Time Machines:. the Principle of Self-Consistency as a Consequence of the Principle of Minimal Action

We consider the action principle to derive the classical, nonrelativistic motion of a self-interacting particle in a 4D Lorentzian spacetime containing a wormhole and which allows the existence of closed time-like curves. For the case of a “hard-sphere” self-interaction potential we show that the only possible trajectories (for a particle with fixed initial and final positions and which traverses the wormhole once) minimizing the classical action are those which are globally self-consistent, and that the “principle of self-consistency” (originally introduced by Novikov) is thus a natural consequence of the “principle of minimal action.”