Fire a single particle at a barrier with two slits. An interference pattern emerges even when particles are sent one at a time. Introduce which-path detection and the pattern disappears. Quantum mechanics predicts these outcomes with extraordinary accuracy. What it does not provide is a widely accepted physical account of the underlying mechanism. We present Binding Geometry, a framework that proposes such a mechanism. In this view, a particle corresponds to a locally jammed region within a frustrated geometric lattice. Each particle carries delocalized geometric slack—void degrees of freedom distributed through the surrounding structure. Because this slack is a property of geometry rather than a localized object, it can extend through both slits simultaneously. Overlapping slack configurations give rise to interference. Introducing a detector adds constraints to the local geometry, forcing the slack to localize into a single configuration and suppressing interference. This behaviour is one instance of a broader proposal: physical reality can be understood as a packing problem in which degrees of freedom arrange under geometric constraints. The structure of those constraints determines coordination numbers, phase thresholds, and the numerical values of physical constants. Established physical theories accurately describe the observable consequences of this packing. Binding Geometry aims to describe the underlying structure from which those consequences arise. The framework leaves all experimentally verified equations of the Standard Model and General Relativity intact. It instead addresses a class of open questions left unresolved by current theory, including the origin of the fine-structure constant, the smallness of the cosmological constant, the existence of three particle generations, and the physical interpretation of quantum measurement. Binding Geometry has been examined across more than forty domains spanning physics, computation, and biology (enumerated in Supplement B), where thresholds and transition points consistently align with predictions derived from packing geometry. The framework also yields falsifiable predictions, including the persistence of evolving dark energy in continued DESI releases and a correlated drift between cosmological parameters and the fine-structure constant.
Fire a single particle at a barrier with two slits. An interference pattern emerges even when particles are sent one at a time. Introduce which-path detection and the pattern disappears. Quantum mechanics predicts these outcomes with extraordinary accuracy. What it does not provide is a widely accepted physical account of the underlying mechanism. We present Binding Geometry, a framework that proposes such a mechanism. In this view, a particle corresponds to a locally jammed region within a frustrated geometric lattice. Each particle carries delocalized geometric slack—void degrees of freedom distributed through the surrounding structure. Because this slack is a property of geometry rather than a localized object, it can extend through both slits simultaneously. Overlapping slack configurations give rise to interference. Introducing a detector adds constraints to the local geometry, forcing the slack to localize into a single configuration and suppressing interference. This behaviour is one instance of a broader proposal: physical reality can be understood as a packing problem in which degrees of freedom arrange under geometric constraints. The structure of those constraints determines coordination numbers, phase thresholds, and the numerical values of physical constants. Established physical theories accurately describe the observable consequences of this packing. Binding Geometry aims to describe the underlying structure from which those consequences arise. The framework leaves all experimentally verified equations of the Standard Model and General Relativity intact. It instead addresses a class of open questions left unresolved by current theory, including the origin of the fine-structure constant, the smallness of the cosmological constant, the existence of three particle generations, and the physical interpretation of quantum measurement. Binding Geometry has been examined across more than forty domains spanning physics, computation, and biology (enumerated in Supplement B), where thresholds and transition points consistently align with predictions derived from packing geometry. The framework also yields falsifiable predictions, including the persistence of evolving dark energy in continued DESI releases and a correlated drift between cosmological parameters and the fine-structure constant.
This work presents a continuous, constraint-based interpretive framework for physical systems that unifies quantum behavior, classical structure, and cosmological evolution without introducing new forces or modifying established equations. Rather than treating quantum mechanics, electromagnetism, and general relativity as fundamentally separate domains, the paper proposes that these regimes can be understood as consistent descriptions of a shared underlying structure. The framework is built on three foundational elements: a non-geometric substrate (P_0) defining admissible configurations, interaction as the propagation of constraint, and geometry as the macroscopic record of accumulated interaction. Within this perspective, physical structure emerges through a continuous progression: distinctions enable gradients, gradients enable interaction, interaction accumulates as constraint, and constraint stabilizes into persistent configurations. The quantum–classical transition is interpreted as a continuous increase in interaction-induced constraint, while spacetime curvature reflects the large-scale organization of these interactions. The framework does not replace existing theories, but instead provides a unified conceptual interpretation that remains fully consistent with established physics across known regimes. Its value lies in clarifying relationships between domains, offering a continuous ontology of physical systems, and suggesting potential directions for further formalization.
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 paper proposes a geometric interpretive framework for a set of foundational phenomena in quantum physics, including the measurement problem, quantum entanglement, and the emergence of classical spacetime structure. Building on the dimensional analogy introduced by Abbott (1884), we develop a model in which observed physical events correspond to lower dimensional intersections of higher-dimensional wave-like structures with an observer's accessible domain. Within this picture, a particle detection event is reinterpreted as the intersection of an extended wave with an observer's plane, and measurement outcomes arise from the geometric relationship between the observer's orientation and the underlying structure, rather than from a physical collapse process. In the context of entanglement, we develop a model in whichcorrelated outcomes observed by spatially separated detectors are understood as local samplings of a single wave generated at a common origin event . The dependence of measurement correlations on detector settings is interpreted in terms of angular separation along the shared wave front, yielding an account consistent with the standard quantum prediction P(same) = cos²(θ/2). The proposal does not modify the mathematical formalism of quantum mechanics and does not introduce novel quantitative predictions at this stage. Its contribution is conceptual: it provides a coherent geometric perspective that unifies several interpretive challenges—wave–particle duality, the measurement problem, and apparent non-locality—within a single structuralpicture. Connections to relational quantum mechanics, holographic duality, and the ER = EPR conjecture are identified as indications of structural compatibility. Open questions and possible directions for formalization are outlined.
