Thinking about a light wave from our ordinary frame of space and time, the light wave runs through the space oscillatingly by the speed light speed c. Maxwell's equaions tell us that the fluctuation of electric field induces the fluctuating magnetic field, and in turn, the fluctuating magnetic field induces the fluctuating electric field. Thus the light propagation, i.e., the electromagnetic wave propagation process is a self-sustained process. There is no problem in this view of light popagation process that is sustained by the mutual alternative induction of electric and magnetic fields, because it is exactly written in the Maxwell's equations.
rot E + dB/dt =0 (1)
rot H - dD/dt =0 (2)
But the problem is this! If we are riding on the beam of light, then the time will stand still, which means that the both of electric field and magnetic field are or will be frosen! That is, if we are riding on the beam of light, then there is no room where the usual Maxwell's equations can hold! That is, though we talk about photon or light wave as if we already understand it well, we actually have not yet know its true creation process nor its annihilation process. How can we imagine a creation process of a frosen electromagnetic wave that pops in this world suddenly at the instance of electronic transition in an atom?