  The discovery by Gott of a remarkably simple spacetime with closed timelike
curves (CTC's) provides a tool for investigating how the creation of time
machines is prevented in classical general relativity. The Gott spacetime
contains two infinitely long, parallel cosmic strings, which can equivalently
be viewed as point masses in (2+1)-dimensional gravity. We examine the
possibility of building such a time machine in an open universe. Specifically,
we consider initial data specified on an edgeless, noncompact, spacelike
hypersurface, for which the total momentum is timelike (i.e., not the momentum
of a Gott spacetime). In contrast to the case of a closed universe (in which
Gott pairs, although not CTC's, can be produced from the decay of stationary
particles), we find that there is never enough energy for a Gott-like time
machine to evolve from the specified data; it is impossible to accelerate two
particles to sufficiently high velocity. Thus, the no-CTC theorems of Tipler
and Hawking are enforced in an open (2+1)-dimensional universe by a mechanism
different from that which operates in a closed universe. In proving our result,
we develop a simple method to understand the inequalities that restrict the
result of combining momenta in (2+1)-dimensional gravity.
