photons would quickly decay into other particles, which means that high energy light cannot propagate over long distances. So the mere existence of high energy light from astronomic sources constrains possible deviations from the limiting velocity. Vacuum Cherenkov radiation at superluminal speed of any particle (protons, electrons, neutrinos) having a charge structure. In this case, emission of Bremsstrahlung can occur, until the particle falls below threshold and subluminal speed is reached again. This is similar to the known Cherenkov radiation in media, in which particles are traveling faster than the phase velocity of light in that medium. Deviations from the limiting velocity can be constrained by observing high energy particles of distant astronomic sources that reach Earth. The rate of synchrotron radiation could be modified, if the limiting velocity between charged particles and photons is different. The Greisen–Zatsepin–Kuzmin limit could be evaded by Lorentz violating effects. However, recent measurements indicate that this limit really exists. Since astronomic measurements also contain additional assumptions – like the unknown conditions at the emission or along the path traversed by the particles, or the nature of the particles –, terrestrial measurements provide results of greater clarity, even though the bounds are wider (the following bounds describe maximal deviations between the speed of light and the limiting velocity of matter): Clock comparison and spin coupling By this kind of spectroscopy experiments – sometimes called Hughes–Drever experiments as well – violations of Lorentz invariance in the interactions of protons and neutrons are tested by studying the energy levels of those nucleons in order to find anisotropies in their frequencies ("clocks"). Using spin-polarized torsion balances, also anisotropies with respect to electrons can be examined. Methods used mostly focus on vector spin interactions and tensor interactions, and are often described in CPT odd/even SME terms (in particular parameters of bμ and cμν). Such experiments are currently the most sensitive terrestrial ones, because the precision by which Lorentz violations can be excluded lies at the 10−33 GeV level. These tests can be used to constrain deviations between the maximal attainable speed of matter and the speed of light, in particular with respect to the parameters of cμν that are also used in the evaluations of the threshold effects mentioned above. Time dilation The classic time dilation experiments such as the Ives–Stilwell experiment, the Moessbauer rotor experiments, and the time dilation of moving particles, have been enhanced by modernized equipment.