Abstract Quantum gravity theories generically predict a discrete structure of spacetime at the Planck scale, yet laboratory‑scale testable signals have remained elusive for a long time. We propose a tabletop experiment based on a squeezed‑light interferometer that exploits the exponential amplification property of squeezed states to probe the intrinsic phase noise arising from microscopic spacetime structures. Two complementary measurements are designed: (i) a Mach–Zehnder interferometer to measure the exponential enhancement of the residual visibility with the squeezing parameter ; (ii) intensity correlation (Hanbury Brown–Twiss) to measure the third‑ and fourth‑order correlation functions of the optical field, from which the non‑Gaussian characteristic ratio is extracted. This ratio is independent of the squeezing parameter and is determined solely by the recursive structure of a discrete spacetime, thus serving as a statistical fingerprint that distinguishes continuous from discrete microscopic structures. We give a clear null hypothesis: a continuous spacetime corresponds to Gaussian phase fluctuations ( with no enhancement), while a discrete spacetime predicts either (binary branch) or (ternary branch) together with the exponential scaling. The two criteria are independent and must be satisfied simultaneously, forming a double falsifiability of the model. Based on existing quantum‑optics technology (squeezing parameter , detection efficiency ), the predicted signal magnitude and the ratios or lie within a detectable range. The proposed scheme does not rely on any specific ultraviolet theory and can be implemented on existing platforms. It can also be combined with cosmological observations of primordial non‑Gaussianity and high‑energy Lorentz violation tests to form a cross‑scale consistency check. 摘要 量子引力理论普遍预言时空在普朗克尺度下呈现离散结构,但实验室尺度的可检验信号长期缺失。本文提出一种基于压缩态光干涉仪的桌面实验方案,利用压缩态的指数放大特性探测时空微观结构导致的内禀相位噪声。我们设计两套互补的测量:(i)马赫‑曾德干涉仪测量压缩光残余可见度随压缩参数 的指数增强行为 ;(ii)强度关联(Hanbury Brown‑Twiss)测量光场三阶与四阶关联函数,提取非高斯特征比值 。该比值与压缩参数无关,仅由离散时空的递归结构决定,构成区分连续/离散微观结构的统计指纹。 本文给出明确的零假设判据:连续时空对应高斯相位涨落( 且无 增强),离散时空则预言 (二元分支)或 (三元分支)且满足指数标度。两条判据独立且必须同时满足,构成模型的双重可证伪性。基于现有量子光学技术(压缩度 、探测效率 ),预言信号量级 、比值 或 ,处于可探测范围。本方案不依赖具体紫外理论,可直接在现有平台上实现,并与宇宙学非高斯性观测、高能宇宙线洛伦兹破缺检验形成跨尺度自洽性检验。
Abstract Quantum gravity theories generically predict a discrete structure of spacetime at the Planck scale, yet laboratory‑scale testable signals have remained elusive for a long time. We propose a tabletop experiment based on a squeezed‑light interferometer that exploits the exponential amplification property of squeezed states to probe the intrinsic phase noise arising from microscopic spacetime structures. Two complementary measurements are designed: (i) a Mach–Zehnder interferometer to measure the exponential enhancement of the residual visibility with the squeezing parameter ; (ii) intensity correlation (Hanbury Brown–Twiss) to measure the third‑ and fourth‑order correlation functions of the optical field, from which the non‑Gaussian characteristic ratio is extracted. This ratio is independent of the squeezing parameter and is determined solely by the recursive structure of a discrete spacetime, thus serving as a statistical fingerprint that distinguishes continuous from discrete microscopic structures. We give a clear null hypothesis: a continuous spacetime corresponds to Gaussian phase fluctuations ( with no enhancement), while a discrete spacetime predicts either (binary branch) or (ternary branch) together with the exponential scaling. The two criteria are independent and must be satisfied simultaneously, forming a double falsifiability of the model. Based on existing quantum‑optics technology (squeezing parameter , detection efficiency ), the predicted signal magnitude and the ratios or lie within a detectable range. The proposed scheme does not rely on any specific ultraviolet theory and can be implemented on existing platforms. It can also be combined with cosmological observations of primordial non‑Gaussianity and high‑energy Lorentz violation tests to form a cross‑scale consistency check. 