### arXiv:1907.05412 [math-ph]AbstractReferencesReviewsResources

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

Jesús Muñoz-Díaz, Ricardo J. Alonso-Blanco

Published 2019-07-11Version 1

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

**Subjects:**83Axx

arXiv:1707.03651 [math-ph] (Published 2017-07-12)

Time in classical and quantum mechanics

arXiv:1205.6353 [math-ph] (Published 2012-05-29)

Coherent Orthogonal Polynomials

arXiv:1109.0126 [math-ph] (Published 2011-09-01)

On simulating a medium with special reflecting properties by Lobachevsky geometry (One exactly solvable electromagnetic problem)