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We consider the action principle to derive the classical, relativistic motionof a self-interacting particle in a 4-D Lorentzian spacetime containing awormhole and which allows the existence of closed time-like curves. Inparticular, we study the case of a pointlike particle subject to a`hard-sphere' self-interaction potential and which can traverse the wormhole anarbitrary number of times, and show that the only possible trajectories forwhich the classical action is stationary are those which are globallyself-consistent. Generically, the multiplicity of these trajectories (definedas the number of self-consistent solutions to the equations of motion beginningwith given Cauchy data) is finite, and it becomes infinite if certainconstraints on the same initial data are satisfied. This confirms the previousconclusions (for a non-relativistic model) by Echeverria, Klinkhammer andThorne that the Cauchy initial value problem in the presence of a wormhole`time machine' is classically `ill-posed' (far too many solutions). Our resultsfurther extend the recent claim by Novikov et al. that the `Principle ofself-consistency' is a natural consequence of the `Principle of minimalaction.'Comment: 39 pages, latex fil

international journal of modern physics d

TIME MACHINES AND THE PRINCIPLE OF SELF-CONSISTENCY AS A CONSEQUENCE OF THE PRINCIPLE OF STATIONARY ACTION (II): THE CAUCHY PROBLEM FOR A SELF-INTERACTING RELATIVISTIC PARTICLE