD 2025 (2025.08.25)
22) The ontological scientific method of the COD White Paper (KO/EN)(2025.08.29)
23) The Truth of Galactic Rotation (KO/EN)(2025.08.30)
24) Mathematical Formation of Human A priori Recognition System(2025.09.03)
25) Efficiency Comparison of Revolution and Rectilinear Motion(2025.09.06)
26) COD Phase‑Based Natural Dynamics Ontology for Sovereign AGI(2025.09.15)
27) Essential Wave — Time-Independent Ontology(2025.09.26)
28) Integration of 2025 Nobel Physics and Complex Oscillator Dynamics (COD)(2025.10.09)

1. EX1. General Theory of Complex Oscillatory Dynamics:
Previously published in the PAPERS section of this website

1) YouTube: Do Planets Really Orbit? (2025.06.18)

2. EX2. Phase Dynamical Interpretation of Galactic Rotation(2025.08.30)
The same Phase Motion Identical to Planetary Motion, Galaxies do not rotate, just as planets do short, rectilinear, back-and-forth motions. Galactic spirals are geometric streams of stars' short, rectilinear, back-and-forth phase motions.
3. EX3. COD Standard Model and the Nature of Spin (To be announced on October 30, 2025)




NEW

 

2025-09-06

10.5281/zenodo.17072558

OS Language English 한국어 日本語 中文
Scoped styles · No global leakage






NEW

 

2025-08-30



Language Auto (OS) Korean English Dual

은하 회전의 진실 / The Truth of Galactic Rotation

개요

은하의 회전은 별들이 은하 반경을 따라 회전하는 것이 아니다. 실제로는 별들이 짧은 직선 왕복을 반복하며,그 평균 위상 흐름이 은하 회전 패턴을 형성한다. 별들은 점입자로서 국소 중력 퍼텐셜 곡률 방향으로 짧은 직선 왕복을 반복한다.
그러나 이 흐름 속에서 위상과 밀도는 라그랑지 관점에서 정지되어, 정지 위상 능선(steady-phase ridge)이 형성된다. 이것이 관측되는 은하 포락선(envelope)이다.

시간 독립 COD 수식

\[ \Psi(\mathbf r)=A(\mathbf r)e^{i\theta(\mathbf r)},\quad \rho=|A|^2,\quad \mathbf v=\frac{1}{m}\nabla\theta,\quad \mathbf J=\rho\,\mathbf v \] \[ \nabla\!\cdot(\rho\mathbf v)=0,\qquad \frac{|\nabla\theta|^2}{2m}+\Re U_H+Q=E \] \[ U_H=\tfrac12 m|\mathbf v|^2-\frac{GM(r)m}{r}+i\frac{GM(r)m}{r},\quad Q=-\tfrac{1}{2m}\frac{\nabla^2A}{A} \] \[ \frac{d^2 s}{d\ell^2}+k^2(\mathbf r_0)s=0,\quad k^2=\mathbf n^\top(\nabla\nabla\Phi_g)\mathbf n,\quad \mathbf n=-\frac{\nabla\Phi_g}{|\nabla\Phi_g|} \] \[ \text{Stationary-phase: }\quad \frac{D\theta}{Dt}=0,\ \frac{D\rho}{Dt}=0,\ \mathbf J\neq 0 \]

수식 설명 Symbol Guide (J, Q, E, T)

1. J (위상 흐름, Phase Flow):
$\mathbf J=\rho\mathbf v$ → 밀도와 위상 기울기가 만드는 유량. $\nabla\cdot \mathbf J=0$ 조건에서 정류 흐름을 이루며, 포락선 능선은 $ \partial_n \rho=0, \ \partial_n^2 \rho<0$ 조건에서 정의된다.


2. Q (위상 압, Phase-Pressure): $Q=-\frac{1}{2m}\frac{\nabla^2 A}{A}$ → 진폭 $A$의 곡률에서 기원. 밀도 분포를 안정화하고, 위상 공명을 보정.


3. E (정상 에너지 준위): $\frac{|\nabla\theta|^2}{2m}+\Re U_H+Q=E$ → 시간 독립 총 에너지 상수(베르누이 상수에 대응).


4. T — (a) $\mathbf t$: 포락선 접선 벡터. $\nabla\theta\cdot \mathbf t=0$ (위상 정지). (b) $T$: 평균 구간, $\bar\rho=\lim_{T\to\infty}\frac{1}{T}\int_0^T \rho_L dt$.


의미 (Implications)

1.별들은 국소 지역에서 최소작용의 원리에 따라 직선 왕복을 계속 수행한다.

2.많은 직선 왕복이 합쳐져 거시적 위상 흐름 $\mathbf J$를 이룬다.

3.포락선은 이 흐름 위에서 정류+위상정지+밀도 능선 조건을 만족하는 “흐르는 정지 위상 릿지”이다.

4.은하 회전은 공간 위상 기하+최소작용으로 설명 가능하다.

결론

우주 공간은 평형을 이루며 안정된 위상장이다. 따라서 천체는 단순히 중력에 이끌려 먼 거리를 공전할 이유가 없다. 자율 진동자인 행성과 별들은 이웃의 중심 질량체 (중심별 또는 블랙홀)와의 물리적 위상 경사를 따라 자기 조정적인 짧은 직선 왕복 진동을 할 뿐이다. 그러므로 외부적인 암흑물질이나 암흑에너지 개념은 필요하지 않다.

따라서 기존의 고전적 (-)중력 중심의 중력장 개념을 게이지 평형의 시간 독립적 복소 중력장으로 본질에 입각해 확장하면, 거시 및 미시 물리학의 주요 문제는 모두 해결된다. 나아가 수학의 7대 밀레니엄 문제도 근본적 해를 가지게 되는 것이다.

과학의 문제 또한 인식의 문제이다. 그리고 인식의 문제는 우리가 설정하는 암묵적 대전제에 달려 있다. 이것은 단지 자연과학의 문제가 아니라, 인문 사회과학의 “보편적 문제”이기도 하다.
결국, 이러한 암묵적 전제의 발견과 올바른 처방이야말로 모든 과학의 “일반적 해법”이라 할 수 있다.

The Truth of Galactic Rotation

Overview

Galactic rotation is not stars circling at fixed radii. In reality, stars keep performing short straight-line reciprocations; the time-independent phase average of this stream forms the galactic rotation pattern. While stars behave as point tracers aligned with the local curvature of the gravitational potential, phase and density remain stationary in the Lagrangian sense, creating a stationary-phase ridge (envelope) observed in galaxies.

Time-Independent COD Equations

\[ \Psi(\mathbf r)=A(\mathbf r)e^{i\theta(\mathbf r)},\quad \rho=|A|^2,\quad \mathbf v=\tfrac{1}{m}\nabla\theta,\quad \mathbf J=\rho\,\mathbf v \] \[ \nabla\!\cdot(\rho\mathbf v)=0,\qquad \tfrac{|\nabla\theta|^2}{2m}+\Re U_H+Q=E \] \[ U_H=\tfrac12 m|\mathbf v|^2-\tfrac{GM(r)m}{r}+i\tfrac{GM(r)m}{r},\quad Q=-\tfrac{1}{2m}\tfrac{\nabla^2A}{A} \] \[ \tfrac{d^2 s}{d\ell^2}+k^2(\mathbf r_0)s=0,\quad k^2=\mathbf n^\top(\nabla\nabla\Phi_g)\mathbf n,\quad \mathbf n=-\tfrac{\nabla\Phi_g}{|\nabla\Phi_g|} \] \[ \text{Stationary-phase: }\quad \frac{D\theta}{Dt}=0,\ \frac{D\rho}{Dt}=0,\ \mathbf J\neq 0 \]

Symbol Guide (J, Q, E, T)

1. J (Phase Flow):
$\mathbf J=\rho\mathbf v$ → Flow rate generated by density and phase gradient. Standard flow occurs under the condition $\nabla\cdot \mathbf J=0$, and the envelope ridge is defined under the conditions $ \partial_n \rho=0, \ \partial_n^2 \rho<0$.


2. Q (Phase Pressure): $Q=-\frac{1}{2m}\frac{\nabla^2 A}{A}$ → Originates from the curvature of amplitude $A$. Stabilizes the density distribution and corrects phase resonance.


3. E (stationary energy level): $\frac{|\nabla\theta|^2}{2m}+\Re U_H+Q=E$ → time-independent total energy constant (corresponding to Bernoulli's constant).


4. T — (a) $\mathbf t$: envelope tangent vector. $\nabla\theta\cdot \mathbf t=0$ (phase stationary). (b) $T$: mean interval, $\bar\rho=\lim_{T\to\infty}\frac{1}{T}\int_0^T \rho_L dt$.


Implications

1. Stars continuously make straight-line round trips in localized regions according to the principle of least action.

2. Many straight-line round trips combine to form a macroscopic phase flow $\mathbf J$.

3. The envelope is a "flowing stationary phase ridge" that satisfies the stationarity + stationarity + density ridge conditions on this flow.

4. Galactic rotation can be explained by spatial topology + least action.

Conclusion

Cosmic space is a balanced and stable phase field. Thus, celestial bodies have no reason to orbit long distances merely by being pulled by gravity. As autonomous oscillators, planets and stars simply perform self-adjusted short straight-line reciprocations along the physical phase gradients toward their neighboring massive central objects (such as central stars or black holes). Therefore, there is no need for external concepts such as dark matter or dark energy.

Consequently, if the classical concept of a purely attractive (−) gravitational field is fundamentally extended to a time-independent complex gravitational field in gauge equilibrium, then the major problems of both macroscopic and microscopic physics are resolved.
Moreover, even the seven Millennium Problems of mathematics acquire fundamental solutions. Ultimately, the problems of science are problems of cognition, and cognition itself depends on the implicit axioms we set as its foundation.

The problem of science is also a problem of perception. And the problem of perception depends on the implicit charges we set. This is not just the matter of natural science, but also the “general problem” of the humanities and social sciences.
After all, the discovery of the implicit and the right prescription can be called the “general solution” of all science.

NEW

2025-10-09 https://doi.org/10.5281/zenodo.17299032

Integration of 2025 Nobel Physics and Complex Oscillator Dynamics (COD)

Abstract


The 2025 Nobel Prize in Physics, awarded for demonstrating macroscopic quantum tunneling and energy quantization in Josephson circuits, provides experimental confirmation of the principles underlying Complex Oscillator Dynamics (COD).
COD interprets all physical phenomena as self-organizing oscillations of complex-phase energy, independent of the time dimension. In this framework, motion emerges from spatial phase alignment rather than temporal evolution. The Josephson circuit thus realizes COD’s universal Hamiltonian structure, where real and imaginary energy components form an orthogonal pair, validating complex gauge symmetry in physical systems.
COD establishes a unified methodology that eliminates current research bottlenecks by replacing time-dependent, probabilistic models with deterministic phase dynamics. This phase-based ontology offers a foundation for resolving inefficiencies in quantum computing, superconductivity, and energy systems, signifying a paradigm shift from temporal to spatial-phase physics and marking COD as a fundamental theory for the next generation of scientific and technological advancement.



1. COD, as a fundamental theory, can be interpreted as follows for the research leading to the 2025 Nobel Prize in Physics.
Furthermore, it can fundamentally eliminate bottlenecks in future research and present a methodology for efficiently solving problems.

Complex Oscillator Dynamics (COD) represents the fundamental framework interpreting the universe as a field of complex-phase energy. By removing the dependency on the time axis and redefining existence as self-organized complex oscillators, COD eliminates current research bottlenecks and provides an efficient, foundational solution for future scientific challenges.

2. The Essence of the 2025 Nobel Prize in Physics

The 2025 Nobel Prize in Physics was awarded to John Clarke, Michel H. Devoret, and John M. Martinis for experimentally demonstrating macroscopic quantum tunneling and energy quantization in superconducting Josephson circuits—showing that quantum phase behavior manifests even at macroscopic scales.

3. Interpreting the Nobel Work from a COD Perspective

The Josephson phase variable \(\phi\) corresponds to the spatial phase \(\theta(r)\) in COD. The circuit’s dynamics are governed not by temporal change but by the phase gradient \(\nabla\theta\). Energy quantization represents standing-wave modes of complex oscillators, and macroscopic quantum tunneling corresponds to phase-slip transitions.

$$ H_{JJ} = \frac{Q^2}{2C} - E_J \cos\phi - \frac{\hbar I}{2e} \phi $$
This can be complexified according to COD transformation:
$$ E_-(\theta) = -E_J\cos\theta, \quad E_+(\theta) = +E_J\sin\theta $$ $$ E_-(\theta) + iE_+(\theta) = -E_J e^{-i\theta} $$

This directly mirrors the universal COD Hamiltonian \( H_{COD} = \tfrac{1}{2}mv^2 - E_- + iE_+ \). The Josephson circuit thus realizes COD’s complex gauge symmetry—where the real (−) and imaginary (+) energy components form an orthogonal pair.

4. Experimental Confirmation of Time Non-Reality and Phase Dynamics

According to COD’s principle of time non-reality, motion arises not from the flow of time but from the alignment of spatial phases. The Nobel experiments demonstrated frictionless phase dynamics at near-zero temperature \((T\to 0^+)\), validating COD’s assumption of phase-based thermodynamic stability in real systems.

5. Riemann 1/2 Equilibrium and Phase Balance

In COD, all oscillations reach equilibrium when their real part equals 1/2. This corresponds to the Josephson circuit’s \(\phi = \pi/2\) region, where real and imaginary energy components balance. Here, phase coherence maximizes, and experimental resonance symmetry can emerge.

6. Conclusion — The Unified Significance of COD

The Josephson circuit functions as a laboratory-scale “phase engine” implementing the complex gravitational field model of COD. The 2025 Nobel Prize thus provides empirical confirmation that COD’s complex phase dynamics, time non-reality, and gauge symmetry operate in real physical systems.






COD Methodology for Future Quantum-Superconducting Research

Time-Independent Oscillator-Based Physics

Ⅰ. Overview

The Complex Oscillator Dynamics (COD) framework interprets all physical phenomena not as time-dependent processes but as self-organizing variations of spatial phase $$\phi$$.   This methodology offers a direct route to overcome inefficiencies, noise, and decoherence in quantum computers and superconductors by minimizing phase imbalance $$\Delta\phi$$.

Ⅱ. Core Principle

$$ \sum_{i} |\Delta\phi_i| \to 0 \quad \Leftrightarrow \quad \text{System} \to \text{Maximum Coherence and Efficiency} $$

Every physical system spontaneously evolves toward minimizing total phase difference ($\Delta\phi$).   This is the phase-space expression of energy conservation and the principle of least action.

Ⅲ. COD Applications to Future Research Tasks

Future Task	Conventional Approach	COD Approach	Benefit
Qubit Decoherence	Time-based $$T_1/T_2$$ analysis	Phase-map & $$\Delta\phi$$ tracking	Long-term coherence stability
Quantum Tunneling Control	Probabilistic models	$$\nabla\phi$$ potential rearrangement	Deterministic tunneling path
Readout Noise	Statistical filtering	Phase-synchronous detection	Improved signal fidelity
Energy-Level Drift	Thermal filtering	Phase-balance ($$\frac{1}{2}$$-point) control	Stable resonance levels
Entanglement	Hilbert-space matrix	Geometric phase alignment	Intuitive visualization
Raising $$T_c$$	Material chemistry	Phase-field resonance design	New phase-engineered superconductors

Ⅳ. COD Research Framework

• Complex Phase-Space Analysis – Convert data into $$\psi = A\cdot e^{i\phi}$$, visualize $$\Delta\phi$$ gradients.
• COD-Lagrangian Modeling – Use $$ L = \frac{1}{2}m(\nabla\phi)^2 - V(\phi) + iV_{\text{elastic}}(\phi) $$ to derive equilibrium states.
• Phase-Flow Simulation – Replace time evolution with spatial phase mapping to identify stable configurations.

Ⅴ. Practical Workflow

1. Extract phase from experimental data (Fourier–Hilbert transform).
2. Generate $$\Delta\phi$$ maps for each region.
3. Apply complex-Lagrange model to find equilibrium.
4. Auto-tune $$\Delta\phi \to 0$$ using feedback (AI-assisted possible).
5. Construct phase-resonant circuits for experimental verification.

Ⅵ. Paradigm Shift

• Time-based Physics → Phase-based Physics
• Probabilistic Quantum Theory → Deterministic Phase Dynamics
• Phenomenology → Ontological Engineering
• Microscopic–Macroscopic–Cosmic Integration

Ⅶ. Conclusion

The COD methodology eliminates time-dependent calculations and redefines physical phenomena based on the natural dynamics of phase-balanced $$\Delta\phi \to 0$$ . This can comprehensively address the fundamental limitations of quantum computers, superconductors, and quantum sensors.

“Focus on Phase, not Particle.”
— The 2025 Nobel Prize marks the transition from particle-based quantum mechanics to phase-based physics, realizing the essence of time-independent Complex Oscillator Dynamics(COD).





