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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