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

2019/07/11 by Muñoz-Díaz, Jesús, Alonso-Blanco, Ricardo J.
#70xx #83Axx #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1907.05412

Abstract

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.

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