Abstract Based on the photon topological origin system established in the publicly archived general outline literature (DOI: 10.5281/zenodo.20757086) and the model framework of the first special topic paper in this series, Research on Quantum Transition Mechanism Based on Photon Figure-Eight Topological Structure (DOI: 10.5281/zenodo.20769730), this paper constructs the microscopic mechanism of quantum tunneling entirely within the three-dimensional physical framework. Under the core assumption that an electron is a self-closed figure-eight topological standing wave structure formed by coiled photons, this paper defines a potential barrier as a localized region of external potential energy field that causes compression and distortion of the electron’s figure-eight standing wave. When the total electron energy is below the classical barrier height, the standing wave undergoes temporary topological distortion within the barrier region, with wavefunction edges penetrating outward and forming a weak tail on the other side. When the phase of this penetrating tail satisfies weak coupling conditions with the standing wave outside the barrier, the entire topological closed loop completes spatial displacement through waveform penetration, without needing to surmount the barrier. This paper adopts the same “base amplitude and superposed amplitude” framework as the first paper: during tunneling, the total circumference and base amplitude of the electron’s figure-eight closed loop remain unchanged, and rest mass remains constant; only the spatial distribution of the standing wave changes temporarily. This model provides a complete physical interpretation of tunneling from the perspective of internal particle topological standing wave, without introducing abstract probability interpretations or complex high-dimensional assumptions. 摘要 本文依托已公开存档的体系总纲文献(DOI:10.5281/zenodo.20757086)所建立的光子拓扑本源体系,以及系列专题首篇《基于光子八字拓扑结构的量子跃迁机制研究》(DOI:10.5281/zenodo.20769730)的模型设定,在纯三维物理框架内构建量子隧穿的微观机制。 基于 “电子为光子自缠绕形成的八字闭环驻波拓扑结构” 这一核心设定,本文将势垒定义为对电子八字驻波产生局域挤压的外部势能场区域。当电子总能量低于势垒经典高度时,电子八字驻波在势垒区发生临时拓扑畸变,波函数边缘向外渗透,在势垒另一侧形成微弱波尾;当渗透波尾与势垒外侧的驻波相位满足弱耦合条件时,整个拓扑闭环通过波形渗透完成空间平移,无需整体翻越势垒。 本文延续首篇的 “基底振幅与叠加振幅” 二分框架:隧穿过程中电子八字闭环总周长、基底振幅不变,静质量保持恒定;临时变化的仅为驻波空间分布形态。全程采用三维直观物理图像,不引入抽象概率诠释或复杂高维假设,跳出传统波函数概率化的数学描述,从电子内部拓扑驻波结构层面给出隧穿完整的物理成因。 关键词: 量子隧穿;八字拓扑;驻波;势垒畸变;波形渗透;弱耦合
Abstract Based on the photon topological origin system established in the publicly archived general outline literature (DOI: 10.5281/zenodo.20757086) and the model framework of the first special topic paper in this series, Research on Quantum Transition Mechanism Based on Photon Figure-Eight Topological Structure (DOI: 10.5281/zenodo.20769730), this paper constructs the microscopic mechanism of quantum tunneling entirely within the three-dimensional physical framework. Under the core assumption that an electron is a self-closed figure-eight topological standing wave structure formed by coiled photons, this paper defines a potential barrier as a localized region of external potential energy field that causes compression and distortion of the electron’s figure-eight standing wave. When the total electron energy is below the classical barrier height, the standing wave undergoes temporary topological distortion within the barrier region, with wavefunction edges penetrating outward and forming a weak tail on the other side. When the phase of this penetrating tail satisfies weak coupling conditions with the standing wave outside the barrier, the entire topological closed loop completes spatial displacement through waveform penetration, without needing to surmount the barrier. This paper adopts the same “base amplitude and superposed amplitude” framework as the first paper: during tunneling, the total circumference and base amplitude of the electron’s figure-eight closed loop remain unchanged, and rest mass remains constant; only the spatial distribution of the standing wave changes temporarily. This model provides a complete physical interpretation of tunneling from the perspective of internal particle topological standing wave, without introducing abstract probability interpretations or complex high-dimensional assumptions. 摘要 本文依托已公开存档的体系总纲文献(DOI:10.5281/zenodo.20757086)所建立的光子拓扑本源体系,以及系列专题首篇《基于光子八字拓扑结构的量子跃迁机制研究》(DOI:10.5281/zenodo.20769730)的模型设定,在纯三维物理框架内构建量子隧穿的微观机制。 基于 “电子为光子自缠绕形成的八字闭环驻波拓扑结构” 这一核心设定,本文将势垒定义为对电子八字驻波产生局域挤压的外部势能场区域。当电子总能量低于势垒经典高度时,电子八字驻波在势垒区发生临时拓扑畸变,波函数边缘向外渗透,在势垒另一侧形成微弱波尾;当渗透波尾与势垒外侧的驻波相位满足弱耦合条件时,整个拓扑闭环通过波形渗透完成空间平移,无需整体翻越势垒。 本文延续首篇的 “基底振幅与叠加振幅” 二分框架:隧穿过程中电子八字闭环总周长、基底振幅不变,静质量保持恒定;临时变化的仅为驻波空间分布形态。全程采用三维直观物理图像,不引入抽象概率诠释或复杂高维假设,跳出传统波函数概率化的数学描述,从电子内部拓扑驻波结构层面给出隧穿完整的物理成因。 关键词: 量子隧穿;八字拓扑;驻波;势垒畸变;波形渗透;弱耦合
