The Four-momentum reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

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.

where

is the energy of the moving body.

Calculating the norm of the momentum-energy quad-vector we obtain:

and since c is a constant we may say that the norm of the four-momentum vector is equal to the body's mass.

If we choose to take the velocity of light as c = 1, then the norm 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.

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