Hello to everybody, the question seems trivial in my mind, yet, is it legal to say that there is not unique frame of 0 total momentum in the Minkowski spacetime plane? I am thinking of two non-accelerating equal masses on a horizontal plane, one is moving horizontally, the other perpendicularly as their respective 2-velocities in the Minkowski spacetime plane indicate. A quick way to find the frame of 0-momentum, one either moves along with the horizontal moving mass and Lorentz-transforms the velocity of the other mass, or does it by following the perpendicularly pointed mass. These two separate methods yield two different results as to the direction of the respected 2-velocities of the masses in the Minkowski plane, very much unlike the Newtonian case where they're the same regardless. So in this case, there must be two frames of 0-momentum. Is this legal to say, or they both cannot be told apart?