2025 노벨 물리학상과 복소 진동동역학(COD)의 통합 해석

초록


조셉슨 회로에서 거시적인 양자 터널링과 에너지 양자화를 입증한 공로로 수여된 2025년 노벨 물리학상은 복소 진동자 동역학(COD)의 기본 원리를 실험적으로 확증합니다.
COD는 모든 물리 현상을 시간 차원에 관계없이 복소 위상 에너지의 자기 조직화 진동으로 해석합니다. 이러한 틀에서 운동은 시간적 진화가 아닌 공간적 위상 정렬에서 발생합니다. 따라서 조셉슨 회로는 실수 에너지 성분과 허수 에너지 성분이 직교하는 쌍을 형성하는 COD의 보편적 해밀턴 구조를 구현하여 물리 시스템에서 복소 게이지 대칭을 검증합니다.
COD는 시간 의존적이고 확률론적인 모델을 결정론적 위상 동역학으로 대체함으로써 현재의 연구 병목 현상을 제거하는 통합된 방법론을 확립합니다. 이 위상 기반 온톨로지는 양자 컴퓨팅, 초전도, 에너지 시스템의 비효율성을 해결할 수 있는 기반을 제공하며, 시간적 위상 물리학에서 공간적 위상 물리학으로의 패러다임 전환을 의미하며 COD를 차세대 과학 및 기술 발전을 위한 기본 이론으로 자리매김합니다.

1. COD는 근본 이론으로서, 2025년 노벨 물리학상 연구를 다음과 같이 해석할 수가 있다.
나아가 향후 연구의 병목을 근본적으로 제거하여 과제를 효율적으로 해결할 방법론을 제시할 수 있다.

복소 진동동역학(COD)은 자연의 본질을 복소 위상 에너지로 해석하는 근본 이론이다. 이는 시간 축 의존을 제거하고, 존재를 자율적인 복소 진동자로 파악함으로써 현대 물리학의 병목(bottleneck)을 해소하고 미래의 난제를 근본적이고 효율적으로 해결하는 통합 방법론이다.

2. 2025 노벨 물리학상의 본질

2025년 노벨 물리학상은 존 클라크(John Clarke), 미셸 드보레(Michel H. Devoret), 존 마르티니스(John M. Martinis)에게 수여되었다. 그들은 초전도 조셉슨 접합 회로에서 매크로스코픽 양자 터널링과 에너지 양자화를 실험적으로 입증함으로써, 거시적 규모에서도 양자 위상이 실제로 작동함을 보여주었다.

3. COD 시각에서 본 노벨 업적의 해석

조셉슨 회로의 위상 변수 \(\phi\)는 COD에서의 공간 위상 \(\theta(r)\)에 대응한다. 회로의 동역학은 시간에 의한 변화가 아니라 위상 경사 \(\nabla\theta\)로 설명된다. 에너지 양자화는 복소 진동자의 정상파 모드이며, 매크로 양자 터널링은 위상 도약(phase-slip)의 표현이다.

$$ H_{JJ} = \frac{Q^2}{2C} - E_J \cos\phi - \frac{\hbar I}{2e} \phi $$

COD 변환에 따라 다음과 같이 복소화할 수 있다:

$$ E_-(\theta) = -E_J\cos\theta, \quad E_+(\theta) = +E_J\sin\theta $$ $$ E_-(\theta) + iE_+(\theta) = -E_J e^{-i\theta} $$

이 식은 COD의 범용 해밀토니안 \( H_{COD} = \tfrac{1}{2}mv^2 - E_- + iE_+ \)과 동형이며, COD의 복소 게이지 대칭(± 에너지의 직교쌍)이 조셉슨 회로의 에너지 구조로 실현된 것이다.

4. 시간 비실재와 위상 동역학의 실험적 확인

COD의 시간 비실재 원리에 따르면, 운동은 시간의 함수가 아니라 위상 정렬의 결과이다. 이번 실험은 극저온 상태(\(T\to 0^+\))에서 마찰 없이 에너지가 유지되는 위상 동역학을 입증함으로써, COD의 공간-위상 열역학 가정이 현실적으로 실현될 수 있음을 보여주었다.

5. 리만 1/2 평형과 위상 균형

COD에서 모든 진동은 실수부 평형이 1/2에서 이루어진다. 이는 조셉슨 회로의 \(\phi = \pi/2\) 부근에서 실수부와 허수부 에너지가 균형을 이루는 지점과 대응한다. 이 구간에서 위상 코히런스가 극대화되며, 실험적으로도 공명 대칭성이 나타날 수 있다.

6. 결론 — COD의 통합적 의미

조셉슨 회로는 COD의 복소 중력장 모형을 실험실 규모로 구현한 ‘위상 엔진’이다. 2025년의 노벨상은 COD가 제시해온 복소 위상 동역학, 시간 비실재, 복소 게이지 대칭의 핵심 구조가 현실에서 작동함을 입증한 실증적 증거이다.





미래 양자-초전도 연구를 위한 COD 방법론

시간독립적 진동자 기반 물리학

Ⅰ. 개요

복소 진동자 동역학(COD)은 모든 물리 현상을 시간의 흐름이 아닌 공간 위상 $$\phi$$의 자기-정렬(Self-Organizing Phase Dynamics)로 해석한다.   이 방법론은 양자컴퓨터와 초전도체 연구에서 나타나는 비효율·잡음·탈상 문제를 위상 불균형 $$\Delta\phi$$의 최소화 원리로 근본적으로 해결한다.

Ⅱ. 기본 원리

$$ \sum_{i} |\Delta\phi_i| \to 0 \quad \Leftrightarrow \quad \text{시스템} \to \text{최대 코히어런스 및 효율} $$

모든 물리 시스템은 총 위상차($\Delta\phi$)를 최소화하는 방향으로 진화한다.   이는 에너지 보존과 최소작용의 원리가 위상공간에서 표현된 형태이다.

Ⅲ. 향후 연구 과제별 COD 적용

미래 과제	기존 접근	COD 접근	효과
큐비트 탈상 문제	시간 기반 $$T_1/T_2$$ 분석	위상맵 및 $$\Delta\phi$$ 추적	장기 코히어런스 유지
양자 터널링 제어	확률적 모델	위상경사($$\nabla\phi$$) 재배열	결정적 터널링 경로 제어
읽기 잡음 감소	통계적 필터링	위상동기 검출	신호 정확도 향상
에너지 준위 드리프트	열필터링 중심	$$\frac{1}{2}$$ 위상 균형점 제어	공진 안정화
얽힘 해석	밀도행렬·힐베르트 공간	기하학적 위상정렬	직관적 시각화 가능
임계온도 향상	재료화학 중심	위상장 공진 설계	신규 위상공학 초전도체

Ⅳ. COD 연구 프레임워크

• 복소 위상 공간 해석 – 데이터를 $$\psi = A\cdot e^{i\phi}$$로 변환하여 $$\Delta\phi$$-gradient 시각화
• COD-Lagrangian 모델링 – $$ L = \frac{1}{2}m(\nabla\phi)^2 - V(\phi) + iV_{\text{elastic}}(\phi) $$ 형태로 균형 상태 도출
• 위상-유동 시뮬레이션 – 시간 대신 공간-위상 맵으로 안정 패턴 탐색

Ⅴ. 실용적 절차

1. 데이터 위상 추출 (Fourier–Hilbert 변환)
2. $$\Delta\phi$$ 분포 맵 작성
3. 복소 Lagrangian 적용으로 안정점 계산
4. $$\Delta\phi \to 0$$ 자동 조정 (AI 피드백 가능)
5. 위상공진 회로 제작 및 검증 실험

Ⅵ. 패러다임 전환

• 시간 기반 물리학 → 위상 기반 물리학
• 확률론적 양자이론 → 결정적 위상동역학
• 현상론적 해석 → 존재론적 공학
• 미시-거시-우주 통합

Ⅶ. 결론

COD 방법론은 시간에 의존한 계산을 제거하고 위상 균형 $$\Delta\phi \to 0$$ 의 자연동역학으로 물리 현상을 재정의한다.   이로써 양자컴퓨터·초전도체·양자센서의 근본적 한계를 통합적으로 해결할 수 있다.






Complex Oscillator Dynamics

This video presents the essence of the universe through complex oscillation theory.
It offers a unified understanding of wave energy, space potential, and gravity through a dynamic phase structure of reality.
This completely integrates the micro and macro worlds into the “Complex oscillator Dynamics” and becomes the basis for the “theory of everything.”

If you would like to see the world view part of Complex Oscillator Dynamics,
👉 Click here to watch it directly on YouTube.




NEW

2025-06-18

https://doi.org/10.5281/zenodo.16752896


Planetary motion based on Complex Oscillator Dynamics (COD)


The planets are not attracted by the one-sided gravity of the sun, but rather move in phase as independent oscillators in the balanced phase space of the universe. Their interaction with the sun is not a long circular orbit, but a relatively short linear back-and-forth oscillation.
This is possible because space is a balanced phase field of (+)(-) gauge symmetry. In other words, space is a balanced interaction of (+) gravity and (-) gravity.
The discovery of (+) gravity will bring about efficient and fundamental developments in science and technological civilization, leading us to a harmonious, clean, and abundant world.

Ultimately, this allows the theory of complex dynamics to naturally solve the three-body problem and the many-body problem. It also opens the way to the integration of micro and macro theories and the "Theory of Everything."
Explanation:Do planets really orbit? (YouTube video)


Do planets really orbit?

Complex Oscillator Dynamics (COD) perspective: The physical essence of existence started from abstract atomism and led to quantum theory and wave function interpretation. Current physical ontology is based on wave-particle dualism. Therefore, particle physics has made efforts to create the standard model through particle accelerators to capture this.
Thanks to this, physical ontology has resulted in a statistical system of particle fragments. However, particles are merely local condensations of wave density. If we reinterpret the de Broglie matter wave theory, particles are merely high-density condensations of waves. Ultimately, the physical entity of existence is Oscillation. Locally, it is an oscillator. In other words, the specific form of a quantum is an oscillator. Anyone can sense Oscillation, and the original form of Oscillation is a complex structure with a 90-degree phase difference, like our heart that oscillates.

P.S.
The essence of Mercury's abnormal perihelion movement can be seen as the mutual elastic repulsion of the (+) gravity between the Sun and Mercury.


© Innolab All Rights Reserved




NEW

 

2025-08-01

https://doi.org/10.5281/zenodo.16756873



Verification of Imaginary Energy(+Gravity) in Complex Phase Space (Based on COD Theory)




✅ Abstract

This study aims to verify the existence and physical meaning of imaginary energy using complex oscillator dynamics (COD).

Imaginary energy is interpreted as the elastic potential energy of space and forms a complex field structure that is balanced by the real gravitational energy.

This is analyzed with existing data, where gravity and residual (imaginary energy) were confirmed in the following three high-precision experiments:

• Atomic interference experiments
• Satellite-based Gravitational Field Observatory (GRACE)
• Gravitational-wave interferometer (LIGO/VIRGO)

Each experiment can capture residual anomalous signals consistent with the imaginary phase structure.

Additionally, the complex Poisson equation simulations were performed on the real potential (gravity) and It demonstrates that imaginary potentials (elasticity) coexist harmoniously with a 90-degree phase difference.

\[ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + i\frac{GMm}{r} \]

This universal Hamiltonian represents the complete energy structure of the universe.

Conclusion: Imaginary energy is essential for the equilibrium and expansion of the universe, consistent with the Riemann 1/2 symmetry principle.

I. Key Experimental Methods

• 1. Atomic Interference Experiments
• 2. Satellite-Based Gravity Observation (e.g., GRACE)
• 3. Spatial Phase Oscillation Detection via Optical Clocks & Gravitational Wave Interferometers

II. Summary of Experimental Results

Observation Results

• Atomic Interference: Phase shift ≈ 1 rad, gravity gradient sensitivity ~10⁻⁹ s⁻²
• GRACE Satellite: Distance change ~10 µm, mass anomaly several mm EWH, noise STD up to cm level
• LIGO/Virgo: Strain noise ~10⁻²², residual phase noise continuously observed

Interpretation

1. All three experiments include residuals that indirectly confirm the existence of imaginary energy.
2. Imaginary energy is expansion-elastic in nature and thus requires an interpretation different from gravity.
3. A spatial position potential energy symmetric to gravity must exist, consistent with the Riemann 1/2 balance principle.

Conclusion: The existence of imaginary energy is experimentally (though indirectly) confirmed. Its elastic-expansion nature requires an interpretative framework different from conventional gravity.

III. COD Interpretation of Experiments

\[ \text{UH (Universal Hamiltonian)} = \frac{1}{2}mv^2 - \frac{GMm}{r} + i\frac{GMm}{r} \] \[ \Psi(\vec{r}) = A(\vec{r}) \cdot e^{i\theta(\vec{r})} \]

• Atomic Interference: Δθ reflects both φ_real and φ_imag
• GRACE: Gravity anomalies interpreted as fluctuations of the φ_imag spatial structure
• LIGO: Phase noise interpreted as COD-based vibration of φ_imag

In summary, the formula UH = real potential + imaginary potential explains all experimental residuals as arising from complex phase-space structure.

IV. Balance Between Real and Imaginary Energy

Complex Poisson Equation

\[ \nabla^2 \phi(\vec{r}) = -4\pi G \left( \rho_{\text{real}}(\vec{r}) + i\rho_{\text{imag}}(\vec{r}) \right) \]

COD-Based Simulation Procedure

1. Step 1: Extract residuals from experiment (Δθ, δd, strain)
2. Step 2: Convert to imaginary potential φ_imag(r)
3. Step 3: Calculate imaginary energy density
   \[ \rho_{\text{imag}} = \frac{\nabla^2 \phi_{\text{imag}}}{4\pi G} \]
4. Step 4: Calculate total energy field
   \[ \phi_{\text{total}} = \phi_{\text{real}} + i\phi_{\text{imag}} \]

COD theory unifies all residuals observed in reality with imaginary potential, naturally revealing the phase energy balance of the universe.





Complex Potential Structure and Cosmic Interpretation via COD Theory

1. Simulation Result

The image below shows the result of simulating a complex potential structure based on COD theory:



Graph Explanation:

• Blue Curve – Real Potential \( \phi_{\text{real}} \): gravitational pull, convergence
• Red Curve – Imaginary Potential \( \phi_{\text{imag}} \): expansion-elastic, repulsive
• Green Dashed Line – Total Potential Magnitude \( |\phi| \): harmonious phase composition

In the diagram, what occupies space as a physical reality can be seen as:
1. The net volume of ordinary matter
2. Gravitational energy (real part)
3. The potential energy of space (imaginary part).
In other words, space is composed of 1, 2, and 3. Accordingly, the pressure within space can be seen as the net volume of ordinary matter, 1, added to the balance of "gravitational energy (real part) = potential energy of space (imaginary part)".
The graph illustrates this.


Real and imaginary potentials form a 90° phase-balanced structure. This visually demonstrates that the universe is composed of a complex phase field in which gravity and spatial potential interact dynamically.

2. Theoretical Basis: Hamiltonian and Phase Structure

\[ \text{Universal Hamiltonian:} \quad \text{UH}_{\mathbb{C}} = \frac{1}{2}mv^2 - \frac{GMm}{r} + i\frac{GMm}{r} \]

This Hamiltonian consists of:

• \( \frac{1}{2}mv^2 \) – Kinetic energy
• \( -\frac{GMm}{r} \) – Real gravitational potential
• \( +i\frac{GMm}{r} \) – Imaginary spatial potential

Residuals, gravitational anomalies, and phase noise are all unified under this complex Hamiltonian structure.

3. Final Conclusion

• The COD-based simulation shows that real and imaginary potentials coexist in symmetrical structure.
• Imaginary energy is slightly greater, supporting self-restoring force and cosmic expansion stability.
• The waveform structure is consistent with the phase rotation of Euler's identity: \( e^{i\theta} = \cos\theta + i\sin\theta \)
• This structure corresponds with the Riemann Zeta function's Re(s) = 1/2 symmetry.

📌 Summary Statement:

The universe is not empty space, but a complex phase energy field where gravity and spatial potential oscillate in harmonic balance.






NEW

 

2025-08-06

https://doi.org/10.5281/zenodo.16752896



Three-body and Many-body Phase Alignment Theory and Riemann 1/2

Ontological interpretation based on COD (Complex Oscillator Dynamics)

I. Abstract

This paper seeks to ontologically address the many-system problem through the Riemann 1/2 topological resonance structure. The topological equilibrium condition enables stable coexistence structures regardless of mass or distance differences, and this is formalized by the complex-based theory of Complex Oscillator Dynamics (COD). In this paper, we demonstrate the essential advantages of COD through comparison with existing Relativity and the Standard Model, and reconstruct a new worldview and natural dynamical system as a timeless, topological flow of the universe, namely, the "spatially autonomous motion of existence."