摘要 量子引力理论普遍预言时空在普朗克尺度下呈现离散结构,但实验室尺度的可检验信号长期缺失。本文提出一种基于压缩态光干涉仪的桌面实验方案,利用压缩态的指数放大特性探测时空微观结构导致的内禀相位噪声。我们设计两套互补的测量:(i)马赫‑曾德干涉仪测量压缩光残余可见度随压缩参数 的指数增强行为 ;(ii)强度关联(Hanbury Brown‑Twiss)测量光场三阶与四阶关联函数,提取非高斯特征比值 。该比值与压缩参数无关,仅由离散时空的递归结构决定,构成区分连续/离散微观结构的统计指纹。 本文给出明确的零假设判据:连续时空对应高斯相位涨落( 且无 增强),离散时空则预言 (二元分支)或 (三元分支)且满足指数标度。两条判据独立且必须同时满足,构成模型的双重可证伪性。基于现有量子光学技术(压缩度 、探测效率 ),预言信号量级 、比值 或 ,处于可探测范围。本方案不依赖具体紫外理论,可直接在现有平台上实现,并与宇宙学非高斯性观测、高能宇宙线洛伦兹破缺检验形成跨尺度自洽性检验。
AbstractDoes Planck-scale spacetime discreteness leave an observable non-Gaussian imprint in low-energy effective theories? This paper constructs a quantum measurement phenomenological framework based on high-order statistics to address this question. By utilizing the exponential enhancement of the third-order cumulant (e^{2r})by squeezed light — a mechanism that can amplify a non-Gaussian signal originally buried in the standard quantum limit to a detectable level (with a net amplification of several orders of magnitude under optimized parameters, relative to coherent-state detection at the standard quantum limit) — together with a giant-Kerr nonlinear medium (taking Rydberg EIT as an example, with gain G\sim{10}^3 ), we propose a joint test protocol consisting of a “dynamical squeezing scaling” criterion and a “static topological shape” criterion. This provides a model-independent mathematical criterion for testing quantum-gravity predictions of non-Gaussianity at tabletop scales, without requiring detailed knowledge of discrete geometry. To address the intrinsic non-Gaussian background that may be introduced by atomic media, we propose a geometric forbiddenness principle based on the separation of integral-manifold dimensions. The core value of this framework lies in providing a clear falsification logic: if future experiments satisfy both criteria simultaneously, new physics is supported; otherwise, specific classes of quantum gravity models are ruled out. Keywords: quantum gravity phenomenology; non-Gaussian phase noise; squeezed light; Rydberg atoms; causal sets; geometric forbiddenness; high-order statistics 摘要 普朗克尺度时空离散性是否会在低能有效理论中留下可观测的非高斯印记?本文构建了一个基于高阶统计量的量子测量唯象学框架,旨在探讨这一问题。利用压缩光对三阶累积量的指数增强(e^{2r})——该机制可将原本淹没在标准量子极限下的非高斯信号放大至可探测水平(优化参数下可获得多个数量级的净放大,相对于标准量子极限下的相干态探测)——结合巨克尔非线性介质(以里德堡EIT为例,其增益G\sim{10}^3),我们提出了“动态压缩标度”与“静态拓扑形状”的联合检验协议,为在桌面尺度检验量子引力的非高斯预言提供了一种对离散几何细节模型无关的数学判据。针对原子介质可能引入的本征非高斯背景,本文提出了基于积分流形维度分离的几何禁戒原理。本框架的核心在于提供了一个清晰的证伪逻辑:若未来实验同时满足双重判据,则支持新物理;否则排除特定类别的量子引力模型。 关键词:量子引力唯象学;非高斯相位噪声;压缩光;里德堡原子;因果集;几何禁戒;高阶统计量
Abstract We propose a tabletop experiment to test spacetime non-Gaussian fluctuations, leveraging the amplification of squeezed light and two independent platforms: a double-slit interferometer and a Rydberg-atom electromagnetically induced transparency (EIT) spectrometer. The interferometer measures residual visibility , while the spectrometer detects an anomalous frequency variance . Both platforms share the same core assumption: an effective skewness parameter characterizing Planck-scale non-Gaussian statistics. As an optional theoretical example, the circular orthogonal ensemble (COE) model predicts , corresponding to signal magnitudes and , within reach of current technology. The central feature is falsifiability: if the observed signal does not follow the scaling, or if is zero within sufficient precision, the hypothesis is ruled out. This constitutes the first tabletop scheme that directly tests spacetime non-Gaussianity without relying on a specific ultraviolet theory, inspired by the cosmic microwave background bispectrum and realizable with existing technology. 摘要 我们提出一个桌面实验方案,利用压缩态光的 放大效应,通过两个独立平台——双缝干涉仪与里德堡电磁诱导透明(EIT)光谱仪——检验时空非高斯涨落。干涉仪测量残余可见度 ,光谱仪探测反常频率方差 。两个平台共享同一核心假设:存在一个有效偏度参数 ,刻画普朗克尺度的非高斯统计。作为可选理论示例,圆正交系综(COE)模型预言 ,对应信号量级为 、,处于当前技术可及范围。本方案的核心是可证伪性:若测得信号与 标度关系不符,或 在足够精度下为零,则假设被排除。这构成了首个不依赖具体紫外理论、直接检验时空非高斯性的桌面实验方案,其灵感源自宇宙微波背景双谱,且可基于现有技术实现。
