One of the simplest non-trivial examples of a four-tensor is the four-displacement , a four-tensor with contravariant rank 1 and covariant rank 0. Four-tensors of this kind are usually known as four-vectors. Here the component gives the displacement of a body in time (time is multiplied by the speed of light so that has dimensions of length). The remaining components of the four-displacement form the spatial displacement vector .
Similarly, the four-momentum of a body is equivalent to the energy-momentum tensor of said body. The element represents the momentum of the body as a result of it travelling through time (directly comparable to the internal energy of the body). The elements , and correspond to the momentum of the body as a result of it travelling through space, written in vector notation as .
- Lambourne, Robert J A. Relativity, Gravitation and Cosmology. Cambridge University Press. 2010.
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