On the equations of motion in Minkowski space

In this paper, we consider the question of addition, subtraction and transition of velocities as 4-vectors in the Minkowski space. The indeterminacies in the space of 4-velocities are discussed in detail and a new method for transition between 4-velocities using a transition tensor P of rank 2 is proposed. The most important properties as well as the physical and geometrical interpretations of the tensor P are also given. Finally, the tensor P is used in obtaining a nonlinear connection and the corresponding equations of motion. These equations differ from the Einstein-Infeld-Hoffmann equations by Lorentz invariant terms of order c(-2).