According to Granot, these results "strongly disfavour" quantum-gravity theories in which the speed of light varies linearly with photon energy, which might include some variations of string theory or loop quantum gravity. "I would not use the term 'rule out'," he says, "as most models do not have exact predictions for the energy scale associated with this violation of Lorentz invariance. However, our observational requirement that such an energy scale would be well above the Planck energy makes such models unnatural."