distance oscillations using LLR. Since time dilation is already confirmed to high precision, a positive result would prove that light speed depends on the observer's velocity and length contraction is direction dependent (like in the other Kennedy–Thorndike experiments). However, no anomalous distance oscillations have been observed, with a RMS velocity dependence limit of , comparable to that of Hils and Hall (1990, see table above on the right). Vacuum dispersion Another effect often discussed in connection with quantum gravity (QG) is the possibility of dispersion of light in vacuum (i.e. the dependence of light speed on photon energy), due to Lorentz-violating dispersion relations. This effect should be strong at energy levels comparable to, or beyond the Planck energy GeV, while being extraordinarily weak at energies accessible in the laboratory or observed in astrophysical objects. In an attempt to observe a weak dependence of speed on energy, light from distant astrophysical sources such as gamma ray bursts and distant galaxies has been examined in many experiments. Especially the Fermi-LAT group was able show that no energy dependence and thus no observable Lorentz violation occurs in the photon sector even beyond the Planck energy, which excludes a large class of Lorentz-violating quantum gravity models. Vacuum birefringence Lorentz violating dispersion relations due to the presence of an anisotropic space might also lead to vacuum birefringence and parity violations. For instance, the polarization plane of photons might rotate due to velocity differences between left- and right-handed photons. In particular, gamma ray bursts, galactic radiation, and the cosmic microwave background radiation are examined. The SME coefficients and for Lorentz violation are given, 3 and 5 denote the mass dimensions employed. The latter corresponds to in the EFT of Meyers and Pospelov by , being the Planck mass. Maximal attainable speed Threshold constraints Lorentz violations could lead to differences between the speed of light and the limiting or maximal attainable speed (MAS) of any particle, whereas in special relativity the speeds should be the same. One possibility is to investigate otherwise forbidden effects at threshold energy in connection with particles having a charge structure (protons, electrons, neutrinos). This is because the dispersion relation is assumed to be modified in Lorentz violating EFT models such as SME. Depending on which of these particles travels faster or slower than the speed of light, effects such as the following can occur: Photon decay at superluminal speed. These (hypothetical) high-energy