This article proposes a unified theory framework encompassing a discrete topological interpretation of physical forces, wave functions, and the nature of space and time. It provides novel explanations for the collapse of wave functions, quantum entanglement, and offers insights into the origins of quantum probabilities. This article also explains the nature of mass, Higgs field, and suggests a path for unifying quantum mechanics and gravity. Elementary particles are represented as defects in discrete topological spaces. Entangled particles are directly connected to each other through a puncture in discrete space, separated by a distance of one Planck length. Wave functions are explained as mechanical stress waves within elastic discrete space. The results of the double-slit experiment are interpreted as wave functions maximizing the probability of rupture in high-stress areas of discrete space with obvious analogies to solid state mechanics. Wave-particle duality is explained as discrete topological defects causing extended distributed stress within space lattice.
This article proposes a unified theory framework encompassing a discrete topological interpretation of physical forces, wave functions, and the nature of space and time. It provides novel explanations for the collapse of wave functions, quantum entanglement, and offers insights into the origins of quantum probabilities. This article also explains the nature of mass, Higgs field, and suggests a path for unifying quantum mechanics and gravity. Elementary particles are represented as defects in discrete topological spaces. Entangled particles are directly connected to each other through a puncture in discrete space, separated by a distance of one Planck length. Wave functions are explained as mechanical stress waves within elastic discrete space. The results of the double-slit experiment are interpreted as wave functions maximizing the probability of rupture in high-stress areas of discrete space with obvious analogies to solid state mechanics. Wave-particle duality is explained as discrete topological defects causing extended distributed stress within space lattice.
This paper proposes the Excitation Field Unification (EMU), a theoretical framework that unifies quantum mechanics and general relativity by redefining the fundamental structure of spacetime. We posit that the universe is not a continuous manifold but a discrete lattice of physical scalar oscillators (Quantum Circulation Loops). By rejecting the probabilis- tic interpretation of the wave function in favor of a realistic "physical rotation" model, we demonstrate that matter and mass emerge inevitably as topological defects (winding num- bers) within this lattice. Furthermore, we derive the wave-particle duality and the de Broglie relations as geometric consequences of pattern propagation on the lattice, without invoking the collapse of a wavefunction. This work constitutes Part I of a trilogy, focusing on the ontology of the quantum state and the origin of mass, setting the stage for the emergence of gravity (Part II) and fundamental constants (Part III).
Description: This study provides a testable geometric origin explanation for wave-particle duality in quantum mechanics, starting from first principles of discrete geometry. Core Scientific Question While the mathematical formalism of quantum mechanics can precisely predict experimental phenomena such as double-slit interference, the physical origin of wave-particle duality itself has long been treated as a fundamental axiom, lacking deeper explanation. This work attempts to answer: Could quantum phenomena arise from the collective statistical behavior of more fundamental discrete geometric structures? Theoretical Framework Based on a recently developed discrete geometry framework, we regard continuous spacetime as emerging from the topological gluing and recursive folding of Cantor sets. This geometric construction naturally leads to defect structures carrying intrinsic degrees of freedom, whose statistical fluctuations manifest as random noise accompanying the geometric phase field. The two-point correlation of the noise characterizes thermalization information, while higher-order correlations carry non-Gaussian information and long-term memory. Core Predictions For the double-slit interference experiment, we derive a coherence evolution formula and make three directly testable predictions: First, even under strong which-path measurement, interference