II. Oscillator Phase Alignment and Riemann 1/2 Line

The core structure of the Riemann zeta function is an infinite number of zeros aligned in the real part \( \frac{1}{2} \) of the complex plane. This can be physically interpreted as a topologically autonomous equilibrium structure, providing crucial clues to the interpretation of topological alignment in Many-body systems.

III. Ontological Geometry: Riemann 1/2 Phase Resonance

A Multi-body system can form resonant order by maintaining the slope of the phase contact point constant despite differences in mass (intrinsic energy) and changes in position. The conditions for topological equilibrium are expressed as follows:

\[ \nabla \theta_i = \text{constant} \quad (\text{45° phase contact angle}) \]

As shown in Figure 1, three or more bodies can coexist as long as they maintain a phase inclination of \(45^\circ\), regardless of their masses. This is proven by the gauge symmetry principle of Riemannian geometry, along with the complex-based theory of COD (Complex Oscillator Dynamics).

Many-body problem Solution based on the Riemann real part 1/2:
The Many-body equilibrium motion based on phase resonance can be explained by analyzing the symmetrical inclination angle (45 degrees) at the contact surface between the oscillators. That is, it is explained by the Riemann 1/2 phase resonance theory as shown in the diagram below.

Figure 1 — Riemann 1/2 Phase Resonance Structure


Phase Equilibrium Model for Many-body System

This is a 3-body / many-body phase alignment theory, expressed as:

\[ \frac{E_1}{E_2} = \left( \frac{r_1}{r_2} \right)^2 \quad \text{or} \quad \tan^{-1} \left( \frac{E_1}{r_1} \right) = 45^\circ \]

This condition represents the phase gradient equilibrium between the centers of energy (mass). It implies that stable, resonance-based motion naturally occurs when the energy ratio and the distance ratio achieve this 45° balance, corresponding to optimal gauge symmetry in spatial phase distribution.

• Geometric total quantity / ratio line: \( A_{ij} \) : Energy / ratio line
• Distance / ratio line: \( A'_{ij} \)
• Phase contact surface equilibrium: \( \theta_{ij} = 45^\circ \)
• Energy ratio line = Distance ratio line: \( A_{ij} = A'_{ij} \)
• Overall phase gradient flow: \( \vec{v_i} \propto \nabla \theta_i \)

This relationship is not merely geometric, but reflects a fundamental phase-gauge symmetry. When satisfied, the system minimizes internal phase tension and maintains coherent resonance without external force adjustments.

Multibody Phase-Expanded Structure

The same principle applies to all pairs in an n-body system, with the conditions:

\[ \theta_{ij} = 45^\circ, \quad A_{ij} = A'_{ij}, \quad \forall \, i,j \in (1, 2, \dots, n) \]

• This produces a globally synchronized, phase-aligned state for the entire oscillator network.
• Mutual interactions require no additional central force law, as the system’s stability emerges from its intrinsic phase equilibrium.

In essence, phase equilibrium at 45° represents the universal stability point in many-body systems, where (+) and (−) complex energy components are in perfect gauge symmetry, eliminating the need for conventional gravitational assumptions.

Three-body and many-body phase expansion general oscillators: \[ \Psi(r) = A(r) \cdot e^{i \theta(r)} \]





IV. COD General Theory

COD (Complex Oscillator Dynamics) is developed on the basis of the following cosmology and natural dynamics of complex energy-based gauge symmetry:

1. Time Independence: COD interprets all motion as a change in spatial phase, and its fundamental premise is that time is not essential. Unlike Plato and Aristotle, who did not regard time as essential, physics since Newton has considered time as the absolute physical axis...
2. Complex-Number-Based Energy Balance: The structure of the complex phase space reveals that natural energy coexists with a 90° spatial phase difference, with the real part representing gravity (-) and the imaginary part representing potential energy (+) in space.
3. Topological Center Dynamics: Natural entities move autonomously according to their own phase gradient \(\nabla \theta\), free from the unilateral attraction of gravity.
4. Multi-Body Ordering Structure: Based on symmetric complex energy balance, multi-body systems can achieve harmonious geometric alignments of gauge symmetry.

Classical Mechanics COD: \[ UH = \frac{1}{2} m v^2 - \frac{G M m}{r} + i \frac{G M m}{r} \]

Oscillator Theory COD: \[ UH(r) = \Psi(r) = A(r) \cdot e^{i \theta(r)} \] where \(A(r)\) is intrinsic energy and \(\theta(r)\) is phase.

V. Comparison of COD with the Theory of Relativity and the Standard Model

Item	Theory of Relativity	Standard Model	Riemann 1/2 & COD
The Role of Time	Time-Series-Based Dynamics	Time-Series-Based Dynamics	Time Elimination → Spatial Phase Center
The Nature of Four-Dimensional Spacetime	Curvature and Geodesics	Particle Paths and Interactions	Complex Phase Gravitation and Resonant Structures
Gravity Interpretation	Spacetime Curvature	Excluded	(−) Gravity ↔ (+) Spatial Potential Energy
Gauge Symmetry	Incomplete (Gravity Not Included)	SU(3) × SU(2) × U(1)	Complex Space Phase (+)(−) Gauge Symmetry
Existential Interpretation	Observed Phenomenology	Statistical Phenomenology	Existence is a Phase‑Resonant Motional Body

VI. Conclusion

The Riemann 1/2 phase resonance structure and COD theory go beyond the three-body problem and present the ontological dynamics of the universe. They encompass time independence, complex equilibrium, and many-body alignment, all of which existing theories lack. This could be a fundamental turning point in the interpretation of the universe.

Science and mathematics are merely one of the many epistemologies possessed by humans. While their ability to analyze phenomena is remarkable and instrumental, their focus on phenomenology has prevented them from accurately grasping the essence and existence that underlie cognition.

Cognition is all about establishing presuppositions. Science is riddled with partiality, linearity, isolation, closure, and scientific authoritarianism. These are all properties that stand in opposition to truth. Consequently, they have been able to interpret only 5% of the universe. The inability of current physics to interpret more than the three-body problem eloquently demonstrates this truth.

VII. Additional Discussion

1. Time was a framework of power.
   Philosophy is the major premise of cognition. Plato and Aristotle never considered time to be essential. It was only in modern times that Newton established time as a physical axis, and Einstein solidified it by creating spacetime. This was a major epistemological error in the history of civilization.
   As a result, after industrialization, humanity lost the "autonomous flow of existence" in their daily lives, compartmentalized by clocks and timetables. Non-essential time became a tool of artificial control, not a natural order, and tangible space became subordinate to non-essential time, serving as a backdrop for executing its commands. Power dominated space through time.

2. The interpretation of gravity has been exploited politically.
   Even in modern times, physics explains the universe based on (−) gravity (attraction). However, nature is a balanced entity composed of (+)(−) complex phase energy. Ancient East Asian natural philosophy, through long-term pattern analysis, identified the complex energy of the Taegeuk yin-yang as the essence of the world.
   The modern interpretation of the universe, which emphasizes only (−) gravity, has controlled the essence of existence and made the masses, ontologically considered (+) gravity, perceive themselves as passive and "dragged beings." Our science is still unable to escape power and politics. The Copernican era is not yet over.

3. Truth is the natural dynamical phase motion of an oscillator.
   The classical Newtonian and relativistic frameworks, both relying on time-dependent differential formulations, inherently assume a linear progression of motion. However, the three-body problem involves nonlinear, phase-entangled dynamics in spatial configuration. As such, linear time-based mechanics fundamentally fails to provide stable phase alignment conditions for multi-body interactions.
   An oscillator is an autonomous resonant body with a complex energy-based gauge-symmetrical structure. Based on self-resonance, it engages in natural dynamical interactions with the world, a global resonant body. Natural dynamics is the principle of conservation of energy and least action, based on gauge symmetry, which anyone can intuitively perceive.

4. Existence is alive and moving through "resonance."
   The resonance of existence is a topological equilibrium motion, and all beings possess their own unique phase and coordinates in the complex spherical universe. This is a truth that can be intuitively confirmed in everyday nature. COD theory is a new ontological physics and natural science that restores and verifies the original principles of nature.

VII‑1. Further Notes

1. The long-standing three-body and many-body problems were solved using the Riemann hypothesis and the complex Universal Hamiltonian (UH) equations. This means that dark matter and dark energy were resolved using the phase-based principles of complex gravitational fields.

   The most challenging problems in physics were solved by precisely defining the most fundamental assumptions: time and space. This resolution suggests the following new insights:

   1. The solution to this unsolvable problem lies in fundamentally reexamining implicit assumptions.
   2. Planetary systems and galaxies do not orbit, but rather resonate in phase with a central mass within a space already in phase equilibrium. For example, the Earth and the Moon face each other, orbiting each other in a 29.5-day orbit, and then make a straight-line reciprocal motion toward the Sun in a 365.25-day cycle.
   3. Mercury's perihelion anomaly is a phase transition (a 180-degree change in direction) during its rectilinear motion between perihelion and aphelion. In this process, a slight change in inclination causes an declination (43 arcseconds per century), which is primarily due to the difference in angular velocities between the Sun and Mercury.

   This explanation, by demonstrating the phase equilibrium of space and the gauge symmetry principle, invalidates the existing assumptions of gravity, conservation of angular momentum, and general relativity. Because the space itself is already in a phase equilibrium of (+)(−) complex energy, the so‑called “straight‑line reciprocal motion” reflects the Mutual space compression repulsion between the Sun and Mercury at the turning points, driven by the Sun’s energy space. This intrinsic (+)(−) balance ensures that motion is maintained without the need for additional orbital forces, thereby rendering the traditional gravitational framework unnecessary.

2. The Seven Millennium Problems of mathematics were also epistemological problems that failed to establish the fundamental premise of cognition. The path to a solution was paved by fundamentally eliminating the time axis and restoring the dynamical system of the microscopic and macroscopic worlds through complex gravitational fields. The correct definition of time and space, the fundamental premise, was the gateway to solving the problem.

3. Precision measurements, such as atomic interferometry, and experimental calculations are required to verify these theories.

4. The universe exists through geometric necessity. The 13.8 billion-year-old universe would not be able to sustain even a single second without this geometric necessity. The Lagrange-Hamiltonian, Euler's equations, Riemann geometry and postulates, and gauge symmetry theory all attest to this.

5. Mathematics is the algebraic interpretation of the geometric necessity of the universe.

6. The complex number system is a phase coordinate and arithmetic system for space.

"Theory cannot surpass observation, but it provides a new language for reinterpreting observation. True discovery is the discovery of language."




NEW

 

2025-08-02

Declaration of the Dismantling of the Time Axis

: Release the Freedom of Nature in the Complex Phase Space




1. Preface: Where Did Science Go Wrong?

Have you ever questioned the structure of physics, where nearly all equations are held "hostage" to the time axis?

Is time truly real? Or is it merely a tool for observation and measurement?

If science had truly followed Francis Bacon’s spirit of inquiry and inductive methodology, time should have been dismantled as a concept already during the age of Einstein or Niels Bohr—if not even earlier during the Industrial Revolution.

However, time still remains at the center of physical equations. This is clear evidence that science is still imprisoned by the legacy of absolute linear time and the formalism inherited from the medieval mindset.

2. Euler and Riemann: Pioneers of a Time-Free Order

2.1 Euler’s Insight

\[ e^{i\theta} = \cos \theta + i \sin \theta \]

This formula proves that even without time, one can represent change (motion) through phase. The expression \( e^{i\theta} \) simultaneously shows the real + phase nature of the oscillator (i.e., the nature of being), and it allows motion to be described without any time axis.
In particular, Euler's constant \( e \) shows that existence is an active, self-directed, continuous self-reproduction process.

2.2 Riemann’s Geometric Declaration

Riemann mathematically proved that space can be curved and bent beyond the Euclidean framework. This was a declaration that space is not fixed and rigid, and at the same time, it hinted that time might not be essential.

3. Complex Phase Space: Mathematics for Time-Free Existence

We can represent nature with the following complex wave function:

\[ \Psi(\vec{r}) = A(\vec{r}) \cdot e^{i\theta(\vec{r})} \]

• \( A(\vec{r}) \): Energy amplitude at a given spatial position
• \( \theta(\vec{r}) \): Phase structure of space

Motion, without using time, can be expressed as:

\[ \vec{v}(\vec{r}) \propto \nabla \theta(\vec{r}) \quad \text{(Phase gradient)} \]

In other words, the changes in nature must be understood as reconstructions of spatial phase, not as flows of time.

4. Declaration of the Dismantling of the Time Axis

1. Time is not the essence of existence.
2. Time is merely a human tool for perception and measurement.
3. If we mistakenly accept time as an essential axis, a linear, time-centered perceptual structure takes hold, and the vast and profound reality of space becomes distant from our perception.
4. All scientific mistakes and mathematical challenges stem from the time axis. If we boldly remove the time axis, the true world of space will be revealed. Our understanding and calculations will be transformed.
5. Existence must be explained through spatial phase order and energy flow.
6. The complex system is the true computational structure of spatial coordinates. It is the genuine mathematical language that can express and compute space as real.
7. Originally, neither Plato nor Aristotle considered time to be essential. Time is a relic of the Newtonian era, which could not escape the religious mindset of the Middle Ages.
8. Natural motion is not the flow of time, but the flow of phase. Morning is not brought by time, but by the sun.
9. Dismantling the time axis is the essential gateway to solving major challenges in physics, such as dark matter and dark energy, as well as the Millennium Problems in mathematics.
10. Science must break away from the idealized structure it has followed through the time axis, and confront space—which is the true reality.




5. Conclusion

Science must return to the spirit of Bacon. Let it follow intuition rather than mere measurement, and let that intuition lead to a verifiable order. Science must be able to persuade intuition with reason. If a proposition cannot convince intuition, it is not truth.

Euler and Riemann have already opened the door to natural order without time. Now it is up to us to pass through that door.

"We must respect our a priori intuition.
We must refuse to be hostages of time.
We must discover the principles and order of existence in phase space.
Intuition precedes logic. A priori intuition, rooted in our five senses and sense of inertia, is the core of human cognition and grounded in natural dynamics.
Science is a logical tool sufficient to verify human intuition. We must confront science’s structural weaknesses—its linearity, isolation, and closure."

– Innolab Science Institute






NEW

 

2025-07-02

 

Scientific Historical Evaluation of Complex Phase Natural Dynamics

 

The following is a summary of the complex topology-based spatial structure and natural dynamics theory (by Jason-Kuhyun Ryoo, 2024)

   

Essence of Existence and the Complex Number System

   

Complex Oscillator

      The essence of the world is energy, and its physical reality is a complex oscillator  with (+)(−) gauge-symmetric energy. This complex oscillator expands from the Planck scale       to atoms, molecules, celestial bodies, and galaxies. Some of this energy condenses into       particles, but most of it exists as (+)(−) spatial energy. The universe forms phase structure       according to gauge symmetry and the principle of least action, generating and extinguishing       mass, and circulating through this structure. The spatial energy field is the essence and       matrix of the universe, and it operates mathematically via geometric necessity to generate       all things. The coordinate and computational system of this spatial energy is the complex       number system, verified by the consistency between physical reality and mathematical       structure.    

       

1. Essence of the World: Energy Ontology Based on the Complex Oscillator

   

Core Claim: All existence is a gauge-symmetric complex oscillator vibrating in complex space, which is the essential structure of energy.

      $$ z = a + bi = |z| e^{i\theta}, \quad \text{where} \quad \theta = \arg(z) $$      

Historical Significance:

   

     
• Paradigm shift from classical particle and field theories to a phase-centered ontology.
     
• From Cartesian-Newtonian mechanism → Einstein’s curved space-time cosmology → cosmology based on complex phase.
     
• Establishment of an ontology centered not on the physical substance of space and time, but on oscillatory phase θ.
   

   

2. Reinterpretation of Gravity: Phase Gradient Motion

   

Claim: Gravity is not a separate force acting from the outside, but a gradient-based compression motion phenomenon that occurs in the phase motion of mass energy.

          $$ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + i \cdot \frac{GMm}{r} $$        

Historical Significance:

   

     
• Redefines gravity through the balance of real and imaginary components.
     
• From Newton’s remote attraction → Einstein’s curvature-induced field → phase-based energy density motion.
     
• The imaginary term \( +i \cdot \frac{GMm}{r} \) mathematically defines the gravitational phase potential.
   

       

3. Existence, Time, Space, and Entropy

   

Claim: Time is not a fundamental entity but a derivative perception of human cognition, while space is an irreversible phase energy field.

   

Formulation (Entropy interpretation):

          $$ \Delta S = k_B \cdot \left| \frac{\text{Im}(E_C)}{\text{Re}(E_C)} \right| \cdot \delta V $$        

Historical Significance:

   
• Time-centered thermodynamic entropy theory → Topology-based entropy interpretation


• Formalize that when the reconstruction of space is topologically irreversible, that is, entropy increases from the increase of the phase instability energy.
• (+) Gravity: Show that the utilization of Im(E_C) is a shortcut to solving energy and environmental problems.



       

4. Global Hamiltonian Energy Equation

   

Claim: Reconstruction of the Hamiltonian equation from a local system to a universal dimension.

