Quantum-Geometric Interferometry: Testing Discrete Spacetime Structure Using Squeezed Light

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)