fringes will exhibit residual visibility due to contributions from higher-order noise correlations, with magnitude between one-thousandth and one-hundredth. This stands in sharp contrast to the complete disappearance predicted by standard decoherence theory. Second, the decoherence process exhibits biexponential behavior, with fast and slow time scales whose ratio ranges from one hundred to one thousand. Third, path information and interference visibility satisfy a specific conservation relation, reflecting the intrinsic constraints on information transformation in discrete geometry. Experimental Proposal We propose a quantum optics experiment using squeezed light to test these predictions. The scheme employs nano-fabricated double slits and single-photon sources with tunable statistical properties, directly verifying the physical effects of higher-order correlations by comparing interference visibility differences between squeezed and coherent light sources. Current single-photon source technology already possesses the capability to resolve the required precision. Scientific Significance If the predictions are confirmed, this would for the first time experimentally establish quantum phenomena as collective statistical manifestations of discrete geometric structures, providing a geometric origin explanation for the Heisenberg uncertainty principle and an objective, consciousness-free mechanism for wavefunction collapse. Furthermore, this would provide tabletop experimental evidence for Planck-scale spacetime discreteness, building a bridge between quantum foundations and cosmological information research. If falsified, this would constrain microscopic parameters in the theory, pushing the model toward more complex colored noise generalizations. 描述: 本研究从离散几何的第一原理出发,为量子力学中的波粒二象性提供了一个可检验的几何起源解释。 核心科学问题 量子力学的数学形式主义能够精确预测双缝干涉等实验现象,但波粒二象性本身的物理起源长期被视为基本公理,缺乏更深层次的解释。本工作试图回答:量子现象是否可能源于更基本的离散几何结构的集体统计行为? 理论框架 基于近期发展的离散几何框架,我们将连续时空视为从康托尔集的拓扑粘合与递归折叠中涌现的结果。这一几何构建自然导出了带有内禀自由度的缺陷结构,其统计涨落表现为伴随几何相场的随机噪声。噪声的两点关联刻画热化信息,而高阶关联则携带非高斯信息和长期记忆。 核心预言 针对双缝干涉实验,我们推导了相干度演化公式,并作出三个可直接检验的预言: 第一,即使在强路径测量下,由于噪声高阶关联的贡献,干涉条纹仍将存在残余可见度,其量级在千分之一到百分之一之间。这与标准退相干理论预言的完全消失形成鲜明对比。 第二,退相干过程呈现双指数行为,存在快慢两个时间尺度,其比值在百倍到千倍之间。 第三,路径信息与干涉可见度满足特定的守恒关系,反映了离散几何中信息转化的内在约束。 实验方案 我们提出了一个基于压缩态光的量子光学实验方案来检验上述预言。该方案利用纳米加工双缝和可调统计性质的单光子源,通过比较压缩态与相干态光源的干涉可见度差异,直接验证高阶关联的物理效应。当前单光子源技术已具备分辨所需精度的能力。 科学意义 若预言被证实,将首次从实验上确立量子现象是离散几何结构的集体统计表现,为海森堡不确定性原理提供几何起源解释,并为波函数坍缩提供无需意识的客观机制。同时,这将为普朗克尺度的时空离散性提供桌面实验证据,架起量子基础与宇宙学信息研究的桥梁。若被证伪,则将约束理论中的微观参数,推动模型向更复杂的有色噪声方向拓展。
We propose a unified physical framework in which four-dimensional spacetime vacuum is the unique physical reality, and all quanta are its localized topological excitations. Matter particles correspond to stable knot-like configurations, while radiation quanta correspond to weak propagating ripples of the same substrate. From this single ontological commitment, we derive: (1) wave–particle duality is resolved—particle behavior belongs to the localized excitation, wave behavior to the disturbance field it generates in spacetime; (2) double-slit interference arises from coherent superposition between a quantum's newly sourced disturbance and its own historical disturbance field, not from ontological self-superposition; (3) the wave function is a statistical tool encoding ensemble distributions of trajectories modulated by disturbance feedback, and collapse is epistemic convergence rather than a physical process; (4) quantum entanglement corresponds to Planck-scale topological connectivity (microscopic Einstein–Rosen bridges), preserving relativistic causality; (5) gravity is the macroscopic accumulation of universal but individually weak quantum–vacuum couplings, explaining both its microscopic weakness and macroscopic dominance without requiring a graviton; (6) the four fundamental interactions are differentiated coupling modes of quanta to one spacetime vacuum field; and (7) apparent dark matter and dark energy are reinterpreted as collective topological curvature and large-scale vacuum self-relaxation, respectively. We formulate falsifiable predictions at both laboratory and cosmological scales, including disturbance–corpuscle separation interferometry, tunable decoherence threshold measurements, and galaxy rotation–topology correlations. The framework compresses the conventional axiomatic structure of quantum mechanics and cosmology into one master axiom and eliminates at least twenty-eight independent interpretive assumptions.
