Mohamed and I have a new paper out on the emergence of a common speed of light in theories where different particles have different limiting speeds (the speed of the particle at very high energy). The motivation of this is that if a universal Lorentz invariance is not imposed, the wave equations of different particles will in general contain different velocities in the relation between time derivatives and space derivatives. Mohamed and I show that if the different particles are interacting, then the interactions yield a scale dependence to this limiting velocity, and the velocities approach each other at low energy. This can be a mechanism for the emergence of a universal speed of light and Lorentz invariance at low energy. There is more to the story, and it is not clear if this mechanism can be effective enough to satisfy the experimental constraints, and this is discussed in the paper.