Illustrating some implications of the conservation laws in relativistic mechanics

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 mass. Extension of the nonrelativistic interaction of particles through a potential to a system that is Lorentz-invariant through order v2∕c2 is found to require new velocity- and acceleration-dependent forces that are suggestive of a field theory where the no-interaction theorem of Currie, Jordan, and Sudershan does not hold.