We present a theoretical framework for detecting non-Gaussian phase noise potentially originating from Planck-scale physics, using squeezed-light amplification and dual-channel validation to achieve exponential signal enhancement (, where is the squeezing parameter) and effective discrimination against classical artifacts. The framework centers on two key innovations: (i) exponential amplification of weak non-Gaussian signals via the Kerr nonlinearity of squeezed light, scaling as ; (ii) a dual-channel design combining interferometry and intensity correlation measurements to establish a “double-decision” logic, testing both the dynamical scaling law () and the static statistical shape (), thereby distinguishing genuine new physics from technical artifacts. Feasibility analysis based on current quantum optical technology shows that optimized signal levels (, significantly deviating from the Gaussian value of 1) are within reach. As an illustrative application, we benchmark the framework against the recently proposed “defect-point” model from normal numbers, which predicts and . Crucially, the framework’s value does not depend on the correctness of any specific model. The proposed experimental design and its false-positive exclusion criteria can be broadly applied to any research area requiring detection of higher-order statistical signatures, including quantum gravity phenomenology, dark matter detection, and quantum metrology. Keywords: non-Gaussian noise, higher-order correlations, squeezed light, feasibility study, quantum gravity phenomenology, double-decision logic 摘要 本文提出一个理论框架,旨在利用压缩态光放大与双通道验证,探测可能源于普朗克尺度物理的非高斯相位噪声,实现信号的指数增强(,其中 为压缩参数)与对经典假象的有效甄别。该框架的核心创新在于:(1)利用压缩态光的克尔非线性实现信号 倍指数放大;(2)通过双通道测量(干涉仪与强度关联仪)建立“双重判决”逻辑,分别检验动力学标度律()与静态统计形状(高阶比值 ),从而有效区分新物理信号与经典技术假象。基于当前量子光学技术参数的可行性分析表明,优化后信号量级(, 显著偏离高斯值1)处于可探测边缘。作为应用实例,本文将该框架对标近期提出的“正规数瑕疵点”离散时空模型(该模型解析预言 ,),但框架本身的价值不依赖于该模型的正确性。本文提供的实验设计及其排假阳性标准,可广泛应用于量子引力唯象学、暗物质探测及量子计量学中任何需要探测高阶统计特征的研究领域。 关键词:非高斯噪声;高阶关联;压缩态光;可行性研究;量子引力唯象学;双重判决
The hypothesis that spacetime possesses a discrete structure at the Planck scale - potentially composed of quantized tetrahedral or simplicial building blocks - arises naturally in background-independent approaches to quantum gravity such as Loop Quantum Gravity (LQG) and Causal Dynamical Triangulations (CDT). In these frameworks, spatial geometry emerges from spin networks of quantum tetrahedra with discrete area and volume spectra, while spacetime evolution proceeds via spin foams or summed triangulations. Roger Penrose’s Objective Reduction (OR) mechanism further posits that quantum superpositions of massive states generate incompatible spacetime curvatures whose gravitational self-energy difference triggers an objective collapse when the associated energy uncertainty reaches ħ/τ, implicitly requiring a non-continuous spacetime geometry. This article presents an exhaustive theoretical foundation and proposes a hybrid tabletop experiment - the Planck Geometry Interferometer - designed to simultaneously measure gravitational phase shifts arising from proper-time differences and spontaneous collapse lifetimes. By placing mesoscopic masses in spatial superpositions and monitoring quantized deviations in phase or collapse time, the experiment can distinguish discrete tetrahedral geometries (LQG-style) from continuous spacetime or pure Penrose foam. Building directly on existing proposals, the setup is shown to be within reach of current optomechanical, cryogenic, and interferometric technologies. Detailed protocols, expected signatures of discreteness, feasibility assessments, and implications for falsifying or confirming Planck-scale discreteness are provided. A negative result would constrain or refute these models; a positive detection of quantization would constitute direct empirical evidence for discrete spacetime.