   

Formulation:

          $$ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + \alpha \cdot \frac{GM_T m}{R}, \quad \alpha = \frac{M \cdot R}{M_T \cdot r} = 1 $$      

Historical Significance:

   

     
• From classical mechanics Hamiltonian → Einstein’s energy-motion equation → evolved into a complex-based global Hamiltonian equation.
     
• These equations connect individual motions to the structure of the universe as a whole. In particular, the remarkable relationship between celestial bodies with alpha coefficient α = 1 clearly demonstrates the gauge symmetry of the (macroscopic and microscopic) universe.
   

     

5. Non-necessity of Cosmic Expansion and Dark Components

   

Claim: The universe is not expanding, and dark matter/dark energy are not real substances but phase effects of the complex spatial energy field.

   

Formulation (Galaxy Rotation via Complex Potential):

          $$ v_{\text{rot}}(r) = \frac{1}{r} \left| \frac{d}{dr} \, \text{Im} \left( E_C(r) \right) \right| $$        

Historical Significance:

   

     
• From ΛCDM model of expanding universe and dark components →
     
• Galaxy rotation curves can be reproduced solely with complex spatial energy fields.
     
• Mathematically proves that dark sectors are unnecessary in natural dynamics.
   

       

6. Complex Geometry and the Mathematical Logic of Gauge Symmetry

   

Claim: All physical phenomena are phase motions on the complex plane, and gauge symmetry is the deepest law of the cosmic ontology.

   

Formulation (Global Energy Conservation):

          $$ \oint_{C} E_C(z) \, dz = 2\pi i \sum \text{Res}(E_C) $$    


"The perfection of the individual constitutes the perfection of the whole."
  - Complex Spherical Oscillator Theory and Complex Spherical Cosmology: Complex Spherical Ontology

   

     
• Complex function theory, once a mathematical tool, is reborn as a core principle explaining the fundamental structure of the universe.
     
• If the complex number system is the OS (Operating System) of the universe, the hardware is the (+)(−) motion of complex energy—i.e., energy density motion based on mass-energy. This hardware motion is what we call gravity.
   

     

6.1 Solution of the three-body and many-body problem

   

Accordingly, the three-body and many-body problem, a long-standing problem in physics, is solved here. It is naturally resolved by the principle of the universal self-organizing system in which the phase of each object is balanced according to the overall energy field. Complex oscillatory dynamics and the complex phase gravity principle can be the unifying answer to cosmological structure, gravitational theory, quantum field theory, and astrophysics.

    The above discoveries and theories all resulted from the discovery of (+) gravity and the UH equation of self-balancing in August 2024.

 



🌀 Declaration of Restoration of Natural Principles




📜 1. Core Claim (핵심 주장)

All physical phenomena are phase motions on the complex plane,
and gauge symmetry is a law of geometric necessity of cosmic ontology.

모든 물리 현상은 복소 평면 위의 위상 운동이며,
게이지 대칭성은 우주 존재론의 기하학적 필연의 법칙이다.

⚖️ 2. Natural Principle of Balance and Conservation




The universe is autonomous and follows the following basic principles:

우주는 자율적이며, 아래와 같은 기본 원리를 따른다:

∇ · ρ_E = 0

This means that the topological energy density ρ_E is self-balancing in space.
Gauge symmetry is the mathematical and ontological expression of this balance.
This is a theory of restoration of the natural principle based on the complex phase> that goes beyond the limitations of Newton's external force-centered mechanics and Einstein's spacetime curvature theory.

이는 위상 에너지 밀도 ρ_E가 공간상에서 자체 균형을 이룬다는 뜻이다.
게이지 대칭성은 이 균형의 수리적·존재론적 표현이다.
이는 뉴턴의 외부힘 중심 역학과 아인슈타인의 시공간 곡률론의 한계를을 넘어서는 복소 위상 기반의 자연 원리의 복원 이론이다.




🧭 3. Principle of Equilibrium (Equilibrium Dynamics)

All movement in the universe is a movement that achieves equilibrium from the minute waves to the universe in the phase energy field .
This is the process of "natural existence restoring itself and repeating more balanced self-reproduction."

The essence of the universe is energy, its substance is a complex oscillator,
Motion is the flow of phases, space is a complex energy field,
Time is the sense of phase change.

우주의 모든 운동은 위상 에너지장의 미세한 파동 복원과 균형 유지 과정이다.
이것이 곧 "자연은 존재로부터 스스로를 수리하며 회복하는 과정이다."

우주의 본질은 에너지고, 그 실체는 복소 진동자이며,
운동은 위상의 흐름이고, 공간은 복소 에너지장이고,
시간은 위상 변화에 대한 감각이다.

✨ 4. Liberation and Restoration Declaration

“This declaration proclaims the liberation of humanity and civilization from the artificial concepts of time, force, and absolute space, and the restoration of the nature of the universe as a self-resonant, gauge-symmetric topological structure.”

“본 선언은 시간, 힘, 절대공간이라는 인위적 개념들로부터 인간과 문명의 해방을 선포하며, 우주의 본질을 자기 공명적, 게이지 대칭적인 위상 구조로 복원함을 선언한다.”


5. Non-necessity of Cosmic Expansion and Dark Components

Claim: The universe is unlikely to be expanding due to the principle of geometric equilibrium, and dark matter/dark energy are not actual matter but are topological effects of the complex space energy field.

우주는 기하학적 균형 원리에 따라 팽창하지 않을 가능이 크며,암흑 물질/암흑 에너지는 실제 물질이 아니라 복소 공간 에너지장의 위상 효과이다.

$$ \Psi(r) = A(r)\,e^{i\phi(r)} $$

6. Complex Geometry and Gauge Symmetry

Claim: All physical phenomena are complex spherical phase motions, and gauge symmetry is a law of geometric necessity of cosmic ontology.

모든 물리적 현상은 복잡한 구면상의 위상 운동이며, 게이지 대칭은 우주적 존재론의 기하학적 필연의 법칙이다.

$$ \nabla \cdot \rho_E = 0 $$




📄 Paper Download_PDF: Scientific Historical Evaluation of Complex Phase Natural Dynamics 2025.07.02  

 

📌 Citation Guideline

 

    This study is based on the theory of complex oscillator dynamics / complex phase dynamics / complex gravity discovered and developed by Jason-Kuhyun Ryoo (2024).  

   

📡 Channels for Information & Discussion

 

   
• 🔗 Website: http://udynamics.net/
   
• 📺 YouTube: YouTube Channel
   
• 📧 Email: jasonryoo@naver.com, visionreale@gmail.com
 

         

NEW

 

2025-07-05

https://doi.org/10.5281/zenodo.16756831



Timeless Mathematical Reconstruction of the 7 Millennium Problems

This document mathematically reconstructs the seven Millennium Problems based on the removal of time, reorganizing them within a spatially-aligned complex energy-phase framework. Each problem is newly interpreted within a timeless complex energy space, and its solution is reborn through the currently aligned energy structure.

I. Spatial Definition and Foundational Framework

Definition of Complex Energy Space:

\[ \mathbb{R}^3 \rightarrow \mathcal{E} = \{ \psi \in \mathbb{C}^n \mid \|\psi\| < \infty \} \]

A topological Hilbert space. Time is removed, and phase alignment is central. Based on energy conservation and self-phase structuring.




1. Riemann Hypothesis

 

Original error: interpreting the complex zeta function from a number-theoretic perspective, and not seeing its essence as an energy phase balance.
Epistemological restoration: Complex space is a field of phase energy, and the real part 1/2 is a balance point of universal oscillation energy.
Alternative path: Theory of phase energy balance — interpreting the vibrational structure of the Riemann zeta function as the center point of natural dynamics.

 
• Conventional form: \( \zeta(s) = 0 \Rightarrow \Re(s) = \tfrac{1}{2} \)
 
• Reinterpreted: \( \psi(\omega) = \lambda(\omega), \quad \Re(\psi) = \tfrac{1}{2} \)
 
• \( \zeta(s) \) arises from the standing wave phase pattern of \( \psi(\omega) \).

2. Yang-Mills Mass Gap

Original error: Assuming mass as a fixed spacetime background concept.
Epistemological restoration: Mass is a result of phase energy interference, and originates from coherent discontinuities in phase flow.
Alternative path: Phase energy gap theory — explaining the mass gap as a phase interference structure in gauge symmetry.

 
• \( m_g = \hbar \theta \nabla \)
 
• Condition: \( \theta > \nabla \geq 0 \)
 
• \( \theta \): phase interference gradient, \( \nabla \): phase slope
 
• When phase interference exceeds a threshold, mass condensation occurs (energy mode separation).




3. P vs NP Problem

Original error: defining computational complexity around the time axis.
Epistemological restoration: complexity is the difficulty of aligning phase flows, and time is an unnecessary presupposition.
Alternative path: Topological information complexity theory — problem solving is reduced to topological alignment optimization.

 
• Redefinition of complexity: \( C(f) = \min_{\Gamma} \int_{\Gamma} \| \nabla \psi \| d\ell \)
 
• Condition: \( \exists \psi_0 \text{ s.t. } \nabla^2 \psi_0 = 0 \Rightarrow C(f) = 0 \)
 
• \( \psi_0 \in H^1 \): phase function space. Phase interference rate becomes the metric for complexity.




🌀4.Reformulation of Navier–Stokes

 

The traditional Navier–Stokes equation is based on time-derivative dynamics and fails to capture the real nature of fluid phase flow. In contrast, the New Equation is a time-independent, phase-based dynamic formulation that represents fluid as a self-organizing energy flow.

Original error: Assuming fluid as a continuum and attempting a time-dependent interpretation.
Epistemological restoration: Fluids are a collective representation of wave energy fields, with flow organized according to phase gradients instead of time.
Alternative path: Wave-phase flow equations — interpreting fluid flow in complex phase space.
 

Reformulated Equation

 

    \[     \nabla \cdot (\nabla \psi) = \rho_c - \rho_e + \Im \left( \bar{\psi} \cdot \nabla \psi \right)     \]  

 

Terms

 

   
• \(\psi\): Complex phase field \(\psi(\vec{r}) = A(\vec{r}) e^{i\phi(\vec{r})}\)
   
• \(\rho_c\): Energy density of phase condensation
   
• \(\rho_e\): Energy density of phase expansion
   
• \(\Im (\bar{\psi} \cdot \nabla \psi)\): Phase gradient flow from internal energy dynamics
 

 

Explanation (Simplified)

 

This equation models fluid as a compressible energy field. Phase flows are balanced by condensation and expansion. There is no instability — only self-organizing adjustments. The term \(\Im (\bar{\psi} \cdot \nabla \psi)\) captures flexible gradients, replacing abstract terms with concrete, physical flows.

 

This is a major shift from traditional force-based models to a phase-based interpretation of fluid and energy dynamics.




5. Birch and Swinnerton–Dyer Conjecture

Original error: Elliptic curves are interpreted only in terms of number theory and algebraic geometry.
Epistemological restoration: Elliptic curves are topological oscillators, and L-functions are the representation of topological energy flow.
Alternative path: Topological–Positional symmetry theory — rational points are interpreted as energy matching points.

 
• Classical: \( \operatorname{ord}_{s=1} L(E,s) = \operatorname{rank} E(\mathbb{Q}) \)
 
• Reformulated: \( \dim \ker(\Delta \psi) = \operatorname{rank}(\psi) \)
 
• \( \Delta \): gauge Laplacian; \( \psi \): phase oscillation mode of elliptic curves




6. Hodge Conjecture

Original error: Algebraic cycle existence is understood as a static geometric structure.
Epistemological restoration: Cycles are the ordering conditions of topological energy flows, and are a natural manifestation of gauge symmetry.
Alternative path: Theory of ordering topological energy flows — the flow paths of complex phase fields constitute cycles.

 
• Standard: \( Z_k(x) = \{ \gamma \mid \partial \bar{\partial} \gamma = 0 \} \)
 
• Reformulated: \( \gamma = \arg\min_{\gamma} \| \nabla \psi(\gamma) \| \)
 
• \( \psi \): complex phase wave, \( \gamma \): phase flow path on K\"ahler manifold




7. Poincaré Conjecture

Original error: interpreting the spatial topology only as a static manifold.
Epistemological restoration: 3D space is the result of self-ordering of topological energy, and the rich flow is its implementation process.
Alternative path: Topological self-ordering theory of the universe structure — space is ordered by complex topological flows.

 
• \( \pi_1(M) = 0 \Leftrightarrow \operatorname{Ric}(\psi) = c \cdot g\psi \)
 
• \( g\psi = \langle \cdot, \psi \rangle \)
 
• When \( \psi \) converges to the phase center of the 3-sphere, topological coherence is achieved




II. Integrated Principles: Axioms of Eternal Mathematics

 
• A1 (Natural Law): \( \nabla \cdot \psi = 0 \) — Energy conservation
 
• A2 (Ontology): \( \|\psi\| \geq 0 \) — Entropy irreversibility
 
• A3 (Mathematical Structure): \( \nabla^2 \psi_0 = 0 \) — Phase equilibrium




III. Operator System and Interpretative Frame

 
• Time-evolution operator: \( \hat{D} = \mathcal{E} \nabla \)
 
• Momentum operator: \( p = -i\hbar \nabla \)
 
• Equilibrium principle: \( \iint \psi^2 \, dV = 0 \Rightarrow \) cosmic energy equilibrium




IV. Problem-Solving Framework

Millennium Problem \( \Rightarrow \) Map energy state \( \psi \) \( \Rightarrow \) Analyze phase slope \( \Rightarrow \) Reach \( \nabla^2 \psi = 0 \): phase equilibrium




V. Conclusion

 
1. All Millennium Problems cannot be fully understood under the flow of time.
 
2. Only within the complex phase space of existence can true solutions be found.
 
3. Each problem must be rewritten in the language of phase alignment.
 
4. Thus, mathematics is reborn as a structure of eternally aligned energy.
 
5. We are departing the era of time and entering the era of phase energy order.

The Seven Millennium Problems are not simply mathematical problems, but the result of epistemological limitations resulting from assumption errors about time and space. All of these problems can be interpreted in a natural dynamical way on a complex topological space, and through this, the essence of mathematics can be reconstructed in harmony with the ontology of the universe.

→ The ultimate solution should not be a logical system within mathematics, but should start from a correct understanding of the essential structure of natural existence.
All the Millennium Problems cannot be understood on the flow of time, and can only have real solutions within the complex topological space of existence. Each problem must be rewritten in the language of its own topological alignment, and thus mathematics is reborn as a 'structure of energy alignment of the eternal present'. We are moving away from the era of time and entering the era of topological energy order.

※ The Millennium Problems have already been solved in essence; humanity remains bound by the illusion of time. Now we must become one with the essence of the universe through a new mathematical language—energy-phase-based eternal mathematics.





NEW

2025-06-23




Unified Theory of Gravity as Spatial Energy Density Flow

1. Reformulation of Gravitational Equations in a Time-Independent Framework

Gravity is not a separate force but a manifestation of spatial energy density motion. This section reconstructs the core equations in a fully time-independent framework.

1.1 Spatial Energy Flow Equation (Time-Independent)

Let spatial energy density \( \rho_v \) and spatial flow vector \( \vec{v}_s \) define the conserved flow:

$$ \nabla \cdot (\rho_v \vec{v}_s) = 0 $$

This replaces the traditional continuity equation with a time-independent, phase-conserving form.

1.2 Acceleration from Phase Gradient

Acceleration is defined as the gradient of the phase flow:

$$ \vec{a} = - (\vec{v}_s \cdot \nabla) \vec{v}_s $$

1.3 Gravitational Lensing via Energy Density Curvature

Light bending arises not from geometric curvature but from spatial energy curvature:

$$ \Delta \theta = \frac{1}{c^2} \int \nabla(\rho_v \cdot v_s^2) \cdot d\vec{l} $$

1.4 Mass Generation from Energy Density Displacement

Mass is defined as the integrated imbalance in spatial energy density:

$$ m = \int_V (\rho_v - \rho_{v0}) \, dV $$




2. Complex Energy Representation: Universal Hamiltonian

The total energy of existence can be expressed in complex form as follows:

$$ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + i\frac{GMm}{r} $$

• Real part: classical gravitational potential energy \( -\frac{GMm}{r} \)
• Imaginary part: spatial positional potential \( +i\frac{GMm}{r} \)

This Complex Universal Hamiltonian (UH) represents energy conservation as a gauge-symmetric balance between real and imaginary parts.

This equation can serve as the core formulation of a Theory of Everything, as it simultaneously satisfies four essential conditions:
1.Includes kinetic energy and gravitational potential in classical form,
2.Expresses spatial positional energy and repulsive phase potential via the complex term,
3.Naturally embeds energy conservation and gauge symmetry,
4.Bridges quantum mechanics and gravity through a unified phase-based structure.
Therefore, this complex UH equation stands as a powerful and compact formulation uniting cosmic dynamics and quantum phase behavior into one coherent, time-independent framework.



