Home / Topics / Momentum & Collisions
Momentum conservation and symmetry
Advanced
Translational symmetry of space implies conservation of momentum.
Noether's theorem: if the laws don't change when the system is shifted in space (translation symmetry), total momentum is conserved.
This is why momentum is conserved in all known interactions.
Conservation can fail in an external potential that breaks the symmetry.
In more detail
Momentum conservation is linked to spatial translation symmetry. By Noether's theorem, the laws of physics being the same everywhere implies that total momentum is conserved.
Real-world uses
- Physicists use symmetry arguments to predict conservation laws in new theories.
- The idea underlies particle classification in the Standard Model.
- Physicists argue that momentum is conserved because the laws of physics do not depend on the position in space where an experiment is done.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
What symmetry gives momentum conservation?
Translation symmetry, the fact that the laws do not change with position.
Who discovered this link?
Emmy Noether proved the general result in 1918.
Which symmetry gives momentum conservation?
Translational symmetry, which means the laws of physics are the same at every location.
Related topics in Momentum & Collisions
Sports impulse examples · Momentum and kinetic energy relation · Hamiltonian momentum