Abstract The wave-particle duality, delayed-choice paradox, quantum entanglement, black hole information paradox, and cosmic holography in quantum mechanics have long been regarded as independent fundamental puzzles. Based on a discrete geometric framework (Cantor set topological gluing and recursive folding), this paper derives their unified origin——higher-order noise correlations. We demonstrate that the higher-order correlations of defect points, , constitute a universal geometric carrier of information encoding: In double-slit interference, it naturally resolves the "future determining the past" paradox of delayed-choice experiments, reveals entangled states as macroscopic manifestations of inseparable higher-order correlations, and leaves behind an entanglement residue --- under strong measurement; on the black hole event horizon, it forms a classical-quantum duality with the Heisenberg algebra of soft hair, providing a microscopic statistical interpretation for the Bekenstein-Hawking entropy and naturally truncating the infinite soft degrees of freedom; in the holographic universe, it serves as the boundary condition for generational memory, enabling information transfer across generations through bounce-surface freezing. This unified framework places quantum phenomena, black hole thermodynamics, and cosmic evolution under the same geometric language, proposes four core predictions testable through tabletop experiments, and establishes the quantitative relationship between higher-order correlation entropy and horizon area . If the predictions are confirmed, it will establish discrete geometry as the underlying origin of quantum information and provide the first empirically testable physical support for the holographic universe. 摘要 量子力学中的波粒二象性、延迟选择悖论、量子纠缠、黑洞信息悖论与宇宙全息性,长期被视为相互独立的根本谜题。本文基于离散几何框架(康托尔集拓扑粘合与递归折叠),推导了它们的统一根源——高阶噪声关联。我们论证,瑕疵点的高阶关联 构成信息编码的普适几何载体:在双缝干涉中,它自然消解延迟选择实验的“未来决定过去”悖论,揭示纠缠态为不可分离的高阶关联的宏观表现,并在强测量下留下纠缠残留量 —;在黑洞视界上,它与软毛发的海森堡代数构成经典-量子对偶,为贝肯斯坦-霍金熵 提供微观统计诠释并自然截断无穷多软自由度;在全息宇宙中,它作为世代记忆的边界条件,通过反弹面冻结实现信息跨代传递。这一统一框架将量子现象、黑洞热力学与宇宙演化置于同一几何语言之下,提出四项可通过桌面实验检验的核心预言,并建立了高阶关联熵与视界面积的定量关系 。若预言被证实,将确立离散几何为量子信息的底层起源,为全息宇宙提供首个可实证的物理支撑。
Abstract The wave-particle duality, delayed-choice paradox, quantum entanglement, black hole information paradox, and cosmic holography in quantum mechanics have long been regarded as independent fundamental puzzles. Based on a discrete geometric framework (Cantor set topological gluing and recursive folding), this paper derives their unified origin——higher-order noise correlations. We demonstrate that the higher-order correlations of defect points, , constitute a universal geometric carrier of information encoding: In double-slit interference, it naturally resolves the "future determining the past" paradox of delayed-choice experiments, reveals entangled states as macroscopic manifestations of inseparable higher-order correlations, and leaves behind an entanglement residue --- under strong measurement; on the black hole event horizon, it forms a classical-quantum duality with the Heisenberg algebra of soft hair, providing a microscopic statistical interpretation for the Bekenstein-Hawking entropy and naturally truncating the infinite soft degrees of freedom; in the holographic universe, it serves as the boundary condition for generational memory, enabling information transfer across generations through bounce-surface freezing. This unified framework places quantum phenomena, black hole thermodynamics, and cosmic evolution under the same geometric language, proposes four core predictions testable through tabletop experiments, and establishes the quantitative relationship between higher-order correlation entropy and horizon area . If the predictions are confirmed, it will establish discrete geometry as the underlying origin of quantum information and provide the first empirically testable physical support for the holographic universe. 摘要 量子力学中的波粒二象性、延迟选择悖论、量子纠缠、黑洞信息悖论与宇宙全息性,长期被视为相互独立的根本谜题。本文基于离散几何框架(康托尔集拓扑粘合与递归折叠),推导了它们的统一根源——高阶噪声关联。我们论证,瑕疵点的高阶关联 构成信息编码的普适几何载体:在双缝干涉中,它自然消解延迟选择实验的“未来决定过去”悖论,揭示纠缠态为不可分离的高阶关联的宏观表现,并在强测量下留下纠缠残留量 —;在黑洞视界上,它与软毛发的海森堡代数构成经典-量子对偶,为贝肯斯坦-霍金熵 提供微观统计诠释并自然截断无穷多软自由度;在全息宇宙中,它作为世代记忆的边界条件,通过反弹面冻结实现信息跨代传递。这一统一框架将量子现象、黑洞热力学与宇宙演化置于同一几何语言之下,提出四项可通过桌面实验检验的核心预言,并建立了高阶关联熵与视界面积的定量关系 。若预言被证实,将确立离散几何为量子信息的底层起源,为全息宇宙提供首个可实证的物理支撑。
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。
This work presents a unified, interpretive account of quantum interference and delayed-choice experiments that applies equally to photons and massive particles. Rather than invoking spacetime trajectories, wave–particle duality, retrocausality, or collapse postulates, the paper locates quantum interference in the coherent evolution of internal, pre-geometric degrees of freedom defined over classical spacetime. Within this framework, “which-path” questions are not merely unanswered but fundamentally ill-posed: interference arises from global coherence of an internal field subject to experimental boundary conditions, while spacetime itself remains single-valued and classical at laboratory scales. The approach reproduces all standard quantum-mechanical predictions without modification and is explicitly interpretive rather than predictive. A central result is a unified explanation of why interference occurs across disparate physical systems—photons, electrons, atoms, and molecules—while decoherence manifests through system-dependent physical mechanisms. Photons and massive particles differ in how internal coherence is lost (e.g., electromagnetic absorption versus collisional and thermal interactions), but not in the underlying principle. Delayed-choice experiments are reinterpreted without paradox: changes to the apparatus modify boundary conditions for the internal field rather than retroactively altering particle histories. By removing spacetime paths from the fundamental ontology, the framework offers a consistent, path-free account of interference, decoherence, and localized detection that preserves the empirical success of quantum mechanics while clarifying its conceptual foundations.
