Principle of equivalence at Planck scales and the zero-point length of spacetime

摘要

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.