Newton's 3rd Law

Suppose that object i exerts a force $f_{j i}$ on the jth object. Likewise, suppose that the jth object exerts a force $f_{i j}$ on the ith object. These two forces are equal and opposite :

f_{j i} = - f_{i j}

It follows that:

An object cannot exert a force on itself
All forces in the Universe have corresponding reactions. The only exceptions to this rule are the fictitious forces which arise in non-inertial reference frames (ex. Coriolis)

This implies that a sudden change on the force acted upon one object should result to immediate change to the force acted upon the other object, independent of the distance between them. This contradicts Special Relativity (information cannot travel faster than the speed of light in vacuum) and therefore is not strictly correct. Therefore:

Condition

The 3rd Law can be regarded as a correct approximation for the investigation of motions of dynamical systems on timescales that are long compared to the time required for light-rays to traverse these systems.