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Quantum or torsion gravity models predict unusual properties of space-time atvery short distances. In particular, near the Planck length, around$10^{-35}m$, empty space may behave as a crystal, singly or doubly refractive.This hypothesis, however, remains uncheckable for any direct measurement sincethe smallest distance accessible in experiment is about $10^{-19}m$ at the LHC.Here we propose a laboratory test to measure space birefringence orrefractivity induced by gravity. A sensitivity $10^{-31}m$ for doubly and$10^{-28}m$ for singly refractive vacuum could be reached with PETRA 6 GeV beamexploring UV laser Compton scattering.

Planck-scale gravity test at PETRA -- Letter of Intent