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We will prove that, in general, a system formed by several particles movingalong relativistic trajectories can not be described by a mechanical system.The contradiction that leads to the previous assertion is due to the fact thata mechanical system defines a second order differential equation and this, inturn, induces an absolute time that will generally be incompatible with theproper times of the different particles.

A mathematical objection to the existence of relativistic mechanical systems of several particles