An obstacle to building a time machine

Gott has shown that a spacetime with two infinite parallel cosmic strings passing each other with sufficient velocity contains closed timelike curves. We discuss an attempt to build such a time machine. Using the energy-momentum conservation laws in the equivalent (2+1)-dimensional theory, we explicitly construct the spacetime representing the decay of one gravitating particle into two. We find that there is never enough mass in an open universe to build the time machine from the products of decays of stationary particles. More generally, the Gott time machine cannot exist in any open (2+1)-dimensional universe for which the total momentum is timelike.