Coordinate transformations Up until now we have assumed that we are given a specific coordinate system and its associated coordinates basis. However, we should also consider what will happen when we transform to a different set of coordinates. This is important as coordinates are in fact arbitrary labels for points in a manifold, and you might want to choose different coordinates under different circumstances. For instance, in the particular case of special relativity, you wish to use the coordinates associated with a given inertial frame, ot those associated with a different inertial frame...