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 G10³), 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G10³), 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
zhengda li (Mon,) studied this question.