On the Post-Galilean Approximation for Weakly Relativistic Systems

The goal of the paper is to explain some recently published paradoxical results of using of so-called post-galilean approximation (weak relativity) in classical electrodinamics of two electron system. This approximation leads to singular behaviour (a jump of velocities) of the system at very small distances. We study the same problem without assumption of weak relativity and show that the motion is completely regular. Precise estimations for minimal distance between electrons are obtained. It is shown that the above mentioned singularities are merely connected with the fact that the post-galilean approximation can not be used at very small distances even for particles with small velocities V « N. Finally we discussed the applicability of the post-galilean approximation in general context and formulate the conditions of its validity for any central potential.