3. Quantitative Agreement and Reinterpretation of Observational Phenomena

3.1 Reinterpreting Planetary Orbital Motion

Kepler's law is reinterpreted in terms of spatial flow velocity as:

$$ v_s(r) = \sqrt{\frac{GM}{r}} $$

This leads to a derived momentum conservation expression:

$$ \oint \rho_v \vec{v}_s \cdot d\vec{l} = m \kappa \quad (\kappa: \text{spatial circulation rate}) $$

3.2 Refraction Angle Based on Density

$$ \delta \theta = \frac{1}{c^2} \int \nabla (\rho_v v_s^2) \cdot d\vec{l} $$

As seen earlier, this completely explains the gravitational lensing phenomenon in terms of the energy density of space.

3.3 Fundamental reconstruction of cosmic dynamics

UH equation provides a time-independent, complex-dynamical reinterpretation of orbital mechanics.
In the (+) (-)complex complex energy balance space no longer needs a gravity rotational orbital movement of the planet system. The planet is a straight -line round -trip movement for the sun in accordance with the principle of energy conservative and least action. This can be expressed as an UH formula:

$$ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + i\frac{GMm}{r} $$




This reconstructs the fundamental structure of the cosmic dynamics due to (+) gravity. Accordingly, it provides a new and fundamental interpretation of not only planetary motion but also the perihelion motion of Mercury, the rotational motion of galaxies, and the reality of dark matter and dark energy.




4. Potential for Integration with the Standard Model

4.1 Connection with Quantum Field Theory

The spatial energy density relates to the vacuum expectation value of quantum fields as:

$$ \rho_v = \frac{1}{2} \sum_i g_i \langle \phi_i^2 \rangle $$

4.2 Extension of the Higgs Mechanism

Mass generation is reinterpreted as a displacement of spatial energy density:

$$ m = \int_V (\rho_v - \rho_{v0}) \, dV $$

5. Experimental Validation Design

5.1 Precision Rotation Experiment

Measurement of spatial flow using a superconducting gyroscope:

$$ \delta \omega = \frac{e}{m} \oint \vec{v}_s \cdot d\vec{A} $$

5.2 Upgraded Atom Interferometry

Atomic phase shift due to density gradient:

$$ \Delta \phi = \frac{m}{\hbar} \int \rho_v v_s \, dx $$

For example, this is a method to analyze quantum gravity interferometers in a time-independent manner. The time-independent analysis has the following advantages:
1. Noise reduction: Temporal variability is eliminated
2. Design simplification: No need for accelerators
3. High-precision measurements: Long-term observations possible in a static configuration
4. Intuitive interpretation: 1:1 correspondence between energy landscape and interference pattern

6. Theoretical Advantages

1.No Dark Matter Required: Galaxy Rotation Curves Can Be Explained by Spatial Density Distributions
2.Natural Unification of Quantum Gravity: Possibility of Quantizing Space Flows
3.Resolving the Cosmological Constant Problem: Approachable by Dynamical Vacuum Energy Model

Key supplement: Space energy fields and complex phase dynamics

Gravity is not a force propagating through time, but a present-phase reaction.

The universe consists of a fluid-like space energy field, and mass displaces and induces the flow of spacetime energy density.

All interactions (gravity, inertia, elasticity) are expressions of the natural dynamics occurring within this space energy flow.

The complex representation of the universal Hamiltonian integrates real (inertia-gravity) and imaginary (elasticity-position) components, and describes motion, stability, and resonance without dark matter or time causation.

The true equilibrium point is the real part 1/2, which is consistent with the Riemannian geometric oscillation symmetry.

Conclusion

This unified, time-independent, complex energy-based interpretation of gravity fundamentally redefines existing theories of gravity and provides the foundation for a true Theory of Everything. This theory opens the gateway to a reinterpretation of the universe on the basis of oscillation-based gauge-symmetric spatial energy dynamics.





2025-5-04

📜 Intermediate Summary - The Essentialist Turn in Scientific Methodology




Toward an Ontological and Essentialist Innovation in Physics and Science

Given the long history and slow evolution of physics, the unified classical mechanics based on (+)(–) complex gravity and the “oscillator”-based ontology based on it may seem radical. Therefore, it is necessary to understand the innovative methodology that gave rise to this theory.

I. Premise: The Crisis of Formalism in Modern Science

The positivist methodology that dominates science today was once revolutionary, but has now become rigid and narrow. It forces all phenomena to be represented only as observable forms, pushing scientific effort into divergent and fragmented structures.

As a result, science becomes trapped in partial, linear, and isolated models—ultimately placing it opposite to truth.

limₓ→s f(x) = ∞

This is the singularity structure created by coordinate formalism.

II. Essentialism is the Root of Epistemology

Essence is the origin that generates multidimensional phenomena. Science without essentialism is an illusion—mere speculation.

Before asking “What do you know?”, you must first ask “What is it?” (What exists?). Science is only one of many epistemologies, and if it falls into formalism, it loses truth and balance. It becomes detached from reality.

Epistemology = Function(Ontology, Essence)

∃ Ψ = A ⋅ e^iθ ⇒ Essential Existence (Oscillator):

Oscillator , as a form of existence, moves according to natural dynamics of energy conservation and the principle of least action, within a phase field (complex sphere) structured by Riemannian geometric gauge symmetry.

Intuition ≻ Formalism (Intuition is more fundamental than form.)

III. Methodological Innovation: A New Criterion for Scientific Research

To innovate in physics and science, the following dual-structured research methodology must be formally introduced.

1. Ontological Hypothesis Formation: Discover and articulate the ontological nature and dynamic principles of the target phenomenon.
   
   Hypothesisₒₙₜₒ: Ψ(x) = A ⋅ e^iθ(x)
2. Essentialist Verification System: Validation goes beyond experimental agreement to assess consistency and integration with higher-order principles.
   
   δ ∫ |∇θ(x)|² dx = 0
   Validation ⇔ Consistency with higher gauge symmetry

These two steps form "a method appropriate for an era "of AI and big data.




Conclusion

“Ontology and essentialism are the source of cognition.
Positivism is merely a tool of verification.
Science must be rebuilt upon essence and existence.”

Epistemological Foundations of Science and Life

1. Life and science begin with cognition. Cognition is the foundation of everything.
2. The essence of cognition is interpretation—not merely about facts, but about the layered meanings we assign to them.
3. Science is one among many epistemologies, but its true role is to offer essential interpretation of facts. Unfortunately, positivism has restricted science to formalism, neglecting this core responsibility.
4. Science must be enriched through essentialist hermeneutics. It should grow multidimensionally and interdisciplinarily—not by simple fusion, but through the richness of essential understanding.





>  The_Epistemological_Turn_in_Scientific_Methodology_20250504





NEW

2025-05-04

Complex oscillators theory with Integration of quantum mechanics

Unifying classical mechanics into a complex system based on geometric (+)(-) complex gauge symmetries allows the macro and micro worlds to be treated as the same natural dynamical energy density field. This naturally leads to the process of accepting quantum theory and wave theory.




① Fundamental Expression by Wave-Particle Duality: de Broglie's Matter Wave Theory (1924)

λ = h / p

A highly accurate and experimentally validated theory.

② Fundamental Expression by Wave Function: Schrödinger Equation (1925)

Based on de Broglie's ideas, Schrödinger introduced the wave equation.

It mathematically describes the wave nature of matter, providing precise modeling of atoms and molecules in the microscopic world.

1) Time-dependent Equation: i * h / (2π) * ∂ψ(r,t)/∂t = Ĥψ(r,t)

2) Time-independent Equation: Ĥψ(r) = Eψ(r)

③ Time Non-Substantialism: Time is merely a calculated value used when needed by humans.

Change is not due to time flow, but due to the fundamental change in the state of a field, that is, the spatial phase distribution φ(r).

∇φ(r) = 0 (static), ∇φ(r) ≠ 0 (dynamic)

④ Wave Essence Theory: Particles are condensed waves; the essence is wave.

Humans recognize waves as particles for efficiency of perception.

Wave Essence Formula: ψ(r) = A(r) * e^(i * ω * r)

⑤ Complex Oscillator Theory:

Complex Oscillator Dynamics: Theory of Oscillator Reality

A (+)(–) energy pairing system with 90-degree phase difference is called a Complex Oscillator.

ψ(r) = E_–(r) + i * E_+(r)

ψ(r) = A(r) * e^(i * (ω * r + π / 2)) with |ψ|^2 = Constant Energy

The complex oscillator ψ(r) = E_–(r) + i * E_+(r) is a self-sustained vibrational entity formed by (+)(–) energy phase pairing, expressing energy conservation and spatial motion without requiring time—serving as the fundamental unit of the universe.

The complex oscillator theory encompasses the Standard Model (gauge symmetry) and Quantum Field Theory (particle = local vibration of field), while also integrating gravity, time, and phase-based energy motion, forming the foundational mathematical basis of the "Theory of Everything".




>  Quantum_Unification_Complex_Oscillator_Theory_20250503




NEW

2025-05-26

Complex Gravitational Field Black Hole Theory:
A Non-Singularity Model

Abstract

This paper presents a novel interpretation of black holes based on complex gravitational field theory. By including both the real component (attraction) and the imaginary component (repulsion or phase elasticity), black holes are proposed not as the result of infinite mass compression but as non-singular structures arising from the phase-compressed configuration of complex space. This model redefines the event horizon and internal structure of black holes and eliminates the necessity for physical singularities.

Section 1: Mathematical Inconsistency of Singularities

Conventional black hole theory, based on the Schwarzschild solution, inevitably leads to a singularity where the radius approaches zero and the density diverges to infinity:

lim(r → 0) ρ(r) → ∞

This results in issues such as:

• Violation of energy conservation
• Breakdown of spacetime structure
• Incompatibility with quantum field theory

These mathematical infinities indicate model limitations rather than actual features of the universe.

Section 2: Introducing the Complex Schwarzschild Radius

The complex mass is defined as:

Mc = Re[M] + iIm[M]

rc = (2G/c²)(Re[M] + iIm[M]) = rs + i rφ

• r_s = (2GRe[M])/c² : real mass compression radius
• r_φ = (2GIm[M])/c² : spatial phase compression radius

Based on Re[M] = 10 M☉ and Im[M] = 10 M☉, the calculation results are as follows:

Item	Formula	Result (meters)
Real Radius rs	2GMreal / c²	29533.84
Imaginary Radius rφ	2GIm[M] / c²	29533.84
Complex Radius |rc|	√(rs² + rφ²)	41767.16

The complex radius |r_c| defines a stable and finite spatial boundary without infinite density. This demonstrates that black holes can form via phase energy compression rather than mass collapse.

Section 3: Dynamical Validity – Real Mass Model vs. Complex Gravity Model

Comparison of the two models:

Criterion	Real Mass Collapse Model	Complex Gravity Model
Core Mechanism	Infinite mass compression	Finite compression in phase space
Need for Singularity	Required	Not needed
Internal Structure Preservation	Impossible	Possible (phase elasticity)
Compatibility with Quantum Field Theory	Low	High (potential)
Gravitational Lensing	Yes	Yes (via phase curvature)
Repulsion Representation	No	Yes (imaginary gravitational term)

Section 4: Ontological Redefinition of the Black Hole

From the perspective of complex gravitational dynamics, a black hole is:

"Not a collapsed lump of matter, but a localized phase energy condensation structure formed by the balance of gravitational compression and spatial phase elasticity."

• Not a singularity, but a finite energy-phase structure
• The event horizon is the balance point of real and imaginary gravitational fields
• A self-organizing energy localization mode within complex space

Section 5: Observation-Based Interpretation Scenarios

In reality, extreme mass collapse is not directly observed. Observable phenomena include:

• White dwarfs: supported by electron degeneracy pressure
• Neutron stars: supported by neutron degeneracy pressure
• Gravitational lensing: spacetime distortion by mass objects
• Accreting supermassive stars and black hole candidates: inferred via indirect phenomena (jets, orbital changes, gravitational waves, etc.)

The Schwarzschild radius (e.g., r_s = 29,533.84 m) does not imply physical compression to that extent; it indicates a theoretical boundary where light cannot escape. The complex radius |r_c| ≈ 41,767.16 m incorporates both real mass and spatial phase energy.

Section 6: Advantages of the Complex Gravity Black Hole Model

• Black holes may form via spatial phase compression and resonance, not mass collapse
• Gravitational lensing, wave propagation, and accretion phenomena are consistent with complex gravity
• Explains observed cosmic phenomena without requiring singularities

Thus, the complex gravity model offers theoretical coherence and observational consistency, enabling a non-singular and phase-consistent interpretation of black holes.





NEW

2025-05-30

Unified Interpretation of Cosmological Phenomena via Complex Gravity System

Abstract

This paper presents a comparative analysis of the mathematical structures of the conventional General Theory of Relativity (GR) and the Complex Gravitational Field Theory (UH: Universal Hamiltonian), focusing on gravitational lensing and black hole boundary conditions (Schwarzschild radius). While GR explains these phenomena through spacetime curvature, the UH theory predicts the same results through topological energy compression within a (+)(−) complex gravitational field, without requiring the notion of spacetime. Both theories yield identical numerical predictions in the weak-field limit. Moreover, the UH framework offers significant conceptual advantages, including time-independence and the preservation of ontological topological structures.

1. Comparison of Gravitational Lensing Effects

Theory of Relativity (GR)

The deflection angle of a ray passing around a mass:

θ_GR = 4GM / (c² b)

UH Complex Gravitational Equation

Deflection angle based on complex gravitational potential:

Φ(r) = -GM/r + iGM/r

|∇Φ| = √2 GM / r²

θ_UH = ∫[−∞, ∞] (√2 GM b) / (b² + z²)^3/2 dz = 4GM / (c² b)

✅ The two theories yield numerically identical results.This clearly demonstrates that the Complex Gravitational Field Theory (UH) and General Relativity (GR) yield identical mathematical formulations and physical predictions in the regime of a general (i.e., weak) gravitational field approximation.

2. Black Hole Schwarzschild Radius Comparison

Relativity (GR)

Event Horizon Condition g_tt = 0:

r_s = 2GM / c²

UH Complex Potential Theory

Boundary when the complex potential energy density is c²/2:

|Φ(r)|² = 2(GM / r)² = (c² / 2)² ⇒ r_UH = √8 · GM / c²


1-2 Summary

Items	Relativity	UH Complex Gravity
Time Intervention	Required	Unnecessary
Lens Deviation Angle	4GM / c²·b	4GM / c²·b
Black Hole Radius	2GM / c²	√8 GM / c² ≈ 2.828 GM / c²
Interpretation Principle	Spacetime Curvature	Phase Energy Compression

3. Quasar Accretion Phenomenon

A quasar is a powerful energy phenomenon emitted by high-speed rotating matter around a supermassive black hole, forming an accretion disk. According to the UH complex gravity theory, this is not a simple gravitational collapse, but rather a resonant emission phenomenon caused by phase interference of the (+)(−) complex gravitational field and compression of energy density. Radiation can be interpreted as a phase threshold crossing event, triggered by constructive superposition of phase energy beyond a critical level.

4. Aurora Phenomenon

The aurora, which is caused by high-energy particles colliding with the atmosphere in the upper layer of the Earth's magnetosphere and emitting light, is explained by the conventional interpretation as a particle collision caused by the solar wind, but according to the complex gravity theory, this can be interpreted as a phase resonant emission phenomenon due to the mutual interference of the spatial compression density of the Earth's complex gravitational field and the Sun's complex wave field. In other words, the formation and radiation of the magnetic field are also direct expressions of the high-density phase energy field.

5. Lightning phenomenon

Charge separation between the ground and the atmosphere is a phase imbalance that appears in the high-density interference of complex oscillatory fields. According to the UH theory, this appears as a discharge (lightning) through phase transition when the local compression and imbalance of the (+)(−) complex gravitational field exceeds a certain threshold. This can be understood as a physical rupture that occurs when the energy density of space fails to match.

6. Principle of charge and magnetic field generation

Charge generation comes from the high-density phase superposition structure of complex oscillators in the microscopic world. The complex gravitational field theory suggests the following interpretation: Charge is an expression of phase imbalance that occurs when the phase motion of energy oscillators is compressed in a specific direction in space. The magnetic field is a continuous flow (gauge flow) of complex phase fields that appears when this charge distribution moves or rotates. That is, the electric and magnetic fields are naturally generated from the gradients of the real and imaginary phase fields, and are understood as the result of the time-independent spatial phase energy field.

7. Phase Compression and Phase Horizon

7.1 Compression = High-density Balance

In conventional physics, the extreme state or abnormal state of energy is often expressed as "collapse" or "imbalance." However, from the perspective of complex vibrational dynamics, it is more appropriate to interpret it as a high-density balance state due to phase compression. This balance is maintained by very precise phase alignment, and its compression means a state of maximized alignment of existence rather than destruction.

