For interacting particles we postulate that
is conserved [ where i labels the particle ] since this is the natural analogue of Newton's law .
Conservation of the time component corresponds to energy conservation [ with rest mass being included in this ]. Conservation of spatial components corresponds to conservation of three- momentum.
Note that 
is evaluated at a particular time by
different observers and they will see different events as
simultaneous. However will be conserved in all
frames.
The center of momentum frame for a particular system of particles is the one in which
