A vector quantity that expresses the relation of the velocity of a body, wave, field, or other physical system, to its energy. The direction of the momentum of a single object indicates the direction of its motion. Momentum is a conserved quantity (it remains constant unless acted upon by an outside force), and is related by
Noether's theorem to translational
invariance . In classical mechanics, momentum is defined as mass times velocity. The theory of Special Relativity uses the concept of
relativistic mass . The momentum of photons, which are massless, is equal to their energy divided by the speed of light. In quantum mechanics,
momentum more generally refers to a mathematical operator applied to the wave equation describing a physical system and corresponding to an
observable ; solutions to the equation using this operator provide the vector quantity traditionally called momentum. In all of these applications, momentum is sometimes called
linear momentum. See also
angular momentum, impulse.