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Testing Planck scale gravity with accelerators

Quantum or torsion gravity models predict unusual properties of space-time at very short distances. In particular, near the Planck length, around 1E-35 m, empty space may behave as a crystal, singly or doubly refractive. However, this hypothesis remains uncheckable for any direct measurement since the smallest distance accessible in experiment is about 1E-19 m at the LHC. Here I propose a laboratory test to measure the space refractivity and birefringence induced by gravity. A sensitivity from 1E-31m down to the Planck length could be reached at existent GeV and future TeV energy lepton accelerators using laser Compton scattering. There are already experimental hints for gravity signature at distances approaching the Planck length by 5-7 orders of magnitude, derived from SLC and HERA data.