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Dual-Layer Light Invariance: The Open-Close Structure of Ma as a Complete Theory of Phi2 Perturbation — Paper 1 of 3D Theory Series

Yoshimitsu Katayama

Published Jun 27, 2026• 0 citations
Publisher

Abstract

This paper is part of the TheYKHC Theoretical Series: 'From Duality to Field: A Three-Dimensional Evolution of Universal Theory' Paper 1: Dual-Layer Light Invariance (2D — The Discovery of Duality) Paper 2: Why Spacetime is (3+1)-Dimensional (2.5D — Polygon Transcendence) Paper 3: Ki-Net Field Evidence (3D — Universal Field Completion) Related: Genki Particle Dance (DOI: 10.5281/zenodo.20955834) The series demonstrates that V = N / D governs reality from the quantum vacuum to the cosmic scale. [Paper 1 of 3 — 2D: The Discovery of Duality] Light is simultaneously wave and particle. This is not a paradox — it is the signature of a dual-layer universe governed by V = N / D. This paper presents the Open-Close Structure of Ma (間) as the fundamental mechanism behind wave-particle duality, demonstrating that phi2 perturbation is the mathematical expression of a universe that oscillates between coherence (N) and dispersion (D). The dual nature of light is the first empirical proof that V = N / D operates at the quantum scale.

DOI
10.5281/zenodo.20956490

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Dual-Layer Light Invariance: The Open-Close Structure of Ma — Paper 1 of 3D Theory Series

