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

TL;DR

This paper argues that relativistic multi-particle systems cannot generally be modeled as mechanical systems due to fundamental conflicts between their induced absolute time and particles' proper times.

Contribution

It provides a mathematical proof showing the incompatibility of relativistic multi-particle trajectories with mechanical system descriptions.

Findings

Relativistic multi-particle systems cannot be described by second order differential equations.

The induced absolute time conflicts with particles' proper times in relativistic settings.

Mechanical systems are incompatible with the relativistic description of multiple particles.

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.