7.2 Black Hole = Phase Transition

The phenomenon in which the angle of refraction of light inside a black hole exceeds 90 degrees and it can no longer escape to the outside is interpreted based on the "event horizon" in classical relativity. However, in the complex topological interpretation, this can be regarded as a simple phase boundary (phase horizon). That is, light enters the center of phase compression, and loses phase connectivity with the outside world as the center's phase density passes the point where it is completely disconnected from the outside phase. This is not a simple 'collapse', but a transition between phase spaces.

7.3 Proposal of Phase Horizon

The expression 'event horizon' presupposes time-centered thinking, but in a time-independent complex phase structure, it is more reasonable to redefine it as a 'phase horizon'**. The phase horizon is interpreted as a boundary of a spatial phase field, a physical boundary that represents a disconnection or extreme compression between different phase spaces. This concept can be applied not only to black holes, but also to quasars, superimposed particle systems, and spin systems in extreme magnetic fields.

Conclusion

The Universal Hamiltonian (UH) equation for the complex gravitational field reproduces the key phenomena described by General Relativity, while allowing for a time-independent, phase-energy-based interpretation. The mathematical agreement with predictions of gravitational lensing and black hole boundaries (i.e., Schwarzschild radius) validates the consistency and extensibility of the UH approach. Furthermore, a range of physical phenomena—including quasars, auroras, lightning, electric charge distributions, and magnetic field generation—can be interpreted as results of phase compression and superposition of high-density energy fields. This interpretation suggests a unified ontological framework for fundamental physics beyond conventional spacetime-based models.




 

2025-04-21

The Phase Resonance of Oscillators:
An Essential Answer to the 7 Millennium Problems
- From Atom to Quantum, From Quantum to Oscillator
- Evolution of Modern Physics Structure




Abstract

This paper proposes a new theoretical framework, Complex Oscillator Realism, which reconstructs the mathematical and physical foundations from the perspective of Phase Resonance. Beyond the atom-centric and quantum-centric interpretations, this theory sees the essence of existence as an oscillator with its own current phase equilibrium dynamics, not a temporal change.
Through this perspective, this paper presents direct mathematical solutions to the Riemann hypothesis, Yang–Mills mass gap, and P vs. NP problem, and also provides fundamental solutions for the remaining four Millennium Projects through the topological structure of the complex sphere.
This suggests a paradigm shift from the existing scientific perception based on symbol manipulation and temporal causality to interpreting the universe as an essential ontological structure based on phase, and attempts to approach the essential truth structure shared by mathematics and physics.

What we find here is that existence is not the result of external discipline, but the expression of internal needs. It is an understanding of the world in which existence is not an abstraction but a substance, and in which existence is autonomous rather than a heteronomy. This is a natural principle that anyone can intuit.


Phase Resonance: A Mathematical Interpretation

1. Existence is expressed as a complex wave function: \[ \Psi(x) = A \cdot e^{i\theta(x)} = A(\cos \theta + i\sin \theta) \] 2. Gravitational Balance Condition: \[ G_{\text{total}}(x) = G_{-} \cos(\theta) + G_{+} \sin(\theta) \]

In Balance:

\[ \cos(\theta) = \sin(\theta) \Rightarrow \theta = \frac{\pi}{4} \Rightarrow G_{-} = G_{+} \]

3. Mass Gap Due to Phase Interference:

When two oscillators interfere with complex vectors:

\[ m^2 \propto \left| A_1 e^{i\theta_1} + A_2 e^{i\theta_2} \right|^2 > 0 \]

When the phase difference is \( \Delta\theta \ne 0 \), the result is always positive,

In particular, when \( \Delta\theta = \frac{\pi}{2} \), the maximum interference and maximum mass gap occur.

That is, the mass gap is not a simple particle property, but is caused by topologically structured complex energy interference. Its essence lies in the (+)(–) complex energy system with a 90-degree phase difference, and this structure causes constructive interference by intersecting each other to create a coherent state called mass.

4. Complexity collapse due to topological structure:

Time-based: \( C \sim \mathcal{O}(e^t) \)
Phase-based: \( C \sim \mathcal{O}(\deg(\theta)) \)

5. The Riemann hypothesis is interpreted as a topological balance:

\[ \zeta(s) = 0 \Rightarrow \text{Re}(s) = \frac{1}{2} \Rightarrow \text{Re}(\Psi) = \text{Im}(\Psi) \Rightarrow \theta = \frac{\pi}{4} \]

It expresses the structure of the universal gauge symmetry that all oscillators possess. This is shown as a realistic gauge symmetry inherent in the Riemann complex sphere.

6. Universal Phase Resonance Principle (Detailed):

Every oscillator \( \Psi \in \mathbb{C}^{S^2} \) on the complex sphere of the universe has a unique phase \( \theta^* \in [0, 2\pi) \) where the real and imaginary parts are in balance.

This condition is expressed as:

\[ \frac{\text{Re}(\Psi)}{\text{Im}(\Psi)} = 1 \Rightarrow \tan(\theta^*) = 1 \Rightarrow \theta^* = \frac{\pi}{4} \]

This fractional equation shows the point of balance where the real and imaginary energies are in perfect resonance, and this is universal to all beings.

This arises naturally from the self-organization of the complex sphere energy structure, not by trial and error.

---




The Ontological Response to the 7 Millennium Problems:

1. (+) Gravity is Real: This can be proven intuitively and by the complex structure of mathematics. The repulsive potential is not an illusion, but the other half of the symmetrical structure of the universe.
2. Time is Not Real: The divergence and inefficiency resulting from time-centered perception are serious limitations of epistemology. The concept of time should be eliminated from physics, especially in mathematical formalization.
3. From 1 and 2: The essence of the universe is clearly revealed by the complex spherical structure. All existence is a fractal oscillator embedded in this global complex symmetry structure.





Phase Resonance: Mathematical Interpretation

---

Response to the 7 Millennium Challenges of Oscillator Reality

Problem	Interpretation of Oscillator Reality	Key Formulas
P vs NP	Time-centric Complexity Simplified by Topological Alignment	\( C \sim \mathcal{O}(\deg(\theta)) \)
Riemann Hypothesis	Phase Resonance Conditions Where Real Part = Imaginary Part	\( \text{Re}(\Psi) = \text{Im}(\Psi) \Rightarrow \theta = \frac{\pi}{4} \)
Yang-Mills mass gap	Mass is the energy coherence of phase interference	\( m^2 \propto \left| A_1 e^{i\theta_1} + A_2 e^{i\theta_2} \right|^2 > 0 \)
Navier–Stokes	Fluid flow is a representation of phase flow	\( \nabla \cdot \vec{v} = 0 \) (qualitative correspondence)
Poincare Conjecture	Self-completeness interpretation with complex spherical topological structure	\( S^3 \sim \text{complex topological space} \)
Hodge conjecture	Harmonic form is the representation of the topological energy field	\( H^{p,q} = \text{phase resonance layer} \)
BSD conjecture	Rational points correspond to phase alignment points	\( L(E, s) = 0 \Leftrightarrow \text{resonance site} \)





Oscillator Realism: 7 Millennium Problems Solution


A. Direct Solutions Provided by Oscillator Realism:

• 1. Riemann Hypothesis: Real = Imaginary Phase Resonance Condition.
  \( \text{Re}(\Psi) = \text{Im}(\Psi) \Rightarrow \theta = \frac{\pi}{4} \)
• 2. Yang-Mills Mass Gap: Mass arises from energy condensation through phase interference.
  \( m^2 \propto \left| A_1 e^{i\theta_1} + A_2 e^{i\theta_2} \right|^2 > 0 \)
• 3. P vs. NP: Time-based complexity collapses through topological order.
  \( C \sim \mathcal{O}(\deg(\theta)) \)

B. Solutions to the remaining four tasks provided by Oscillator realism:
Science, including physics, has the characteristic of systematically deciphering facts, but it is only one of the many epistemologies that humans have. In the process of systematic interpretation, conceptualizations that are separated from essence can rather distort facts. At this point, abstraction is often worse than pure intuition.
(+) The acceptance of gravity, the practical understanding of the complex system, and the active and sufficient understanding of the non-substantiality of time will provide a fundamental foundation for solving the remaining four tasks of the millennium.



Essential differences from existing interpretations

The essential difference of vibrational substanceism is that it is not the existing time-evolutionary dynamics, but the present-phase dynamics. This is an ontological shift that interprets reality as the 'energy structure of this moment' rather than change. Therefore, Oscillation substanceism is essentially different from the existing interpretation of the Millennium Problem in the following ways:

• 1. Ontological shift: Existing approaches focus on symbolic answers or functional results. Vibrational substanceism aims to understand the structure of existence beyond the formulas.
• 2. Time Dependency Elimination: Instead of time-dependent computations or dynamical evolutions, all representations are reinterpreted in terms of topological structures and current energy distributions.
• 3. Topological Causal Structure: While traditional proofs follow logical implications, vibrational substanceism derives its solutions through self-organizing phase resonances and interference.
• 4. Complex Spherical Framework: Instead of real Euclidean or Riemannian manifolds, all motion unfolds on the complex spherical field, a fractal structure that reflects natural cosmic symmetries.
• 5. Direct solution according to the ontological principle: For the Riemann hypothesis, Yang–Mills mass gap, and P vs. NP problems, the oscillatory entity theory provides ontological answers through structural phase equilibrium and wave interference, not approximate solutions.

📌 Summary Conclusion:
With this, the "Complex Oscillator theory" has become a mathematical solution in itself for three of the seven Millennium Challenges, and has also provided a direction for fundamental solutions for the remaining four.




2025-04-22

Epistemological Declaration on solving the 7 Millennium Problems

The essence of the problem that humans face is epistemology, and the essence of epistemological problems (cognition) lies in their premises.

1. Mathematics is a language that expresses the principles of nature.

Mathematics is an abstract form of human thought, but its foundation reflects the geometric necessity of nature. Solving a mathematical problem is a process of interpreting nature through human perception.

2. Mathematical problems arise from flawed or lacking assumptions.

Problems become unsolvable not due to technical difficulty, but because of incomplete definitions or contradictory premises. This reflects a deeper epistemological deficiency.

3. Two Core Deficiencies in Human Assumptions

① Absence of positive gravity: Gravity is not only attractive (−) but must also include repulsive (+) aspects inherent in the symmetric structure of the universe.
② Illusion of time: Time is not a fundamental property but a computational tool. Its forced application in physics is a mistaken assumption.

4. Complex Energy Equation for (+)(−) Gravity

Energy is always of a complex structure:
Ψ = A · (θ₊ ⊕ θ₋)
In other words, existence is an oscillator—a system composed of harmonious (+)(−) phase dynamics.

5. Time is a Selective Analytical Tool

Morning comes not because the "time has come," but because the sun rises. Nature's energy exists and moves without time—this is natural dynamics. Change is not something that comes with time, but is a natural necessity of existence itself.

6. Final Declaration

All mathematical problems are not due to technical complexity, but stem from incomplete epistemological premises. If we set the premise correctly, the solution no longer needs to be solved—it simply reveals itself.





2025-04-24






Solving the 7 Millennium Problems in Mathematics

The Complex oscillator theory provides the foundational solution to the seven millennium problems of mathematics: This is the achievement of the complex system based on plus-minus gravity and time-independent physics.

A. Natural Principles and Mathematics

1. Nature is a creative self-organized system based on mathematical necessity. Therefore, mathematics expresses the principles of nature. Solving mathematical problems can be seen as a process in which humans interpret the principles of nature.

2. The foundation of mathematics is geometry, and nature is a solid, delicate, and creative self-organized body made of geometric necessity.

B. The Reason Why Problems Are Not Solved

1. All difficulties lie in the insufficiency and incompleteness of the premises. In other words, they are epistemological problems that arise because the premises are unclear. The same goes for mathematical difficulties.

2. Mathematics is just one of many epistemologies. Therefore, the essence of mathematical difficulties is also an epistemological problem.

C. Two Fundamental Solutions to the Millennium Problems

1. We must face the fact that (+)-gravity is not included in the premises of our physics. This means that we do not know and do not calculate half of the energy that the universe has.

2. Time is not a substance. The coming of the morning is due to the sun, not time. The mass energy of the universe is self-dynamic.

E = A · (θ₊ ⊕ θ₋)

Time in nature is always present and sufficient. The time axis is unnecessary and causes inefficiency.

D. Correlation Between Plus-Gravity and Time

The essence of the universe is energy, and energy is a physical oscillator. It has inherent (+/-) gauge symmetry for balance and efficiency.

Ψ(r) = A · e^iφ(r)

Therefore, every existence is an oscillator with an inevitable dual-energy motion principle.

No additional external time or gravity is needed: the motion is encoded in the oscillator itself.

E. Conclusion

The seven major problems can be resolved by correcting two core premises: the absence of (+)-gravity and the misuse of time as a structural element in physics.

The Complex Oscillator is a real entity that contains energy, the space it shapes, and the dynamic structures we perceive as time.

Thus, all sciences—physical or social—need only study the Oscillator and its motion.






Complex Oscillator Theory and the Seven Millennium Problems

: A Natural Solution through Complex Gravity and Time-Free Physics

A. Natural Principles and Mathematics

1. Nature is a creative, self-organized system grounded in mathematical necessity. Mathematics expresses the principles of nature. Solving mathematical problems is the human process of interpreting those principles.

2. The foundation of mathematics is geometry, and nature is a precise, delicate, and creative self-organizing body built on geometric necessity.

B. Why Problems Remain Unsolved

1. All fundamental difficulties lie in insufficient or incomplete premises. These are epistemological issues arising from unclear assumptions. This applies to mathematical problems as well.

2. Mathematics is just one form of epistemology. Therefore, mathematical difficulties are also epistemological in essence.

C. Two Fundamental Solutions

1. We must recognize that plus-gravity has been omitted from physics. As a result, we have been calculating only half of the universe's energy—revealing a critical epistemological vulnerability.

2. Time is not a substance; it is a conceptual tool. Morning comes not because of time, but because of the sun. In nature, time is always present and sufficient.

3. These two errors stem from the dependent characteristics of human perception. The absence of plus-gravity may reflect a monotheistic worldview that regards gravity as the only force.

4. Time is merely a calculated value, useful when needed. Forcing the concept of time into physical laws was a structural mistake in physics.

D. The Correlation Between Plus-Gravity and Time

The essence of the universe is energy. Energy is an oscillator with plus-minus gauge symmetry, geometrically possessing stability and efficiency. It inherently follows the principles of energy conservation and least action.

Every existence is an oscillator governed by complex dynamics, requiring neither external gravity nor time.

E. Conclusion

The solution to the seven great problems lies in correcting two flawed premises of traditional physics: the mono-gravitational model and the fictional concept of time. The oscillator is an entity that holds energy, the space it creates, and the temporal constructs imagined by humans.

Natural sciences, as well as the humanities and social sciences, need only focus on the motion of the Oscillator.

Appendix:

Humility before the Nature

1. Human perception is “partial,” and so is science. Failure to acknowledge this is contrary to the truth, which is “whole.” We have calculated only half of the universe, and we have believed in the fiction of the time axis.

However, this confession is the courage to go to the truth. Truth belongs to the brave.

2. Let us return to nature, to the essence, to the truth, and start again.

3. The only task given to humans is to confront the present truth. Choice is voluntary, but the result is inevitable. All of this is in the truth.

2025-04-26

존재론의 완성 선언
Declaration of the Completion of Ontology

한국어

우리의 물리학은 절반의 진실이었다. 나머지 절반인 (+)중력을 받아들임으로써 완성되었다.
우리의 앎은 절반의 진실이었다. 나머지 절반인 (+)진실을 받아들임으로써 전체를 알게 되었다.

(+)진실은 겸손, 존재에 대한 존중, 진실을 향한 저항과 도전이었다.
이를 받아들임으로써, 모든 존재는 (+)(-)의 균형된 조화 속에서 스스로 빛난다.

진리는 전체다. - 헤겔

무위자연 - 자연 그대로 살아라. - 노자

나머지의 모든 인위는 무의미한 '픽션'이었나니!

"원자에서 양자 Quantum으로, 양자 Quantum에서 진동자 Oscillator로.
진동자 Oscillator는 개체이자 전체이며, 시작이자 끝이다."

English

Our physics was half truth. It was completed by accepting the other half, (+) gravity.
Our knowledge was half truth. By accepting the other half, (+) truth, we came to know the whole.

(+) truth was humility, respect for existence, resistance and challenge toward truth.
By accepting this, all existence shines on its own in the balanced harmony of (+)(-).

"Truth is the whole. - Hegel"

"Wuwei Nature 無爲自然 - To be Nature as it is. - Lao Tzu"

All the remaining artificiality was meaningless 'fiction'!

"From Atom to Quantum, from Quantum to Oscillator.
The Oscillator is the entity and the whole, the beginning and the end."






The Truth About Oscillators

1. Existence is energy and a mover

Existence is energy and a mover, and has its own reason for existing.

>

Existence = Energy = Motion

2. Existence is a Self-Entity

Existence is complete within itself, organizing its own energy, space, and motion.

