# Why can you treat coordinates as vector in flat spacetime?

In a manifold there is a distinction between points and vectors, but in flat spacetime this seems to disappear.

For example in Minkowski spacetime you can define a coordinate 4-vector $(x_0,x_1,x_2,x_3)=(ct,x,y,z)$ and do whatever you do with usual vectors (norm, scalar product, components transformations...). The point is that if you are in a general manifold you can't to this, because the coordinates of a point are not components of a vector.

Why is this legitimate?

• Because Minkowski space is $\mathbb{R}^4$, which is a vector space? – ACuriousMind Jan 3 '15 at 17:09