  An infinite number of elastically colliding balls is considered in a
classical, and then in a relativistic setting. Energy and momentum are not
necessarily conserved globally, even though each collision does separately
conserve them. This result holds in particular when the total mass of all the
balls is finite, and even when the spatial extent and temporal duration of the
process are also finite. Further, the process is shown to be indeterministic:
there is an arbitrary parameter in the general solution that corresponds to the
injection of an arbitrary amount of energy (classically), or energy-momentum
(relativistically), into the system at the point of accumulation of the
locations of the balls. Specific examples are given that illustrate these
counter-intuitive results, including one in which all the balls move with the
same velocity after every collision has taken place.
