Institute of Theoretical Physics · Faculty of Mathematics and Physics, Charles University
Phys. Rev. D 82, 124056 (2010)
We study a system of an elastic ball moving in the non-relativistic spacetime with a nontrivial causal structure produced by a wormhole-based time machine. For such a system it is possible to formulate a simple model of the so-called `grandfather paradox': for certain `paradoxical' initial conditions the standard straight trajectory of the ball would self-collide inconsistently. We analyze globally consistent solutions of local equations of motion, namely, we find all trajectories with one self-collision. It is demonstrated that all standard initial conditions have a consistent evolution, including those `paradoxical' ones, for which the inconsistent collision-free trajectory is superseded by a special consistent self-colliding trajectory. Moreover, it is shown that for a wide class of initial conditions more than one globally consistent evolution exist. The nontrivial causal structure thus breaks the uniqueness of the classical theory even for locally deterministic physical laws.
@article{UTF423,
author = {Dolanský, J. and Krtouš, P.},
title = {{Billiard in the space with a time machine}},
journal = {Phys. Rev. D},
volume = {82},
pages = {124056},
year = {2010},
doi = {10.1103/PhysRevD.82.124056},
eprint = {1011.2881},
archivePrefix = {arXiv},
}