This work presents a geometric–topological field model in which the affine connection is treated as the sole fundamental dynamical variable, while metric structure, matter, and effective particle dynamics emerge as secondary descriptions. Matter is interpreted as localized, topologically nontrivial configurations of the connection field. A central prediction of the model is that quantum interference is sensitive to geometric complexity, leading to a geometry-dependent suppression of interference visibility and a geometry-induced phase accumulation. These effects are investigated in the context of atom interferometry, with particular emphasis on Mach–Zehnder and large-momentum-transfer (LMT) configurations. Interference fringes are analyzed to extract visibility, and an exponential suppression law as a function of geometric complexity is observed. Statistical robustness is assessed using bootstrap resampling, yielding a strictly positive suppression coefficient. In addition to visibility loss, a geometry-dependent linear phase accumulation is identified, with different rates for simple and complex interferometer geometries. The results suggest that quantum coherence can be interpreted as an emergent manifestation of underlying geometric constraints, and that atom interferometry provides a direct experimental probe of such geometric effects. The presented framework yields clear, falsifiable interferometric signatures that can be tested with existing experimental platforms.
This work presents a geometric–topological field model in which the affine connection is treated as the sole fundamental dynamical variable, while metric structure, matter, and effective particle dynamics emerge as secondary descriptions. Matter is interpreted as localized, topologically nontrivial configurations of the connection field. A central prediction of the model is that quantum interference is sensitive to geometric complexity, leading to a geometry-dependent suppression of interference visibility and a geometry-induced phase accumulation. These effects are investigated in the context of atom interferometry, with particular emphasis on Mach–Zehnder and large-momentum-transfer (LMT) configurations. Interference fringes are analyzed to extract visibility, and an exponential suppression law as a function of geometric complexity is observed. Statistical robustness is assessed using bootstrap resampling, yielding a strictly positive suppression coefficient. In addition to visibility loss, a geometry-dependent linear phase accumulation is identified, with different rates for simple and complex interferometer geometries. The results suggest that quantum coherence can be interpreted as an emergent manifestation of underlying geometric constraints, and that atom interferometry provides a direct experimental probe of such geometric effects. The presented framework yields clear, falsifiable interferometric signatures that can be tested with existing experimental platforms.
It is often argued that the sensitivity of atom interferometer depends on the geometry of the interfering atom paths, conventionally, atom interferometer are usually configured to be sensitive to all deformations including tensor and scalar field deformations, it is a promising and robust tool for obtaining a highly sensitive and accurate measurements of gravitational signals, as such they are potentially capable of testing a wide range of fundamental physics questions including gravitational decoherence. Therefore, motivated by the recent search to improve the sensitivity of the next generation atom interferometer, we derived a broad class of equations that obeys a specific geometric configuration for the interfering paths for a 2-level atom interferometer model, and in doing so, we further analysed various configurations for the geometric interpretation, in addition to interferometric influence phase shift and a possible decoherence factor which could lead to a systematic theoretical framework for future sensing of weak forces, due to, for example, gravitational waves and light dark matter.
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。
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 record presents a short, time-stamped research note proposing a clean control experiment aimed at clarifying the physical origin of recently observed quantum-metric-induced trajectory bending in quantum materials. While such effects are commonly interpreted as arising from geometric structure in Hilbert space, an open question remains as to whether an effective temporal or phase-delay contribution may act as the underlying generator of the observed metric. The proposed protocol isolates temporal phase modulation from spatial geometry by keeping particle trajectories and external forces fixed while varying only the effective phase, delay, or frequency associated with the quantum state. The experiment constitutes a null test: a positive outcome would indicate a temporal contribution to the effective metric, while a null result would strengthen a purely geometric interpretation. The proposal requires no new instrumentation and is compatible with existing solid-state platforms (such as oxide-interface two-dimensional electron gases), topological or quantum Hall interferometers, and cold-atom interferometric systems. This note is intended as a conceptual and experimental guide rather than a report of new data.
Structured light provides high-dimensional Hilbert spaces holding tremendous potential for fundamental quantum optics and quantum technologies. However, existing characterization methods, like Hong-Ou-Mandel (HOM) interference, typically assume perfectly tuned conditions, overlooking the geometric physics governing spatial mode evolution. Here, we establish topological quantum interferometry driven by an interaction-based geometric phase, the exchange Berry phase (BPX). Our formalism generalizes q-plate state generation and characterization to arbitrary topological charges and (de)tuning conditions, demonstrating that BPX acts as a geometric marker governing spatial interference. We show BPX serves as a deterministic control parameter, decomposing two-photon spatial patterns into geometry-dictated fundamental modes. This mapping reveals topological invariants and phase singularities that function as a non-tomographic witness for state dimensionality estimation, circumventing full-state reconstruction. Being device-independent and highly scalable, this approach enables scalable high-dimensional characterization and topologically protected state selection, with direct applicability to quantum metrology and high-capacity quantum networks.
The coherence effects induced by external photons coupled to matter waves inside a Mach–Zehnder three-grating interferometer are analyzed. Alternatively to atom–photon entanglement scenarios, the model considered here only relies on the atomic wavefunction and the momentum shift induced in it by the photon scattering events. A functional dependence is thus found between the observables, namely the fringe visibility and the phase shift, and the transversal momentum transfer distribution. Good quantitative agreement is found when comparing the results obtained from our model with the experimental data.