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