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This paper is part of the TheYKHC Theoretical Series: 'From Duality to Field: A Three-Dimensional Evolution of Universal Theory' Paper 1: Dual-Layer Light Invariance (2D — The Discovery of Duality) Paper 2: Why Spacetime is (3+1)-Dimensional (2.5D — Polygon Transcendence) Paper 3: Ki-Net Field Evidence (3D — Universal Field Completion) Related: Genki Particle Dance (DOI: 10.5281/zenodo.20955834) The series demonstrates that V = N / D governs reality from the quantum vacuum to the cosmic scale. [Paper 1 of 3 — 2D: The Discovery of Duality] Light is simultaneously wave and particle. This is not a paradox — it is the signature of a dual-layer universe governed by V = N / D. This paper presents the Open-Close Structure of Ma (間) as the fundamental mechanism behind wave-particle duality, demonstrating that phi2 perturbation is the mathematical expression of a universe that oscillates between coherence (N) and dispersion (D). The dual nature of light is the first empirical proof that V = N / D operates at the quantum scale.
This paper is part of the TheYKHC Theoretical Series: 'From Duality to Field: A Three-Dimensional Evolution of Universal Theory' Paper 1 (DOI: 10.5281/zenodo.20956491): Dual-Layer Light Invariance (2D — The Discovery of Duality) Paper 2 (DOI: 10.5281/zenodo.20956493): Why Spacetime is (3+1)-Dimensional (2.5D — Polygon Transcendence) Paper 3 (DOI: 10.5281/zenodo.20956499): Ki-Net Field Evidence (3D — Universal Field Completion) Foundation (DOI: 10.5281/zenodo.20955834): Genki Particle Dance — Why the Quantum Foam Dances V = N / D governs reality from the quantum vacuum to the cosmic scale. [Paper 1 — 2D: Discovery of Duality] Light is simultaneously wave and particle. This is not a paradox — it is the signature of a dual-layer universe governed by V = N / D. The Open-Close Structure of Ma (間) is the fundamental mechanism behind wave-particle duality. Phi2 perturbation is its mathematical expression.
Based on the quantum field theory and classical electromagnetic field theory, the behaviors of the electromagnetic field in the boundary of the classical environment and the quantum environment were studied, and three dead-points and five paradoxes, like Lorentz-Compton paradox, non-conservation of the energy of the electromagnetic field before and after quantization due to a number of zero-point energy, the non-self-consistence of the wave-particle duality, etc, were discovered. Through analyzing these dead-points and paradoxes, we found that these paradoxes are related to each other, and all wrapped together. The core problem is the non-self-consistence in the theoretical system and the ambiguity in the mechanism of the wave-particle duality. Based on resolving the classical electromagnetic field into the electromagnetic element-waves according to the photons, a third kind of wave-particle duality, the particle-like characteristics of the classical electromagnetic field in structure, was put forward, and the structure of n-shape of three kinds of wave-particle duality was revealed. So, in wave-particle duality, the wave and the particle are staggered in existing time, or in existing form, either in imagination or in reality, and the third kind of wave-particle duality will be combined into a unit with the first kind of wave-particle duality, Einstein's wave-particle duality of light, and the second kind of wave-particle duality, de Broglie's wave-particle duality of matter particle. Hence, a self-consistent picture of wave-particle duality of light was set up, and three dead-points and five paradoxes of the electromagnetic field in the boundary of the classical environment and the quantum environment were dispelled. In the last, a crucial experiment was designed for testing this picture.
Standard physics is built upon a foundational duality: the macroscopic world governed by deterministic classical mechanics and general relativity, and the microscopic world governed by probabilistic quantum mechanics, whose foundational expression is the Heisenberg uncertainty principle . This paper demonstrates, within the Conjugate Photonic Model (CPM), that this duality is an artefact of incomplete knowledge rather than a property of nature. Three universal constants — the speed of light , the vacuum impedance , and Planck's constant — operate identically at both the microscopic (electron hopfion, photonic disc) and macroscopic (FEL, optics, electromagnetism) scales, eliminating the conceptual basis for dual physics. The Heisenberg principle is reinterpreted as a statistical consequence of measuring the time-average of the deterministic trajectory of the electron hopfion at traversal frequency , inaccessible to current temporal resolution but not inaccessible in principle. The Schrödinger cat paradox is resolved: the cat has a definite state at all times, determined by the internal phase of the electron hopfion. A structural equation for photon emission as a function of is derived: . The Free-Electron Laser provides the experimental isolation mechanism that forces the deterministic machinery into full visibility. The universe is a single, causal, deterministic system of organised EM field — the apparent duality dissolves when the internal phase variable is recognised as the missing element of the description.
Based on the quantum field theory and classical electromagnetic field theory, the behaviors of the electromagnetic field in the boundary of the classical environment and the quantum environment were studied, and three dead-points and five paradoxes, like Lorentz-Compton paradox, non-conservation of the energy of the electromagnetic field before and after quantization due to a number of zero-point energy, the non-self-consistence of the wave-particle duality, etc, were discovered. Through analyzing these dead-points and paradoxes, we found that these paradoxes are related to each other, and all wrapped together. The core problem is the non-self-consistence in the theoretical system and the ambiguity in the mechanism of the wave-particle duality. Based on resolving the classical electromagnetic field into the electromagnetic element-waves according to the photons, a third kind of wave-particle duality, the particle-like characteristics of the classical electromagnetic field in structure, was put forward, and the structure of &pgr;-shape of three kinds of wave-particle duality was revealed. So, in wave-particle duality, the wave and the particle are staggered in existing time, or in existing form, either in imagination or in reality, and the third kind of wave-particle duality will be combined into a unit with the first kind of wave-particle duality, Einstein's wave-particle duality of light, and the second kind of wave-particle duality, de Broglie's wave-particle duality of matter particle. Hence, a self-consistent picture of wave-particle duality of light was set up, and three dead-points and five paradoxes of the electromagnetic field in the boundary of the classical environment and the quantum environment were dispelled. In the last, a crucial experiment was designed for testing this picture.
Contemporary physics and Quantum Field Theory (QFT) have long regarded "Wave-Particle Duality" as a mysterious attribute built into microscopic entities, and have dimensionally reduced "Virtual Particles" in the quantum vacuum to transient, random ghosts limited only by Heisenberg's uncertainty principle. This phenomenological mathematical treatment has thoroughly stripped wave phenomena and vacuum fluctuations of their substantive geometric significance. Grounded in the extreme topological framework of the 0/∞\infty∞ Null Model, this research proposes a pure mechanical re-interpretation model that completely discards statistical probability theory. This paper rigorously demonstrates at the level of geometric ontology: the physical three-dimensional cosmic manifold we inhabit is, in fact, encapsulated within a "4D Riemann Spherical Membrane" forged by the extreme crushing of countless deadlocked particles and possessing a global, infinite gravitational potential. For topological boundaries such as photons, which encapsulate an absolute vacuum internally and have a rest mass of m=0, they are not subject to inertial drag in three-dimensional space, yet simultaneously endure an "infinite topological gravity from all directions" originating from the 4D shell. This global infinite pull endows the photon with its true kinematic limit—namely, "Infinite Speed." Driven by a propagation rate approaching infinity, the photon, within a macroscopic finite time resolution, instantaneously traverses all spatial coordinates within the three-dimensional geometric interstices, thereby exhibiting a pervasive, continuous "Wave State" characterized by interference. The so-called "Observer Collapse" is by no means an idealistic magic involving the intervention of subjective consciousness, but rather an unavoidable substantive physical collision exerted upon this infinite-speed topological boundary by a macroscopic multi-field coupled system possessing massive mass (such as a measuring instrument). This cosmic-scale "Braking Effect" forces the photon to be forcibly dragged down and dimensionally reduced to the maximum geometric tangent limit tolerable by the macroscopic 3D universe (the speed of light c), thereby converging and anchoring into a "Particle State" possessing definite coordinates. Simultaneously, this research redefines the ontology of wave functions and virtual particles. The wave function is not an abstract probability, but an "acting force information structure" excited by the infinite phase transition energy of the "Singularity Big Bang" and "Singularity Big Crunch." These acting forces act like absolutely rigid straight lines in mathematics, penetrating the entire 3D spacetime. When this 1D straight line encounters the infinite gravitational traction of the 4D spatial membrane, it inevitably generates extreme high-frequency geometric oscillations. The "infinite points" presented by the shattering of the straight line under infinite-speed oscillation are precisely the virtual particles observed by quantum mechanics. Virtual particles have never randomly "generated and annihilated" out of thin air in the vacuum; rather, they are the substantive topological fluctuations of the underlying 1D geometric straight line alternating between a continuous wave state (line) and a discrete particle state (point) at infinite speed.
[Amrita Field Theory — Domain Classification] This paper belongs to the Amrita Field Theory (AFT) research program,a unified information-field framework integrating consciousness,causality, physical law, and statistical structure. Core domains addressed in this paper: • Physical interface of AFT• Cosmology and field-level interpretation of physical phenomena This work places the nature of light inside the three-layer ontology of Amrita Field Theory (AFT). In AFT, a maximally coherent L0 “light domain” underlies an L1 information/Amrita field and the ordinary L2 domain of spacetime, matter, and life. Within this framework, photons are interpreted as directed interference packets in L1, and the familiar properties of light in physics—finite and universal speed c, null proper time, wave–particle duality, and its central role in causality and nonlocal correlations—are reinterpreted as emergent features of an information-theoretic compression from L1 to L2. Light speed appears as the maximal rate at which locally decodable information can be updated in the emergent spacetime representation; photons “do not age” because they are relational patterns rather than time-evolving objects at the deeper field level. The paper also sketches how early-universe global coherence, quantum entanglement, and visual perception fit naturally into this picture, positioning light as the primary interface between a timeless coherent domain and the lived world of space, time, and conscious observers.