This paper presents a groundbreaking unified framework that bridges quantum information theory and black hole physics by introducing the concept of universal informational phase conservation. Through rigorous simulation of 8-12 qubit systems, we first establish a precise power-law scaling for information leakage: η ∝ N^(-0.43), demonstrating the emergence of near-perfect information conservation in larger quantum systems. A key structural parameter, Δ₀ ≈ 8.0, is identified as the regulator of information flow. We then perform a revolutionary extrapolation, applying this quantum scaling law to resolve the long-standing black hole information paradox. Our model demonstrates that information loss in Hawking radiation becomes negligible (η_BH ~ 10^(-33)) for astrophysical black holes, naturally ensuring information conservation without violating unitarity. The framework is further unified by reinterpreting the consciousness field (from the AOUF v2.5 model) as a cosmic-scale informational phase coordination field (Φ), which governs information dynamics from quantum to cosmic scales. Predictions for anomalous gravitational wave frequency shifts and photon ring brightness enhancements are derived and shown to be consistent with public data from LIGO and the Event Horizon Telescope. This work provides the first quantitative link between microscopic information scaling and macroscopic information paradoxes, offering a testable pathway towards a theory of quantum gravity. Keywords: Information Conservation, Black Hole Information Paradox, Quantum Scaling Laws, Page Curve, Quantum Gravity, Consciousness Field, Δ₀ Parameter, Holographic Principle
The double-slit experiment is the heart of quantum mechanics, yet its standard interpretation relies on the postulate of wavefunction probability amplitude. Starting from Space Ontology, we demonstrate that interference phenomena can be entirely derived from the geometric properties of classical spatial modes, without introducing probability amplitudes. Each slit is modeled as a localized soliton solution of the spatial orientation field equation; the interference pattern arises from the linear superposition of two mode energy densities in the far field. The key discovery is that the interference visibility V is uniquely determined by the geometric entanglement entropy E_geo of the modes, satisfying V = tanh(2E_geo). Here E_geo = ln Lambda(alpha) is a function of the mode's shape parameter alpha — a Gaussian mode (alpha=2) has zero entropy and cannot interfere, while a flat mode (alpha>2) carries large coherent capacity. This theory naturally explains the which-way and quantum eraser experiments: path marking introduces a third mode that dilutes correlations via the many-body correlation reduction theorem; erasure corresponds to the decoupling of that mode. As a flagship validation, we show that the theory quantitatively accounts for the macroscopic interference of 7000-atom sodium clusters, predicting a coherence width of approximately 66 nm — confirmed by experiment. Two testable predictions are proposed: a boundary shape compression effect, and a material-dependent visibility for nanoclusters of different compositions. This work demonstrates that wave-particle duality is not a mysterious quantum feature, but a manifestation of the geometric entanglement entropy of spatial modes — the flatter the mode, the greater the coherence capacity, and the clearer the interference. This paper is the second in the first series (17 papers total) of Space Ontology.
This work proposes a theoretical framework in which entropy is treated as a geometric degree of freedom in an extended quantum state space. By introducing a resolution parameter defined as the inverse of von Neumann entropy, an informational metric is constructed on the space of density matrices. Within this framework, a causal structure emerges from a null condition on the metric, defining a light-cone-like boundary for the propagation of quantum correlations. Entanglement propagation is derived and shown to depend on entropy evolution, leading to a dynamical causal structure. In the near-equilibrium limit, the model reproduces a Lieb–Robinson-type bound with finite correlation speed. Connections to holography are established by interpreting entropy as a radial coordinate controlling scale, and an analogue of the Ryu–Takayanagi relation is derived, where entropy corresponds to the length of minimal curves in the informational geometry. Black hole horizons are interpreted as maximal entropy surfaces corresponding to a collapse of distinguishability in quantum state space. The framework suggests that spacetime geometry, causality, and gravitational behavior may emerge from entropy-weighted quantum information structure. This work is an independent theoretical exploration aimed at providing a unified perspective linking quantum information, geometry, and gravity.
This work presents an extended, mathematically complete formulation of the Information Geometry Unification Principle (IGUP), a foundational framework in which quantum mechanics, statistical thermodynamics, general relativity, and spacetime geometry emerge from a single information-theoretic ontology. We begin with rigorous axioms defining information as the primary physical substance, then systematically construct the Bures–Fisher–Rao metric on the manifold of quantum density matrices. We derive the universal information action functional and perform full variational derivations to obtain the unified field equations. We show explicitly how standard physical theories including the Schrödinger equation, Heisenberg picture, Liouville mechanics, classical thermodynamics, and Einstein field equations are recovered in appropriate limiting regimes. We further derive geometric expressions for entanglement, entropy, temperature, energy, and force. The theory resolves longstanding conceptual tensions between unitary quantum evolution and gravitational irreversibility, provides a natural resolution to the black hole information paradox, and yields eight concrete, experimentally testable predictions. This extended version includes full tensor calculus, covariant derivatives, curvature expansions, and limit theorems, amounting to a self-contained theory of everything based on Geometry=Information.