Four-momentum

In special relativity, four-momentum is a four-vector that replaces classical momentum; the four-momentum of a particle is defined as the particle's mass times the particle's four-velocity.

Since the four-velocity is a unit four-vector, the length of the four-momentum is equal to the mass.

In reactions between an isolated handful of particles, four-momentum is conserved. The mass of a system of particles may be more than the sum of the particle's masses, since kinetic energy counts as mass. As an example, two particles with the four-momentums {5, 4, 0, 0} and {5, -4, 0, 0} both have the mass 3, but their total mass is 10. (Note that the length of the four-vector {t, x, y, z} is .)

The scalar product of a four-momentum and the corresponding four-acceleration is always 0.

See also: four-vector, four-velocity, four-acceleration, four-force.