Billiard ball in the space with a time machine

Jindřich Dolanský and Pavel Krtouš
Phys. Rev. D 82, 124056 – Published 23 December 2010

Abstract

We study a system of an elastic ball moving in the nonrelativistic 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have a consistent evolution, including those paradoxical ones, for which the inconsistent collision-free trajectory is superseded by a special consistent self-colliding trajectory.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.

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  • Received 12 October 2010

DOI:https://doi.org/10.1103/PhysRevD.82.124056

© 2010 The American Physical Society

Authors & Affiliations

Jindřich Dolanský* and Pavel Krtouš

  • Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 180 00 Prague 8, Czech Republic

  • *dolanskyy@gmail.com
  • Pavel.Krtous@utf.mff.cuni.cz

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Issue

Vol. 82, Iss. 12 — 15 December 2010

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