The development of relativistic physics requires the use of a geometry adequate to account for the structure of spacetime. Whereas special relativity describes the non-quantum physical world in a nongravitational context in which spacetime is flat, the gravitational effects generated by general relativity must also account for the additional complexity of the curvature of spacetime.

Four-dimensional vectors thus take into account the special requirements of space-time geometry, i.e., the fact that space-time has four dimensions, as opposed to the three dimensions of Euclidean space. They accordingly have several applications in the context of relativistic physics. These applications include the use of translation vectors, which represent displacements in the four-dimensional continuum space-time model, the more abstract consequences of special relativity such as time dilation, length contraction or the addition of relativistic velocities, and the more elaborate descriptions of space and time by observers measuring...