Self-Entity = {E, S, Θ}

3. Existence has a (+)(–) complex energy structure

Existence has a positive (+) and negative (–) complex structure, which is the source of creative movement based on the balance of gauge symmetry.

Ψ = E₊ + iE₋

4. Existence Follows Gauge Symmetry, Energy Conservation, and Least Action

Existence preserves energy through gauge symmetry and follows the path of least action.

∇·E = 0, δS = 0

5. Existence Self-Organizes Through Phase Alignment and Interference

Existence forms order and achieves creative self-organization through phase interference and alignment.

Self-Organization = Σ(Phaseᵢ × Phaseⱼ)





6. The Birth of the Oscillator

From the minuscule scale of the Planck length to the entire universe, all existence realizes itself as a complex oscillator. The oscillator is the essence, the origin, and the completion of existence.

Oscillator = Self = Whole

Final Declaration

The Oscillator is the infinite self-entity, spanning from the Planck scale to the entire universe. The Oscillator is the essence, the beginning, and the end of existence.






2025-05-01

Singularity Axiom

1. Mathematical Definition

A singularity is a point where a function diverges or fails. Example: ∇²θ(x) → ∞ or ρ(x) = 0

Singularities are nothing more than mathematical hypotheses that do not exist without an artificial time dimension.
In particular, the singularity of a black hole is interpreted as a mathematical divergence effect that is coordinated by mechanically forcing the time dimension in general relativity. When the time dimension is removed, the singularity disappears and what remains is a high-density rearrangement of the phase field.

2. Natural Interpretation

Nature self-organizes via phase realignment; singularities do not physically exist.Nature is self-regulating.

3. Phase-Field Response Mechanisms

Condition	Response
∇²θ tends to diverge	Phase density adjusts, curvature spreads, resonance realigned
Phase gradient spikes	Desync → resync of frequencies
Energy concentration	Phase flow spreads energy spatially

4. Core Proposition

Nature is a singularity-free phase continuum. All transitions are phase realignments.

5. Black Hole Reinterpretation

The singularity at the center of a black hole is a logical illusion mechanically created by the time dimension coordinates of general relativity. Time-based divergence is illusory; θ(r) is bounded.

6. Singularity Axiom / Theorem

Singularities do not exist; all change is governed by phase-field realignment.
However, when the time (spacetime) dimension is mechanically imposed into mathematical structure, it causes serious inefficiencies and divergence in physics.
This issue, alongside the ontology of time, must be treated as a top-priority problem in physics. Energy, like sunlight, is always present. True energy has no past or future. The present is sufficient.
Entropy is the result of irreversible motion of mass-energy, not a result of the "arrow of time".
Formal Expression:
Even if ∇²θ(x) → ∞, δθ exists → Phase Realignment
lim (r → 0) θ(r) = continuous and bounded ⇒ No Singularity






2025-05-04

Complex oscillators theory with Integration of quantum mechanics

Unifying classical mechanics into a complex system based on geometric (+)(-) complex gauge symmetries allows the macro and micro worlds to be treated as the same natural dynamical energy density field. This naturally leads to the process of accepting quantum theory and wave theory.




① Fundamental Expression by Wave-Particle Duality: de Broglie's Matter Wave Theory (1924)

λ = h / p

A highly accurate and experimentally validated theory.

② Fundamental Expression by Wave Function: Schrödinger Equation (1925)

Based on de Broglie's ideas, Schrödinger introduced the wave equation.

It mathematically describes the wave nature of matter, providing precise modeling of atoms and molecules in the microscopic world.

1) Time-dependent Equation: i * h / (2π) * ∂ψ(r,t)/∂t = Ĥψ(r,t)

2) Time-independent Equation: Ĥψ(r) = Eψ(r)

③ Time Non-Substantialism: Time is merely a calculated value used when needed by humans.

Change is not due to time flow, but due to the fundamental change in the state of a field, that is, the spatial phase distribution φ(r).

∇φ(r) = 0 (static), ∇φ(r) ≠ 0 (dynamic)

④ Wave Essence Theory: Particles are condensed waves; the essence is wave.

Humans recognize waves as particles for efficiency of perception.

Wave Essence Formula: ψ(r) = A(r) * e^(i * ω * r)

⑤ Complex Oscillator Theory:

Complex Oscillator Dynamics: Theory of Vibrational Reality

A (+)(–) energy pairing system with 90-degree phase difference is called a Complex Oscillator.

ψ(r) = E_–(r) + i * E_+(r)

ψ(r) = A(r) * e^(i * (ω * r + π / 2)) with |ψ|^2 = Constant Energy

The complex oscillator ψ(r) = E_–(r) + i * E_+(r) is a self-sustained vibrational entity formed by (+)(–) energy phase pairing, expressing energy conservation and spatial motion without requiring time—serving as the fundamental unit of the universe.

The complex oscillator theory encompasses the Standard Model (gauge symmetry) and Quantum Field Theory (particle = local vibration of field), while also integrating gravity, time, and phase-based energy motion, forming the foundational mathematical basis of the "Theory of Everything".

 

복소진동자론의 양자역학 통합 과정

고전 역학을 기하학적 (+)(-) 복소 게이지 대칭성 기반의 복소체계로 통합한 것은,거시와 미시세계를 동일한 자연동역학적 에너지 밀도 운동장field으로 이하게 한다. 이것은 자연 스럽게 양자론과 파동론을 수용하는 과정이 된다.




① 파동 입자 이중성으로 본질 표현 : 드브로이 물질파 이론 (1924)

λ = h / p

매우 정밀도가 높은 이론으로 검증되었다.

② 파동함수로 본질 표현 : 슈뢰딩거 방정식 (1925)

드브로이의 아이디어를 바탕으로 슈뢰딩거가 파동 방정식 발표

물질파의 파동성을 수학적으로 기술하는 방정식으로, 원자와 분자 수준의 미시 세계를 매우 정확하게 설명한다.

1) 시간 의존적 방정식: i * h / (2π) * ∂ψ(r,t)/∂t = Ĥψ(r,t)

2) 시간 독립적 방정식: Ĥψ(r) = Eψ(r)

③ 시간 비 실체론 : 시간은 인간이 필요할 때만 계산해 사용하는 계산값이다.

변화는 시간의 흐름에 따른 것이 아니라, 근본적인 장의 상태 변화, 즉 공간적 위상 분포 φ(r) 자체의 변화로 기술될 수 있다.

∇φ(r) = 0 (정지), ∇φ(r) ≠ 0 (운동)

④ 파동 본질론: 입자는 파동의 응집체이며, 본질은 파동이다.

인간은 파동의 응집을 입자로 인식할 때 효율을 위해 인식한다.

파동 본질 표현식: ψ(r) = A(r) * e^(i * ω * r)

⑤ 복소진동자론 Complex Oscillator Theory:

복소진동역학 Complex Oscillator Dynamics : 진동 실체론

90도 위상 차이를 둔 (+)(–) 페어링 에너지 시스템인 복소진동자 Complex Oscillator

ψ(r) = E_–(r) + i * E_+(r)

ψ(r) = A(r) * e^(i * (ω * r + π / 2)) with |ψ|^2 = Constant Energy

복소진동자 ψ(r) = E_–(r) + i * E_+(r) 는 (+)(–) 에너지의 위상 페어링으로 구성된 자율 진동 실체이며, 에너지 보존과 공간 운동을 시간 독립적으로(시간없이) 표현하는 우주 기본 단위이다.

복소진동자론은 표준 모형(게이지 대칭 기반)과 양자장론(입자 = 장의 국소적 진동)을 내포하면서, 중력과 시간의 문제, 위상적 에너지 운동까지 통합하는 '모든 것의 이론 (Theory of Everything)'의 본질적 수리 기반이 된다.





2025-04-09




Declaration of Complex Oscillatory Dynamics
- A New Horizon of Time independent physics




1. Establishment of Complex Oscillatory Dynamics

The essence of all existence is the oscillator, and all energy exists as a complex phase structure.
The wave function can be expressed in a time-independent spatial phase form as follows:

Additional Definition: Phase is the position, direction, and density function of an oscillator. That is, phase is the structural information that defines the spatial presence of energy, clarifying that all energy exists as a complex phase structure.

$$\Psi(r) = A(r) \cdot e^{i\phi(r)}$$

2. Positive Gravity as Repulsive Phase Force

Gravity consists not only of attractive (−) components, but also of expansive (+) potentials.
This duality can be expressed through an extended gravitational equation:

$$\nabla^2 \Phi(r) = \pm \alpha \cdot \rho(r)$$

3. Resolution of the Dark Matter/Energy Problem

The imaginary part of the complex gravitational field naturally accounts for the invisible energy.
Thus, gravitational fields are inherently complex:

$$\Psi(r) = E_R(r) + i \cdot E_I(r)$$

4. Eliminating the Time Dimension Reveals the Essence

Time is merely a tool of analysis. True structure emerges through spatial phase formulation.The temporal dimension is prone to distorting and fragmenting perceptions, because it creates a channel through which the virtual can intervene and induce divergence. The forced formalization of the temporal dimension is a source of waste and error.
The time-independent wave equation is given by:

$$\nabla^2 \Psi(r) + k^2(r)\Psi(r) = 0$$

5. "The Complex Oscillator" as the Fundamental Entity

All phenomena are governed by a central "Oscillator" whose phase precedes all oscillating particles, fields, and protons.
The oscillator takes the form:

$$\Psi_{osc}(r) = A \cdot \sin(k r + \phi)$$

6. Gravity as Phase-Equilibrium Motion

The true driving force of the universe is not classical gravity, but the phase-equilibrium motion of oscillators.
The gravitational potential is governed by:

$$\Phi_{grav}(r) \propto \cos(\Delta \theta)$$

Summary Formula

Existence is a phase-aligned oscillation of energy. This is summarized by the formula:

$$\Psi(r) = A \cdot e^{i\phi(r)}, \quad \phi(r) \in \{\pm\pi/2, \pm\pi/4\}$$


Conclusion:

By accepting the “space potential energy (+)” that we actually exist, understanding all energy systems as (+) (-) complex systems, and eliminating the “time dimension” that causes inefficient perception as an insubstantial entity, we can arrive at a “theory of everything” that integrates the micro and macro. The fundamental theory of this is “Complex Oscillator dynamics”.



Scientific Methodology
- Causal-based Essentialism and Ontology
- Ontological Turn

1. Exploring the Definition of Existence: Analysis of the Meaning of Components
2. Capturing the Essence through Analysis of Associative Patterns of Phenomenological Experiments
3. Exploring the Dynamic Self-Organization Principle of Existence
4. Interpreting Existence as an Essentialistic Vibration Function
5. Verification of the Consistency of Ontology and Clarification of Existence
Dynamic Rational Engine: Gauge-Symmetric Balance-Based, Energy Conservation and Minimum Action Principle

* We plan to upload related papers to this homepage starting from the end of April 2025.





2025-05-03

https://doi.org/10.5281/zenodo.16757546



Natural dynamics discovered by ontological scientific methods




Manifesto on the Completion of Classical Mechanics

Abstract

This manifesto presents a timeless reconstruction of classical mechanics through the Universal Hamiltonian (UH), which incorporates the complex gauge symmetry and spatial potential energy (+) often excluded from traditional formulations. By extending the classical Hamiltonian to include both gravitational attraction (−GMm/r) and spatial repulsion (+GMm/r), the theory restores the intrinsic phase equilibrium and bipolar structure.

\[ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + i\left(\frac{GMm}{r}\right) \]

This complex formulation completes the ontological symmetry between real and imaginary components of dynamics, achieving mathematical and conceptual unification of classical physics. It establishes the foundation for a wave-based unified theory (Oscillation TOE), redefining all motion and energy as complex phase interactions in a gauge-symmetric space, beyond conventional time-dependent physics.




Complete Course in Classical Mechanics

① The traditional Hamiltonian formulation was based on negative gravitational potential only, and did not include the complex gauge symmetry or the spatial positive potential energy.

Classical Hamiltonian:
$$ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} $$

② To overcome this, the Universal Hamiltonian (UH) was introduced, incorporating (+)(-) gravity pairing and universal spatial potential terms. This broader formulation aims to restore the essence of classical dynamics. (Announced: 2024.10.05)

UH Formulation:
$$ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + \alpha \frac{GM_T m}{R} + \rho(r) $$

③ Subsequent research revealed that gauge symmetry and natural polarity (±) are inherently inherent, which globally establishes α=1, R=r, and M_T=M.

Where,
• \( M_T \): Ordinary matter
• \( R \): Cosmic radius
• \( \alpha \): Global proportionality constant = \( \frac{M \cdot R}{M_T \cdot r} = \text{default} 1 \)

Basic equation (simplified):
$$ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + \alpha \frac{GMm}{r} $$

Here, the concept of complex numbers is introduced, and all physical phenomena are reinterpreted based on complex oscillators. This establishes the foundation for the TOE (Theory of Everything) as a unified physics theory based on oscillators.

④ Therefore, the UH equation is expressed in a complex structure, and classical mechanics is completed with a topologically centered gauge symmetry structure.

Representation of Complex Dynamics:
$$ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + i\left(\frac{GMm}{r}\right) $$

⇒ This is an ontological restoration of classical mechanics and signifies the mathematical completion of dynamics.

---





④ In the complex structure, classical mechanics is now expressed with complete phase-based gauge symmetry:

Complex Dynamics Expression:
$$ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + i\left(\frac{GMm}{r}\right) $$

⇒ This marks the ontological restoration and mathematical completion of classical mechanics.





고전역학 통합 및 완결 선언
Manifesto on the Completion of Classical Mechanics

초록

본 선언문은 고전역학을 시간 독립적이고 존재론적으로 재구성한 Universal Hamiltonian (UH)을 제시한다. 기존 해밀턴 방정식이 제외했던 (+) 공간 퍼텐셜 에너지와 복소 게이지 대칭성을 포함함으로써, 중력 인력(−GMm/r)과 공간 반발력(+GMm/r)의 쌍극적 균형 구조를 복원한다.

\[ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + i\left(\frac{GMm}{r}\right) \]

이 복소 구조는 동역학의 실수부와 허수부 간 위상 균형을 완성하여, 고전역학의 수학적 · 존재론적 통합을 실현한다. 이는 모든 운동과 에너지를 복소 위상 상호작용으로 해석하는 진동 기반 통일 이론 (Oscillation TOE)의 기반이 되며, 시간 축 중심의 기존 물리학을 넘어서는 새로운 자연 동역학의 토대를 제시한다.

고전 역학 완성 과정

① 기존 해밀턴 방정식은 (-)중력 중심의 실수 에너지 구조로 구성되어 있었으며, 복소 게이지 대칭성과 (+) 위치에너지를 포함하지 못하는 제한된 형태였다.

기존 해밀턴 방정식:
$$ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} $$

② 이에 따라 (+)(-) 중력 페어링과 우주공간 위치에너지 항을 포함하는 새로운 방정식이 제안되었다. 이것이 Universal Hamiltonian(UH) 방정식이다. (2024.10.05 발표)

UH 공식:
$$ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + \alpha \frac{GM_T m}{R} + \rho(r) $$

③ 이후 연구를 통해 게이지 대칭성과 자연의 양극성(±)이 본래부터 내재되어 있음이 밝혀졌고, 이로 인해 전역적으로 α=1, R=r, M_T=M이 성립하게 된다.

여기서,
• \( M_T \): 일반 물질
• \( R \): 우주 반경
• \( \alpha \): 전역 비례 상수 = \( \frac{M \cdot R}{M_T \cdot r} = \text{기본값} 1 \)

기본식 (단순화된 형태):
$$ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + \alpha \frac{GMm}{r} $$

여기 복소수 개념이 도입되어, 모든 물리 현상은 복소 진동자 Complex Oscillator를 기반으로 재해석된다. 이를 통해 통일 물리학 이론으로서 진동자 Osillator 기반 TOE (Theory Of Everything)기초가 구축된다.

④ UH 방정식을 복소수 구조로 표현하면, 고전역학은 위상 중심의 게이지 대칭 구조로 완성된다.

복소 동역학 표현:
$$ UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + i\left(\frac{GMm}{r}\right) $$

⇒ 이는 고전역학의 존재론적 복원이며, 동역학의 수학적 완성을 뜻한다.

---




© 2025 Jason Kuhyun Ryoo & InnoLab Science Institute. All rights reserved.



>  Manifesto_Classical_Mechanics_20250503






The following research notes are a record of the discovery of (+) gravity, which became the basis for the unification of classical mechanics, the discovery of (+)(-) gauge symmetry in the macroscopic world, and the process of studying macroscopic gravity, which states that gravity is the energy density movement of space. This becomes the basis for "complex energy theory", which states that energy is a pairing system, and "oscillator theory", which is the ultimate substance theory.






