Time machines: the Principle of Self-Consistency as a consequence of the Principle of Minimal Action

TL;DR

This paper demonstrates that the principle of self-consistency in time travel scenarios naturally emerges from the classical principle of minimal action, using a particle model in a wormhole spacetime.

Contribution

It shows that the principle of self-consistency is a direct consequence of the action principle in a classical particle model with self-interaction in a wormhole spacetime.

Findings

Self-consistent trajectories are the only minimal action solutions.

The principle of self-consistency arises naturally from the action principle.

Applicable to particles traversing wormholes with fixed endpoints.

Abstract

We consider the action principle to derive the classical, non-relativistic motion of a self-interacting particle in a 4-D 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.'