Abstract We take physical distinguishability as the sole primitive of physics: two states are distinct if and only if some measurement can tell them apart. From this single principle, a geometry emerges on the space of all physical states. Its universal threshold — the point where the rate of change of distinguishability saturates — is simultaneously the quantum speed limit, the event horizon of a black hole, and the critical point of a thermodynamic phase transition. Quantum mechanics, general relativity, and thermodynamics are three expressions of the same geometric threshold on different state spaces; the constants ℏ, c , and k B are conversion factors between them. Within this structure, we identify a parameter-free geometric mechanism that yields the Schrödinger equation; the Einstein field equations, exactly on the horizon and in the bulk to corrections below 10⁻³² for stationary configurations (the fully dynamical case is not established here); the Lorentzian signature of spacetime; and a structural mechanism that reduces the standard 10¹²³ discrepancy of the cosmological constant problem to order unity, conditional on two framework-internal postulates (Section 13.8). Applying this, the framework evaluates a vacuum length scale of ~88 μm and energy ~2.25 meV from the observed dark-energy density, placing the dominant source in the lightest neutrino sector. The framework further suggests that macroscopic quantum coherence suppresses geodesic distinguishability — the Bose–Einstein condensate (BEC) analogue of the Meissner effect — with a predicted breathing-mode shift of ~1.5 mHz in ⁸⁷Rb. IBM Quantum experiments on three independent 156-qubit Heron processors show excitation probabilities differing by a factor of ≈3.7 across protocols with identical control parameters but different geometric paths, consistent with the prediction that endpoint distinguishability governs the outcome. Cross-backend transfer errors remain below 1%. Physical reality is what is distinguishable. The laws of nature are the geometry of distinguishability.
Decades of work in geometric quantum mechanics and decoherence theory have clarified how quantum behaviour arises from underlying symplectic and dynamical structures, yet both leave unresolved why measurements yield definite outcomes with |ψ|² frequencies. This paper proposes a deterministic geometric account that retains the strengths of those approaches while eliminating the need for stochastic collapse or multiple-world postulates. The result is a unified description in which observed statistics follow from conserved geometry rather than from probabilistic axioms. Physical reality is represented by a single trajectory ω(t) evolving under Hamiltonian flow on a compact symplectic manifold Σ. Interaction with an environment imposes new constraints that dynamically partition Σ into isolated outcome regions {Ωᵢ}, whose invariant volume ratios μ(Ωᵢ)/μ(Ω₀) reproduce Born weights. Outcome definiteness arises from trajectory confinement within an isolated region, and the framework predicts a quantitative correspondence between interference visibility V and the dynamical separation I of outcome regions. In the macroscopic limit, V ≈ 1 − I, so high separation (I → 1) corresponds to classical definiteness and negligible remaining visibility. The exact functional form, together with parameter-free calculations and proposed experimental tests, is developed in the forthcoming Paper C and a companion note (2025–2026). The paper establishes a complete ontological basis for deterministic quantum measurement, defines how isolation and re-isolation govern the appearance of classicality, and clarifies compliance with Bell, Kochen–Specker, Fine, and PBR constraints. It shows that a finite, measure-preserving geometry can reproduce the statistical structure of quantum theory while remaining open to empirical refutation. This framework, termed Constraint-Surface Dynamics, thus offers a deterministic and falsifiable alternative foundation for quantum mechanics.
Abstract We take physical distinguishability as the sole primitive of physics: two states are distinct if and only if some measurement can tell them apart. From this single principle, a geometry emerges on the space of all physical states. Its universal threshold — the point where the rate of change of distinguishability saturates — is simultaneously the quantum speed limit, the event horizon of a black hole, and the critical point of a thermodynamic phase transition. Quantum mechanics, general relativity, and thermodynamics are three expressions of the same geometric threshold on different state spaces; the constants ℏ, c , and k B are conversion factors between them. Within this structure, we identify a parameter-free geometric mechanism that yields the Schrödinger equation; the Einstein field equations both on the horizon (exactly) and in the bulk (to corrections smaller than 10⁻³² at all accessible energies); the Lorentzian signature of spacetime; and a structural resolution of the cosmological constant problem, reducing the standard discrepancy of 10¹²³ to order unity. Consequently, the framework evaluates a vacuum length scale of 88 μm and energy 2.25 meV from the observed dark-energy density, placing the dominant source in the lightest neutrino sector. The framework further suggests that macroscopic quantum coherence suppresses geodesic distinguishability — the Bose–Einstein condensate (BEC) analogue of the Meissner effect — with a predicted breathing-mode shift of ~1.5 mHz in ⁸⁷Rb. IBM Quantum experiments on three independent 156-qubit Heron processors show excitation probabilities differing by a factor of 3.8 across protocols with identical control parameters but different geometric paths, consistent with the prediction that endpoint distinguishability governs the outcome. Cross-backend transfer errors remain below 1%. Physical reality is what is distinguishable. The laws of nature are the geometry of distinguishability.