Based on the photon topological origin system established in the publicly archived general outline literature (DOI: 10.5281/zenodo.20845911) and the model framework of the previous two papers in this series (Quantum Transition, Quantum Tunneling), this paper constructs the microscopic mechanism of the photoelectric effect entirely within the three-dimensional physical framework. The photoelectric effect is not a particle process of photons "hitting" electrons, but a process of energy coupling and topological dissociation between continuous light waves and the figure-eight topological closed-loop structures of electrons at metal surfaces. Light waves arrive at the metal surface as continuous wave fields and resonantly couple with the electron's figure-eight closed-loop standing waves. Only when the light wave frequency satisfies the resonance condition of the closed-loop standing wave can the integral unit of energy be absorbed, increasing the electron's superposed amplitude to the emission threshold. When the superposed amplitude reaches the energy threshold corresponding to the work function, the topological closed loop partially dissociates, and the electron escapes the metal surface binding. This paper continues the "base amplitude and superposed amplitude" framework from the previous papers: electrons change only their superposed amplitude and equivalent energy upon absorbing light wave energy; the closed-loop ontology remains intact before emission. After emission, electrons continue to move as free particles. This model provides a complete physical interpretation of the photoelectric effect from the perspective of internal topological structure, without introducing particle models of "photon-electron collisions" or abstract probability interpretations. 中文摘要 本文依托已公开存档的体系总纲文献(DOI:10.5281/zenodo.20845911)所建立的光子拓扑本源体系,以及系列专题前两篇(量子跃迁、量子隧穿)的模型设定,在纯三维物理框架内构建光电效应的微观机制。 光电效应不是光波"撞击"电子的粒子过程,而是连续光波与金属表面电子八字扭结闭环之间的能量耦合与拓扑解离过程。光波以连续波动场的形式抵达金属表面,与电子八字扭结闭环驻波发生共振耦合;只有当光波频率满足闭环驻波的共振条件时,整份能量才能被吸收,使电子叠加振幅增大至逸出阈值;当叠加振幅达到逸出功对应的能量阈值后,电子拓扑闭环发生部分解离,脱离金属表面束缚。 本文延续前两篇的"基底振幅与叠加振幅"二分框架:电子吸收光波能量后仅改变叠加振幅与等效能量,闭环本体结构在逸出前保持完整;逸出后电子以自由行波形态继续运动。全程采用三维直观物理图像,不引入"光波-电子碰撞"的粒子模型或抽象概率诠释,从电子内部拓扑结构层面给出光电效应的完整物理解释。 关键词: 光电效应;八字扭结;驻波;共振吸收;逸出功;拓扑解离;连续光波
Note: This paper is the technical companion to the interpretive study “Beyond Exponential Decay: Interpreting Quantum Tunneling as Wave Stress Accumulation” (Zenodo DOI: 10.5281/zenodo.18001177). Standard quantum tunneling is commonly described using stationary solutions of the Schrödinger equation, in which wavefunctions decay exponentially inside classically forbidden regions. In a recent interpretive work, tunneling was reexamined within the Total Wave Modified Schrödinger Equation (TWMSE) as a process of wave stress accumulation, in which exponential spatial decay coexists with slow, logarithmic-like temporal buildup under continuous incidence (Larry Lim Kheng Cheong, 2025, Zenodo, https://doi.org/10.5281/zenodo.18001177). That study was intentionally presented in a conceptual and pedagogical manner to make the physical interpretation accessible to a broad audience. The present paper serves as a direct technical continuation of that interpretive study. Its purpose is to provide an explicit time-dependent formulation, numerical setup, and illustrative simulation of tunneling within the TWMSE framework, without diluting the interpretive clarity of the earlier work. By separating interpretation from formal development, the two papers together address distinct audiences: the first emphasizing physical intuition, and the present work focusing on mathematical structure and dynamical behavior. A minimal collapse–interference functional is introduced for a one-dimensional finite potential barrier, and its effect under continuous wave incidence is examined. Numerical simulations demonstrate that while the spatial wave profile inside the barrier retains its standard exponential decay, the accumulated interference exhibits sublinear, logarithmic-like temporal saturation over time due to feedback in the modified dynamics. Standard quantum mechanics is recovered as a limiting case. These results provide a concrete, testable illustration of how time-dependent accumulation and threshold-like behavior can emerge in tunneling systems while preserving full compatibility with established quantum mechanics.