Abstract Experimental tests of quantum gravity have long been limited by the extreme energy scale of the Planck regime. In recent years, theoretical proposals for testing gravitational non-Gaussianity using tabletop quantum systems have made significant progress, but existing schemes face severe challenges in experimental feasibility: the BEC+Feshbach scheme of Howl et al. relies solely on the square of the atom number for sensitivity, yielding a weak signal; the recently proposed squeezing-enhanced dual-platform scheme by Li [2] amplifies the signal to but suffers from system complexity and cross-correlation difficulties. This paper simultaneously proposes two complementary experimental frameworks: Scheme A (Theoretical Benchmark) establishes a “gold standard” paradigm for quantum gravity tests within a rigorous theoretical framework (number-squeezing, precise Feshbach cancellation, exponential scaling law); Scheme B (Exploratory Precursor) is based on a set of engineering-friendly alternative assumptions (bidirectional quantum interface, gradient field spatial averaging, differential measurement), aiming for a near-term proof-of-principle exploration of the core phenomenon of “squeezing-enhanced non-Gaussian signals.” The two schemes share the same physical core: squeezing-enhanced non-Gaussian signals serve as a potential discriminative signature of quantum gravity. This paper details the theoretical foundations, experimental designs, feasibility assessments, and application scenarios of both schemes, providing alternative pathways for research groups with different experimental capabilities. Scheme B significantly lowers the environmental and technical barriers, making it possible to conduct proof-of-principle experiments in standard cold-atom laboratories; Scheme A provides a complete theoretical framework for future high-precision verification. The two schemes are proposed in parallel and complement each other, jointly forming a complete research roadmap from “preliminary detection” to “rigorous testing.” Keywords: quantum gravity; non-Gaussianity; BEC; squeezed states; tabletop experiments; theoretical benchmark; exploratory precursor 摘要 量子引力的实验检验长期受限于普朗克能标的极端能量尺度。近年来,利用桌面量子系统检验引力非高斯性的理论方案取得了重要进展,但现有方案在实验可行性上面临严峻挑战:Howl等人的BEC+Feshbach方案灵敏度仅依赖原子数平方 ,信号微弱;李政达 [2] 近期提出的压缩增强双平台方案虽将信号放大至 ,但系统复杂、互相关困难。本文同时提出两种互补的实验框架:A方案(理论基准型) 在严格的理论框架内(数模压缩、Feshbach精确调零、指数标度律判决)建立量子引力检验的“黄金标准”范式;B方案(先导探索型) 基于一组可工程化的替代性假设(双向量子接口、梯度空间平均、差分测量),旨在近期内对“压缩增强的非高斯信号”这一核心现象进行原理性探索。两种方案共享同一物理内核:压缩增强的非高斯信号是量子引力的潜在判决性特征。本文详细阐述两种方案的理论基础、实验设计、可行性评估和适用场景,为不同实验条件的团队提供可选择的路径。B方案显著降低了实验的环境和技术门槛,使其可能在常规冷原子实验室内进行原理探索;A方案则为未来精密验证提供了完整的理论框架。两种方案并行提出,互为补充,共同构成从“初步探测”到“严格检验”的完整研究路线。 关键词:量子引力;非高斯性;BEC;压缩态;桌面实验;理论基准;先导探索
If the structure of spacetime is discrete, then Lorentz symmetry should only be an approximation, valid at long length scales. At finite lattice spacings there will be small corrections to the Dirac evolution. In particular, the lattice structure will be reflected in a modification of the free-particle dispersion relation. We show that these can produce a surprisingly large phase shift between the two arms of a nonparallel interferometer. This method could be employed to test any model that predicts a direction-dependent dispersion relation. Here, we calculate the size of this phase shift for a particular model, the three-dimensional quantum walk on the body-centered cubic lattice, which has been shown to give rise to the Dirac equation in the continuum limit. Though the details of this model will affect the size of the shift, its magnitude is set largely by dimensional analysis, so there is reason to believe that other models would yield similar results. We find that, with current technology, a modest-sized neutron interferometer could detect lattice spacings as small as ${10}^{\ensuremath{-}31}\text{ }\text{ }\mathrm{m}$, 13 orders of magnitude smaller than the scale probed by the LHC. A suitably scaled-up experiment could possibly detect lattice spacings even at the Planck scale.