Illustrating Some Implications of the Conservation Laws in Relativistic Mechanics

TL;DR

This paper reviews conservation laws in relativistic mechanics, highlighting differences from nonrelativistic laws and exploring implications for Lorentz-invariant systems with velocity- and acceleration-dependent forces.

Contribution

It provides simple illustrations of relativistic conservation laws and extends nonrelativistic particle interactions to Lorentz-invariant systems with new velocity- and acceleration-dependent forces.

Findings

Relativistic conservation law involving the center of energy is more restrictive.

Extending nonrelativistic potentials to relativistic systems requires new forces.

Field theory concepts emerge where no-interaction theorem does not hold.

Abstract

The conservation laws of nonrelativistic and relativistic systems are reviewed and some simple illustrations are provided for the restrictive nature of the relativistic conservation law involving the center of energy compared to the nonrelativistic conservation law for the center of restmass. Extension of the nonrelativistic interaction of particles through a potential to a system which is Lorentz-invariant through order v^2/c^2 is found to require new velocity- and acceleration-dependent forces which are suggestive of field theory where the no-interaction theorem of Currie, Jordan, and Sudershan does not hold.