时空的量子基准：基于晓晓半径的拓扑熵引力理论
Xiaoxiao Radius as the Quantum Benchmark of Spacetime: A Topological-Entropy Theory of Gravity
本文提出以“晓晓半径”作为统一量子引力与宏观宇宙现象的基准尺度。利用Atiyah-Patodi-Singer指标定理，我们将边界陈-西蒙斯拓扑整数唯一地映射为具有明确物理意义的晓晓半径 R = \ell_P \sqrt{\tilde{\eta}} ，其中拓扑量子数 \tilde{\eta} 由宇宙空间截面的自旋配边类一次性确定，无连续可调参数。该半径在量子层面上定义时空的拓扑熵 S_{\text{top}} = \pi k_B (R/\ell_P)^2 ，成为引力与惯性的起源。理论不包含任何连续可调参数，数值预言仅依赖于整数 \tilde{\eta} 与基本常数 \hbar、c、G。由晓晓半径可直接导出：（1）引力常数 G 的微观解释；（2）考虑量子拓扑涨落后宇宙常数的有效值 \Lambda_{\text{eff}} = +3/R_U^2，与 Planck 2018 观测值在 3.6\sigma 内一致；（3）星系旋转曲线精确描述，对SPARC样本拟合优度 \chi^2/\text{d.o.f.} = 1.04，优于传统冷暗物质模型。本工作将引力的本质归结于时空拓扑量子基准，并提供可在太赫兹与纳赫兹波段检验的实验预言。
物理学自然科学研究方法自然科学理论
晓晓半径拓扑熵量子引力宇宙常数暗物质APS指标定理
张雁秋.时空的量子基准：基于晓晓半径的拓扑熵引力理论[EB/OL].(2025-10-30)[2025-11-02].https://chinaxiv.org/abs/202510.00196.点此复制
We propose the Xiaoxiao Radius as a fundamental quantum benchmark that unifies quantum gravity with macroscopic cosmological phenomena. By means of the AtiyahPatodiSinger index theorem, the boundary ChernSimons topological invariant is uniquely mapped onto a physically meaningful length scalethe Xiaoxiao Radiusdefined asR = _P ,_P = (G/c),where the topological quantum number is fixed once and for all by the spin-cobordism class of a spatial section of the Universe and contains no continuous tunable parameters. At the quantum level this radius encodes the topological entropyS{top} = k_B (R/_P),which is argued to be the microscopic origin of both gravitation and inertia. The theory is parameter-free; all numerical predictions depend only on the integer and the fundamental constants , c, G. From the Xiaoxiao Radius we derive:(1) a microphysical explanation of Newtons constant G;(2) an effective cosmological constant {eff} = +3/R_U that agrees with the Planck 2018 measurement to within 3.6;(3) a modified gravitational potential that accurately reproduces the flat rotation curves of 175 SPARC galaxies (/d.o.f. = 1.04), outperforming the standard cold-dark-matter model. The work reduces gravity to a topological quantum benchmark of spacetime and yields testable predictions in the terahertz and nanohertz bands.ORCID: https://orcid.org/0009-0004-4870-9470Keywords Xiaoxiao radius; topological entropy; quantum gravity; cosmological constant; dark matter; APS index theorem
Xiaoxiao radiustopological entropyquantum gravitycosmological constantdark matterAPS index theorem
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