The Copenhagen interpretation of contemporary quantum mechanics has long reduced the behavior of microscopic particles to the abstract probability amplitude superposition of the wave function Ψ(x,t). This mathematical-statistical treatment fails to encompass the ontological substantiality of wave phenomena at the mechanical level and within the geometry of general relativity. Rejecting the assumptions of continuous media and probability clouds, this study proposes a geometrodynamical reconstruction of the wave function, predicated upon the dynamic Riemann sphere topological framework of the Grand Unified Theory of Cosmic Mind (GUTCM). The research posits that the physical essence of the wave function is not a diffuse probability cloud, but rather a matrix of "Discrete Repulsive Forces" generated by underlying topological boundaries to resist spatial fusion. Based on the boundary conditions of absolute vacuum—possessing no temporality, no spatial extension, and no energy—the wave functions excited by singularity phase transitions (the Big Bang and the Big Crunch) manifest as one-dimensional rigid lines of acting force with pan-temporality and pan-spatial extension, permeating the physical universe. The intertwining of this infinite number of one-dimensional wave functions constitutes the observationally perceived "quantum vacuum" and physical "space." The displacement of physical particles within this grid is strictly equivalent to inducing "Topological Ripples" that alter the grid's tension. The arrow of time is thus defined as the macroscopic transmission vector of this global acting force; moreover, all physical interactions rely on this wave function grid for transmission, thereby establishing the mechanical foundation for the conservation of cosmic information. This paper further establishes the "Topology of Resonance Counting." When a wave function curls inward within a manifold to form a particle boundary, if an information deadlock of A≡¬A forms internally, it will superimpose codirectionally in phase space and generate the topological rigidity of Intrinsic Spin. If it merely forms a decoherent livelock, due to the lack of a spin mechanism, its trajectory is instead passively towed by spatial topological ripples. The rest mass and energy levels of a physical entity are strictly quantified herein as macroscopic dynamical readings of the high-frequency mutually repulsive resonance conducted by particles within a closed manifold. Ultimately, this study integrates this resonance mechanism with Riemann sphere gravitational dynamics. "Virtual Particles" in quantum field theory are, in fact, wave-state entities with a rest mass of m₀ =0. Subject to the infinite-velocity inside-out folding and gravitational interaction of the Riemann sphere, this wave state executes high-frequency cycles without time delay on a null geodesic where the subjective proper time is dτ≡0. Quantum superpositions and continuous wave phenomena in macroscopic observations are, in reality, "Spacetime Aliasing" effects generated by the sampling rate limits of measuring instruments when microscopic entities undergo extreme high-frequency mechanical oscillations. This theory eliminates indeterministic assumptions, converging microscopic quantum phenomena into an objective mechanical system governed by a generalized Pauli exclusion principle as its geometric code and constrained by Riemann sphere gravity.
We present the An Theory, a unified physical framework derived from one assumption (space consists of discrete, indivisible field quanta) and one rule (adjacent field quanta attract each other, with strength proportional to the product of their excitation levels, and strictly conserved total excitation). This rule is not ad hoc: it is structurally isomorphic to van der Waals forces, nuclear binding, the Casimir effect, and Bose–Einstein condensation. From this single rule, we derive the following key results: (1) stable self-bound topological structures with a “hard core + extended ripple” profile, which accounts for wave-particle duality and yields the Born rule in the weak-excitation limit; (2) Newtonian gravity (F ∝ M1M2/r²) as the macroscopic sum of all nearest-neighbor attractions, where the inverse-square law arises solely from 3D geometry and flux conservation; (3) gravitational and motion time dilation, the equivalence principle, the constancy of c, and Lorentz invariance as emergent phenomena; (4) an all-or-nothing threshold mechanism for quantum measurement, providing complete local realist accounts of double-slit interference, quantum erasure, delayed choice, and entanglement; (5) three independent fundamental forces—gravity (baseline attraction), the strong force (high-excitation contact binding, verified across 225 parameter combinations), and the electric force (permanent stress from topological orientation knots, verified in 2D and 3D)—with the magnetic force as the dynamic effect of moving electric charges; (6) the 3D Topological Slot Model, where fractional quark charges arise from the three orthogonal dimensions of space, and all 12 Standard Model fundamental fermions are classified by “geometric complexity × excitation level”; (7) quark confinement, verified using a three-component coupled GL equation with Josephson phase-locking; (8) the mass hierarchy resulting from coherence-length relaxation versus strong-force compression; (9) the topological origin of spin-1/2 from the double-connectedness of SO(3); (10) E = mc² derived from wave mechanics. The framework yields three falsifiable predictions: no fourth-generation fermions, no magnetic monopoles, and no fractional charges other than multiples of 1/3. Its central decisive prediction—a sharp threshold step in interference visibility versus path-marker coupling strength—is qualitatively incompatible with standard quantum mechanics and testable with existing equipment. All results follow from the single assumption + single rule, with no free parameters introduced beyond the foundational rule.
This paper introduces a novel theoretical framework that bridges discrete and continuous descriptions in physics through a unified probabilistic approach. At its core, the framework demonstrates how continuous forms naturally emerge from discrete entities via probability distributions, providing fresh insights into phenomena ranging from classical mechanical systems to quantum mechanics. The work develops a rigorous mathematical formalism that includes a geometric interpretation through Riemannian metrics and extends naturally to relativistic systems.What sets this approach apart is its ability to describe transitions between discrete and continuous regimes using a single mathematical structure, while maintaining compatibility with both classical and quantum mechanical descriptions. The framework introduces a continuity probability function that characterizes systems across all scales, offering new perspectives on wave-particle duality and the emergence of continuous forms in nature. By providing a unified mathematical language for describing such phenomena, this work opens up new possibilities for understanding the relationship between discrete and continuous aspects of physical reality.