Statement 1 - Let's assume a charged particle emitting radiation isotropically in it's rest frame, when boosted in another frame we get the relativistic beaming effect. This results in anisotropy of the radiation emitted by the charged particle in the boosted frame. Statement 2 - But a particle emitting an-isotropically (like beaming) in it's rest frame should have a non-zero back reaction force on it, for the radiated energy comprises a non-zero (i.e net) momentum in the forward direction. My question is, since an inertial particle emitting isotropically have zero four force vector in it's rest frame, transforming this vector to any boosted frame should again give the zero four force. But according to statement 2 we should have a non-zero back reaction force on the emitting particle. That is, is there a difference between, a particle described by statement 2 and a particle viewed in a boosted frame in statement 1. Thanks.