The nonlocal correlation mechanism of quantum entanglement and the underlying dynamics of barrier penetration in quantum tunneling constitute long-standing foundational explanatory gaps in standard quantum mechanics. While the standard theory can accurately describe the phenomena and provide probabilistic outcomes, it cannot offer a geometric-topological origin at the spacetime level. Based on the foundational axioms of three-dimensional vector light-speed helical spacetime, this paper establishes a self-consistent geometric explanatory framework: microscopic quantum effects are attributed to emergent behaviors arising from the helical structure of spacetime, topological bonding, and spacetime curvature resonance. The contributions of this paper include: 1. Establishing the core axioms of three-dimensional helical spacetime and a three-level spacetime normalization equation, constructing a low-energy emergence mechanism for four-dimensional Minkowski spacetime, and resolving the self-consistency conflict between the old and new definitions of spacetime; 2. Deriving the topological throat structure for two-particle entanglement based on the principle of topological bonding stability, providing the spacetime geometric origin of nonlocal correlations in entanglement and a finite propagation time delay; 3. Building an eigenfrequency model of spacetime distortion in the potential barrier, formulating the geometric resonance condition for quantum tunneling, and deriving a discrete resonance tunneling prediction distinct from the WKB approximation; 14. Independently deriving the mass-energy equivalence relation, the Lorentz transformation, and the Bohr radius from the model’s axioms, thereby verifying the low-energy self-consistency of the frame work; 5. Presenting a complete first-order perturbation integral derivation for the hydrogen 1S-2S transition, yielding a quantifiable and verifiable prediction for a spectral shift; 6. Explicitly listing the mathematical limitations of the model, its boundary of applicability, and falsifiable experimental protocols. This framework offers a geometric alternative explanatory system distinct from standard quan tum mechanics and quantum field theory. All quantitative results and predictions are preserved for long-term academic scrutiny. Keywords: vector light speed; helical spacetime; topological throat; spacetime topological bonding; geometric resonant tunneling; quantum entanglement; hydrogen atomic spectral shift
The quantum tunneling phenomenon has long been explained by quantum mechanics using abstract concepts such as probability waves and wave function collapse. However, the essence of its microscopic physical mechanism—how and why a particle can traverse a classically forbidden region—has never been clearly elucidated, leading to a schism between the physical laws governing the micro- and macro-worlds. Based on the Great Tao Model and the Unified Theory of Atomic and Molecular Structure, this paper, for the first time, constructs a complete, self-consistent, and quantifiable framework for a classical physical explanation. The core of this framework clarifies the microscopic physical mechanisms of "local weakening of the Existence Field" and "formation of a directional field channel", reducing the tunneling process to a deterministic sequence of events: "information coupling → field weakening → channel formation → classical penetration". The study rigorously derives the quantitative relationships between the field strength weakening coefficient, the field channel width, and the penetration probability. Its mathematical form is compatible with the empirical formula of quantum mechanics, but its physical connotation is fundamentally different. Case studies demonstrate that this theory can uniformly explain the atomic-scale resolution of scanning tunneling microscopy (STM), the deterministic energy release in α-decay, and the physical necessity for the impossibility of macroscopic object tunneling. Starting from the first principles of classical physics, this paper provides a new paradigm for understanding tunneling that aligns with physical intuition, has a clear mechanism, and is subject to experimental verification, achieving a logical unification of micro- and macro-physical laws.
This work presents a systematic study on the dual nature of quantum tunneling within the self-consistent axiomatic framework of Boundary Interface Theory (BIT). It strictly distinguishes two fundamentally distinct quantum tunneling mechanisms: nuclear fusion tunneling, which arises from 4D normal‑direction yielding of the boundary membrane and the unraveling of rigid topological knots; and electron tunneling, which corresponds to direct 4D normal‑direction penetration of membrane standing waves. The theory provides a unified microscopic geometric and mechanical origin for quantum tunneling and the strong interaction without introducing new particles, free parameters, or extra dimensions. Both Chinese and English full texts are included for open access and cross‑lingual academic reference.
At the turn of the twentieth century, the establishment of quantum theory propelled rapid advancements, particularly in the understanding of quantum tunnelling—a fundamental phenomenon in quantum mechanics crucial for various physical processes. The quantum phenomenon of particle passes through potential barriers is of great importance. In classical physics, when the energy of a particle is less than the height of a double barrier structure, it is impossible for it to pass through. However, quantum mechanics allows a particle to penetrate the barrier and emerge on the other side. This paper explores the quantum tunnelling effect, focusing on the single potential barrier model in one dimension and subsequently extending to the double potential barrier model. The Schrödinger equation provides the foundational framework for elucidating the motion of microscopic particles, emphasizing wave-particle duality inherent in quantum mechanics. The analysis of the single potential barrier model involves solving the Schrödinger equation in different regions, determining wave functions and coefficients through boundary conditions. The transmission coefficient is derived, representing the probability of a particle passing through a barrier. In the case of a “thick” barrier, an approximate form for transmission coefficient is provided, demonstrating the exponential decrease in transmission probability with increasing barrier thickness.