The rest mass of a system of two photons in different inertial reference frames : 0 + 0 = 0 and 0 + 0 > 0

We show that the rest mass of a system consisting of two photons is a relativistic invariant having the same magnitude in all inertial reference frames in relative motion. A scenario which starts with two photons where their frequencies are equal to each other the magnitude of the rest mass of the system depends on the angle θ’, made by the momentums of the two photons being equal to zero for θ’=0 and θ’=2π and maximum (2hν’) for θ’=π. The behavior of the photons when detected from two inertial reference frames is illustrated using a relativistic diagram which displays in true values the physical quantities (scalar and vector) introduced in order to characterize the dynamical properties of the photon. We consider that the obtained results should be taken in the discussions, some time fierce, between those who ban the concept of relativistic mass and those who consider that its use is harmless. PACS: 03.30.+p