  The deflection, though, means that the linear momentum of the particle has changed from what is was before L-. But that is impossible, by conservation of linear momementum. No matter how the incoming particle interacts with particles in the time-travel region, or how those particle interact with each other, total linear momentum is conserved by the interaction. And whatever net linear momentum the time-travelling particles have when they emerge from L-, that much linear momentum most be absorbed at L+. So the momentum of the incoming particle can't be changed by the interaction: the particle can't have been deflected. (One could imagine trying to create a sort of “S” curve in the trajectory of the incoming particle, first bending to the left and then to the right, which leaves its final momentum equal to its initial momentum, but moving it over in space so it misses L+. However, if the force at issue is repulsive, then the bending back to the right can't be done. In the mirror example above, the path of the incoming particle can be changed without violating the conservation of momentum because at the end of the process momentum has been transferred to the mirror.)