Principle of Equivalence makes effects of classical gravity vanish in local inertial frames. What role does the Principle of Equivalence play as regards quantum gravitational effects in the local inertial frames? I address this question here from a specific perspective. At mesoscopic scales close to, but somewhat larger than, Planck length one could describe quantum spacetime and matter in terms of an effective geometry. The key feature of such an effective quantum geometry is the existence of a zero-point-length. When we proceed from quantum geometry to quantum matter, the zero-point-length will introduce corrections in the propagator for matter fields 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 non-trivial demand is actually satisfied. Surprisingly, the Principle of Equivalence, operating at sub-Planck scales, ensures this consistency in a subtle manner.

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普朗克尺度的等效原理、局部惯性系中的 QG 和时空的零点长度

等效原理使经典重力效应在局部惯性系中消失。等效原理在局部惯性系中的量子引力效应方面起什么作用？我在这里从一个特定的角度来回答这个问题。在接近但稍大于普朗克长度的介观尺度上，人们可以根据有效几何学来描述量子时空和物质。这种有效量子几何的关键特征是零点长度的存在。当我们从量子几何学到量子物质时，零点长度将以特定方式在传播子中引入对物质场的修正。另一方面，不能忽视细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，这两种修改——来自两个不同的方向——是相同的。我表明这个非平凡的需求实际上得到了满足。令人惊讶的是，在亚普朗克尺度上运行的等效原理以微妙的方式确保了这种一致性。