The predicted quantum gravitational effects are very subtle and extraordinarily difficult to measure. We expect that they become relevant at the so-called Planck scale of lengths or energies. In particular, the Planck energy is approximately GeV, while the highest energies achieved in the contemporary particle accelerator experiments are GeV. These 15 orders of magnitude discrepancy means that studying physics at the Planck scale is beyond the range of even future conceivable accelerators.
However, the situation is not as hopeless as it may seem. The chance to empirically verify some predictions of quantum gravity is provided by astrophysical and cosmological observations. Two main approaches may be distinguished here. The first one is based on looking for quantum effects in the early Universe, by studying such quantities as correlations in the cosmic microwave background radiation. The second approach uses the fact that tiny quantum gravitational corrections can in principle be enhanced for particles produced in astrophysical events and travelling to us from the extremely large distances, so that these corrections eventually become measurable. In particular, it concerns high energetic photons and neutrinos from the gamma ray bursts.