At mesoscopic scales close to, but somewhat larger than, Planck length, one could describe quantum spacetime and matter in terms of a quantum-corrected geometry. The key feature of such a description is the introduction of a zero-point length into the spacetime. When we proceed from quantum geometry to quantum matter, the zero-point length will introduce corrections in the propagator of matter field in a specific manner. On the other hand, one cannot ignore the self-gravity of matter fields at the mesoscopic scales and this will also modify the form of the propagator. Consistency demands that these two modifications coming from two different directions are the same. I show that this nontrivial demand is actually satisfied. Surprisingly, the principle of equivalence, operating at Planck scales, ensures this consistency in a subtle manner.

中文翻译：

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普朗克尺度等价原理与时空零点长度——量子物质与几何的协同描述

在接近但略大于普朗克长度的介观尺度上，人们可以用量子校正几何来描述量子时空和物质。这种描述的关键特征是将零点长度引入时空。当我们从量子几何走向量子物质时，零点长度将以特定的方式在物质场的传播子中引入校正。另一方面，不能忽视介观尺度物质场的自引力，这也会改变传播子的形式。一致性要求来自两个不同方向的这两种修改是相同的。我证明了这个不平凡的需求实际上得到了满足。令人惊讶的是，在普朗克尺度上运行的等效原理以一种微妙的方式确保了这种一致性。