No 2, Vol. 27, 2011, pages 195-202

IN SPACETIMES WITH TIME MACHINES

A rough similarity between self-inconsistent evolutions of classical solid balls in spacetimes with wormholes (serving as time machines) and evolutions of quantum-mechanical microparticles is discussed. Within our discussion, wormholes are specified by a microscopic typical size of their mouths, and classical solid balls are divided into two categories: small and large balls. For geometric reasons, small balls can move through wormholes with microscopic mouths, while traverse of large balls through wormholes is forbidden. A new principle of self-consistency is suggested which admits partially inconsistent evolutions of small solid balls on closed timelike curves associated with wormholes. According to the new principle, evolutions of small solid balls on closed timelike curves can be self-inconsistent (they can violate conventional causality), but these evolutions change the past of small solid balls in the way keeping evolutions of large solid balls unambiguous. With the new principle, self-inconsistent evolutions of small classical balls in spacetimes with wormholes are roughly similar to unitary evolutions of quantum microparticles. Also, in a rough approximation, specific collisions between large and small classical balls - collisions each resulting in absorption of a small ball (having ambiguous trajectories that violate conventional causality) by a large ball - in spacetimes with wormholes are similar to quantum-mechanical measurement (wave function reduction) events. |

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