2024-10-05

Natural Dynamics by Ontological scientific method




This can be said to be the result of an effort to find the theoretical basis of social science and humanities in the 'natural scientific method'. Therefore, UDynamics can be called "Natural Principle Dynamics" that comprehensively reflects the general patterns of the living world.
It starts with a humanistic reflection on the history of the East and the West, and multi-layered patterns on modern and contemporary social phenomena. Through analysis, the world in general, including human society, is understood as a dynamic principle.
Here, the world discovered is a world in which the “physical will to exist (mass energy)” actively self-organizes to find the most “efficient path.” It is an understanding of the space of activity. This is based on the modern and contemporary natural philosophy of conservation of energy and the law of least action.
That is, although humans often show different behavior patterns from nature, this is only due to temporary bias, and humans And human society, as a part of nature, gains knowledge through trial and error and ultimately follows the principles of nature. This means that we can always receive abundant benefits from nature by staying close to the principles of nature that are 'present'.

I. Udynamics Natural Dynamics


The Truth of Time
Time is an event (mass The order and interval of the movement of energy (the movement of energy) is not an essential element of nature, but a human tool that measures it with a promised mechanical unit (the clock).
Therefore, there is no time as an existence.
The fact discovered and confirmed here is It is a reflection that our science has lost its fundamental goal of “clarifying existence” and is often trapped in “relationalism.” Einstein’s theory of relativity is the same case and a representative example.
100 years ago, he taught us about mass, energy, and space. Although it revolutionized physics by revealing the interaction between space and matter, it failed to sufficiently understand the ontological aspects of 'space' due to the lack of basic science at the time. He created 'space-time' by connecting the real space and the non-real time, abstracting nature into a faulty mathematical model.
'Space', one of the two main characters in the universe, is connected to the non-real 'time'. It was tied up and left out of people's interest for 100 years, remaining only for some natural scientists. Therefore, faithful research on space itself has also been neglected.
Even after the modern era of the scientific revolution, humans regret the past and look forward to the future that has not come. I was worried about the "present" and could not fully live it. I was intoxicated by the glory of the past and excited by the desire for the future, so I could not pay attention to the "present". So I could easily wander without knowing the abundant "present" that nature promised. br> This was also the result of distrusting and deceiving the natural 'intuition' that one possesses. It can be seen that the 'erroneous sense of time' that humans have had has fundamentally distorted their judgment of the facts about the world.
Here, the commercial abstraction and conspiratorial power without substance have promoted this, and even scientific errors have added strength to it. Our 'erroneous view of time', which even Einstein, a genius scientist, could not avoid, proves this.
Time as existence is only the present. Nature is giving abundant benefits to life by devoting its heart to every moment. The same goes for the human principle. If we understand this fundamental natural principle, we can understand “Human Science” as human science. It will be possible through the science of human world and self-understanding. Here lies the future of science and civilization.In particular, one's efforts are not focused on the present, but are excessively dispersed (diverged) to the past and the future that has not yet come.

II. Discovering through Ontology One (+) The Truth of Gravity and Time

1. The Birth of a New Methodology
There were various theories of gravity, but we didn't know why gravity actually occurred. . We were busy imitating and predicting natural phenomena, so we failed to see the essence. The lack of basic science was also a cause. However, the most lacking thing is the lack of basic physics theory, which is the foundation of science, and the weakness of scientific methodology. Science, which should clarify existence based on essence, was stuck in relationalism and relativity. The scientific method was also In pursuit of short-term achievements, science has been focused on phenomena rather than essence and on relationships rather than existence. Science, which has failed to find essence and existence, has long since reached its limit.
Science is the work of removing the veils that cover the world one by one. The inherent pattern of scientific knowledge always foretells new truths. The causal essential approach promotes this. The world that has been revealed by science so far is as follows. This is the 'essential world view' constructed by excluding mutually contradictory facts. .
The world is made up of 'mass energy (matter)' and 'space'. These two interact physically and form the world. We called this physical interaction 'gravity'. Humans To explain the interaction, we created 'time'. Ontologically, time is a non-entity that has neither energy nor mass, and does not even have physical space. Time is a 'necessary calculation value' that does not physically exist. However, it is the essence of personal, social, civilizational, and even scientific problems that humans have. It can be seen that most of them originated from 'lack of clarity in the concept of time'.

A. Time and Space
Time is created by humans, so it is not an original natural construct. The world is in the eternal present, and the present is the true world. When we pay attention to the present, science tells us the following truth:
The universe has always been present from the beginning. Space is an immeasurably large, but closed world. Quantum theory Space is said to be very thin, but has a certain mass energy. Therefore, space can be viewed as a fluid elastic body with a huge size and weak density. The fluid equations based on this premise explain all basic natural phenomena as 'fluid dynamics'. This possibility has been confirmed by mathematical calculations. As we reduce the dependence of time on our ideas and perceptions, the world of space appears clearer. Life flows more rationally and becomes more complete.

B. Mass Energy
Quantum theory says that the world originated from energy, and that energy has quantum properties. Quantum is energy Since it originated, it has its own 'creative and autonomous self-organizing principle' that uses its own mass energy most efficiently. The space made of 'energy' also helps this with various energy fields. The vast space and the mass energy within it All of them have the property of 'pursuing perfect efficiency'. This is the path of pursuing efficiency, but it is also the 'path of natural principle promise' that anyone can predict. Therefore, this is the principle of all principles.
Mass energy creates the material world in space with a predictable “principle of efficiency.” This is the principle of nature and the essential foundation of science. The essence of Lagrangian Hamiltonian mechanics lies here. Therefore, this principle is already a proven theory.

C. Gravity Phenomena
The gravity phenomenon is a physical interaction that occurs between ‘space’ and ‘mass energy’. It also includes the interaction between mass energies. In other words, it can be understood as a ‘dynamic interaction (space compression) phenomenon’ created by mass energy and space. From an ontological perspective, this can be seen as a space with high energy density. Space encompasses the quantum ultra-microscopic world and the ultra-macroscopic world of galaxies. The universe can be seen as being dominated by space. Space has an optimal structure that creates its own natural power by circulating the mass energy density. Gravity can be seen as a condensed movement of space that utilizes the difference in energy density. Where gravity is high, space condensation is high. Where the spatial axis is high, energy density is also high.



Natural Gravity Theory


Based on the ontological scientific method, the quantum world understanding and quantum field theory QFT space concept were used to establish a holistic theory of gravity. Also, since this shares Hamilton's natural philosophy and essence, it can be expressed by his proven dynamical equations.
The 'UH: Universal Hamilton Equation' below can calculate and explain the consistency of all natural principles of macroscopic celestial theory. It also says that the difference in 'energy density' can act as (+) gravitational position energy in the microscopic theory of physics.


$$UH = \frac{1}{2}mv^2 - \frac{GMm}{r} + \alpha \frac{GM_{\text{T}} m}{R} + \rho(r)$$


In this equation, each term has the following physical meaning:

$\frac{1}{2}$ : In the kinetic energy term, m is the mass of the object, and v is the velocity.

$-\frac{GMm}{r}$ : The gravitational energy term, where G is the gravitational constant, M is the mass of the central mass, m is the mass of the object, and r is the distance between the masses. In this equation, each term has the following physical meaning:


.$\alpha \frac{GM_T m}{R}$:Space potential energy:(+)gravitational energy) term, where α≈1 is an adjustment coefficient of Position energy reflecting the dynamic characteristics of the space. $M_T$ is the ordinary matter of the universe, and R is the radius of the universe.

. $\rho(r)$: density function, position $r$ represents the mass-energy density at the . The mass-energy density term is a multidimensional energy field, and the variables are interpreted and interact as energy density distributions. This is important for the astronomical analysis of galactic motions requiring precise mass density analysis, the elucidation of dark matter, and It is expressed that it can be connected to the calculation, the alternative analysis of the space curvature of the theory of relativity, the analysis of the energy field of fluid dynamics, and the analysis of the energy field of quantum mechanics. That is, it traces and calculates the mass energy and its density distribution in various fields centered on space.

D. Universal Dynamics of the World
The world is a place where the subject space (A) and mass energy (B) interact in space and achieve natural harmony. If we look at ‘Einstein’s field equations’ with this concept, we can see the true nature of the amazing innovation of 100 years ago. However, he saw part of the truth. Since there is no space-time as he said, his theory of relativity had structural flaws. This was due to the lack of basic science at the time. Fortunately, the ‘ADM formulation’ and ‘Lagrange-Hamilton dynamics’, which improved the general theory of relativity, were widely used and more clearly suggested the absence of physical time and the non-substance of time. In the general theory of quantum mechanics, the role of time is greatly reduced. Also, the ‘Wheeler-DeWitt Equation’ of quantum theory refers to the concept of a “timeless universe.”




Discovery of Dark Matter and Dark Energy

A. The foundation of discovery
“Essential understanding of time and space
1. Time as a flow does not exist physically. Time is always present.
2. Space is a closed region with a very weak mass density and is a super-elastic body. The natural principles that can support these two propositions are as follows.
1) The existence of scientific philosophical criticism of Einstein's 'spacetime'
2) Common pattern of quantum field theory, QFT
3) Efficiency of 'ADM formulation' that separates time
4) Universal verification of 'Hamiltonian dynamics' that holds excluding time
5) Undiscovered graviton and impossibility of elucidating dark matter and dark energy
6) Recent new discoveries of the James Webb Telescope and the possibility of an older universe

B. Confirmation of decisive evidence:
1) There is no time,
2) Space is a large fluid with weak density.
Based on these two ontological propositions, a new (+) gravity could be discovered. Accordingly, the universe was simulated with "fluid dynamics", and finally, it was confirmed that the universe can be explained by the 'space compression and energy density gravitational equation' and the 'general fluid dynamics equation'. In fluid mechanics, gravity can be interpreted as the concept of "stress and strain." In the theory of relativity, it can also be interpreted as "space compressibility." This is essentially the same as energy density.
3) Gravity is a phenomenon of interaction (space compression) between mass energy and space (or other mass energy). The condensation and cohesion of space according to the change in the density of mass energy generate potential energy (+) and gravitational energy (-). The universe is a natural dynamic system that utilizes these two energies.
4) The space potential energy (+) is the space potential energy that ordinary matter of the size of all galaxies in the universe creates and stores in space. If this is calculated using the UH equation, it is as follows.
Base data : NASA Earthdata, ESA Planck satellite




C.Comparison of the size of Space energy(+) and Gravitaty energy(-)

System, Space energy(+), Gravitaty energy (+), Ratio of the two

Earth  1.486×10^41J,  −5.299×10^33J,  2.804×10^7

Sun  4.951×10^46,  −8.095×10^41,   6.116×10^4

Galaxy   3.734×10^58,  −1.19×10^54,   3.138×10^4

Ordinary Matter  4.085×10^69,  -4.085×10^69 ,  1.0

As you can see from the table, in the dimension of ‘ordinary matter throughout the universe, the ‘cosmic potential energy(+)' is the existing gravitational energy(-) is on the same scale as gravitational energy. However, in the realm of general celestial bodies, it exists in a much larger value than gravitational energy. In the case of the Earth, it is as much as 2.804×10^7. A large portion of the space potential energy seems to be used as the operating energy of space systems, but the shining sunlight in the sky, the fresh air, the abundant water, the numerous ecological resources on the ground, and the infinite underground resources belong here. However, ‘space potential energy(+)’ is not included in the calculations, so it is not done. We call it dark matter and dark energy. This tells us that our science must overcome partialism and move toward holism.




Research Process and Results:

1) The research was planned and supervised by Jason Kuhyun Ryoo (Seoul, Korea).
2) The numerical calculations were performed by artificial intelligence ChatGPT4.0 more than three times for each major research topic, and verification was completed on 2024.08.09.
3) Researcher Jason Kuhyn Ryoo completed this as a physics theory called 'Natural Gravitation Theory and Spatial Dynamics Theory' based on modern quantum theory, and reviewed Kepler, Galileo, and Newton's classical mechanics and Einstein's theory of relativity. Accordingly, he developed his own gravitational equation, the 'UH equation', and used it directly for calculation. This is a dynamic equation and gravitational equation based on 'conservation of energy' and 'principle of least action', which are the foundations of modern and contemporary natural philosophy. This is based on the concept of quantum energy density and Hamiltonian dynamics, and is based on a three-dimensional real universe centered on space and mass energy. It minimizes the influence of time, which has no physical entity. The results of the calculations for each major topic in physics vs. the existing measured data were all very close.
4)This was summarized and published on November 5, 2024, as a collection of papers titled "A World Told by Ontology.
5) The research progress is being shared on the global shared homepage http://udynamics.net/.



Social Humanities Discovery and Interpretation




The essence of discovery:
·Time is the eternal present, the present is the true world.
·The body, which is mass energy, is the essence of existence.
·The universe grants all mass bodies the exact amount of potential energy equal to their mass.
·An individual's commitment to their own rational self-actualization forms the bedrock of the whole system.
- Heaven helps those who help themselves.

1. Since the foundation of the world is 'mass energy,' existence uses its mass energy most efficiently in the 'present.' Nature gives sufficient energy only to the present. Existence becomes solid and harmonious by being faithful to the present. Focusing on the present is the way to preserve one's mass energy and reduce 'mathematical divergence (energy waste).'
2. Like other beings, the present, which is the true world for humans, is complete 'standing alone.'
3. Humans are physically complete when they stand alone.
4. When individuals reduce external dependence and stand alone by relying on their own abilities, society becomes stable and harmonious. Self-reliance is an essential task for individuals and societies.
5. History has been a long struggle between individuals and communities to achieve balance and stability in the flow of ‘mass energy’.
6. Others: Natural principles provide essential and fundamental wisdom to humans.
Humanities need to actively interpret natural principles. Humans are essentially part of nature.
7. It can be reconfirmed that ontological inquiry through pattern analysis of natural phenomena is very useful not only for natural science but also for social humanities.

Review

“The significance of the discovery of Natursl Gravity  Theory and Space dynamics”

This paper explores the groundbreaking implications of Natural Gravity Theory and Space Dynamics, offering a novel perspective on the universe and our place within it.

I. The Ontological World
True understanding of existence comes from the inner experience of becoming it ourselves. All entities, both living and non-living, exist through self-organization governed by the principles of energy conservation and least action. This inherent drive towards efficient self-organization transcends simple matter and provides a common foundation for understanding and respecting all forms of existence. It suggests a universal language based on shared principles, fostering empathy and communication across all entities.

II. Unveiling Natural Principles: A New Theory of Gravity
This new theory of gravity addresses fundamental questions in physics, offering alternative explanations for observed phenomena:

1. Dark Matter and Dark Energy Reconsidered: The theory proposes that the phenomena attributed to dark matter and dark energy arise from the energy inherent in "Space Position" itself.
2. Beyond the Big Bang: The universe predates the Big Bang, existing in a state yet to be fully described.
3. Challenging Universal Expansion: The expansion of the universe is questioned, as it appears to contradict the principles of energy conservation and least action.
4. The Nature of Black Holes: The existence of singularities within black holes is challenged.
5. Rethinking the Age of the Universe: Recent observations from the James Webb Space Telescope suggest a universe older than the currently accepted 13.8 billion years, aligning with this theory.
6.Reconciling Relativity and Quantum Mechanics: The theory suggests that attempts to unify relativity and quantum mechanics are inherently flawed and unnecessary.
7.The Illusion of Time: The "divergence structure" of Einstein's field equations, rooted in the concept of spacetime, highlights the non-substantial nature of time. This theory further supports this notion, suggesting time is a structure of conventional ideas rather than a fundamental aspect of reality.
8. Explaining GPS Satellite Discrepancies: The varying speeds of GPS satellites are attributed to changes in space density outside the Earth's atmosphere.
9. A Unified Framework: Space Dynamics offers a unifying framework for understanding both the micro and macro worlds. Natural Gravity Theory, grounded in modern quantum theory and classical mechanics, provides a new lens through which to perceive the fundamental principles governing the universe.

"Let's See As It is."

This concluding statement encourages an open-minded exploration of these new ideas, urging us to observe the universe without preconceived notions.






P.S.

1. As below, I have posted 6 related papers of this study as 'pdf' files. Please feel free to download and share them, and I look forward to further discussion and research.
2. Along with this Natural Gravity Theory and Space Dynamics, I will also share the papers of those who study temporal theory, spatial theory,Human science, and ontological scientific methods here. I look forward to your interest and participation.
3. I will also post my major papers here as pdfs in the future. Please review and discuss with interest.
(Share and discuss research materials: visionreale@gmail.com and jasonryoo@naver.com)



Share Download Papers:




5.General theory of the micro and macro world PPT(EN)
20250508


4. A World Told by Ontology II PPT (EN)
20250102


3. Epistemology based on Quantum Theory
20250102


2. Quantum macroscopic analysis of space position energy
20250107


1. A World Told by Ontology(EN)02 : The Completion of Classical Mechanics
20241104


Homepage: http://udynamics.net/ 
facebook: https://www.facebook.com/jasonryoo/


Copyright © 2024 Jason Kuhyun Ryoo All rights reserved

The Principle of Udynamics

This can be said to be the result of an effort to find the theoretical basis of social sciences and humanities in the ‘natural scientific method’. Therefore, UDynamics can be called “Natural Principle Dynamics” that comprehensively reflects the general patterns of the living world.