The canonical Lorentzian manifold is Minkowski spacetime, where M = R 4 and g is the flat Minkowski metric. The names for the tangent vectors come from the physics of this model. The causal relationships between points in Minkowski spacetime take a particularly simple form because the tangent space is also R 4 and hence the tangent vectors may be identified with points in the space. The four-dimensional vector X = ( t , r ) is classified according to the sign of g ( X , X ) = − − c 2 t 2 + ‖ ‖ r ‖ ‖ 2 , where r ∈ ∈ R 3 is a Cartesian coordinate in 3-dimensional space, c is the constant representing the universal speed limit, and t is time. The classification of any vector in the space will be the same in all frames of reference that are related by a Lorentz transformation (but not by a general Poincaré transformation because the origin may then be displaced) because of the invariance of the metric.