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

A. Carlini·V. P. Frolov·M. B. Mensky·I. D. Novikov·H. H. Soleng
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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.'

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A. Carlini, V. P. Frolov, M. B. Mensky, I. D. Novikov, H. H. Soleng. 1996-02-07. Time machines: the Principle of Self-Consistency as a consequence of the Principle of Minimal Action. https://doi.org/10.1142/s0218271896000588

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