4-momentum

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Including a time element of energy as

This four element vector transforms as a tensor

And as such constitutes a four-vector, a rank 1 tensor, called the 4-momentum. The mass of a particle is an invariant given by the spacetime length of the 4-momentum according to

which for the metric of special relativity yeilds

For a particle with mass, the 4-momentum can be related to the 4-velocity by