Billiard in the space with a time machine

Details Billiard in the space with a time machine Billiard in the space with a time machine

2010-11-12

arxiv.org/abs/1011.2881v1

Phys.Rev.D82:124056,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, 16 figures

Scientific paper

10.1103/PhysRevD.82.124056

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a consistent evolution, including those `paradoxical' ones, for which the inconsistent collision-free trajectory is superseded by a special consistent self-colliding trajectory.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.

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