International Journal of Theoretical Physics, Vol. 38, No. 8, 1999 Escape to Infinity Jon Perez Laraudogoitia 1 Received January 19, 1999 This paper shows how solutions to the equations of Newtonian mechanics, which become unbounded in a finite time, may be obtained for the case of rigid bodies of an arbitrary size subject to mutual elastic collisions alone, without any gravitational interaction. The absence of gravitation makes it possible to obtain by a new procedure a sort of singularity similar to those found for the n-body problem over the past 20 years. The solutions found for the equations in dynamics which, for initial conditions given at t0, become unbounded in a finite time are interesting for at least two reasons: (a) they constitute cases of singular solutions, that is, solutions defined analytically on some maximal interval [t0, t1), with t 1 , `; and (b) they lead to a peculiar form of nondeterministic evolution of dynamic systems, since if lim t®t 1 )(q i (t)) 51`, so that the system particles escape to infinity in a finite time, the temporal inversion of this process entails the unpredictable and spontaneous appearance of particles coming from spatial infinity. A solution which becomes unbounded in a finite time naturally requires that the velocity (and therefore the kinetic energy) of the particles involved also grows in an unbounded way in that time. Mather and McGehee (1975) showed how this can happen by considering point particles subject to their mutual gravitational interaction and likewise subject to elastic binary colli- sions between some of them. More specifically, they used a system with four point particles in unidimensional movement, and they fixed initial conditions so that the distance )r i 2 r j) between two particular particles tended to zero for t ® t 1 . In such a case their potential gravitatory energy of interaction 2 Gmi mj /)ri 2 rj ) tends to 2` for t ® t1 and, as the system is conservative, 1 Departamento de Logica y Filosofia de la Ciencia Universidad del Pais Vasco, 01006 Vitoria Gasteiz, Spain. 2231 0020-7748/99/0800-223 1$16.00/0 q 1999 Plenum Publishing Corporation