Since a world line w ( τ τ ) ∈ ∈ R 4 determines a velocity 4-vector v = d w d τ τ that is time-like, the Minkowski form η η ( v , x ) determines a linear function R 4 → → R by x ↦ ↦ η η ( v , x ) . Let N be the null space of this linear functional. Then N is called the simultaneous hyperplane with respect to v. The relativity of simultaneity is a statement that N depends on v. Indeed, N is the orthogonal complement of v with respect to η. When two world lines u and w are related by d u d τ τ = d w d τ τ , then they share the same simultaneous hyperplane. This hyperplane exists mathematically, but physical relations in relativity involve the movement of information by light. For instance, the traditional electro-static force described by Coulomb's law may be pictured in a simultaneous hyperplane, but relativistic relations of charge and force involve retarded potentials.