Difference between revisions of "Noether's Theorem"
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'''Noether's theorem''' is a mathematical theorem that relates [[symmetry|symmetries]] of a [[Hamiltonian]] or [[Lagrangian Dynamics|Lagrangian]] system to conserved quantities. The theorem states that for every continuous symmetry there is a conservation law. For example, the invariance of time translation (i.e, the laws of physics do not change with time) leads to the conservation of energy. The invariance of spatial translation (i.e, the laws of physics are the same everywhere) leads to conservation of momentum. | '''Noether's theorem''' is a mathematical theorem that relates [[symmetry|symmetries]] of a [[Hamiltonian]] or [[Lagrangian Dynamics|Lagrangian]] system to conserved quantities. The theorem states that for every continuous symmetry there is a conservation law. For example, the invariance of time translation (i.e, the laws of physics do not change with time) leads to the conservation of energy. The invariance of spatial translation (i.e, the laws of physics are the same everywhere) leads to conservation of momentum. | ||
| + | ==See also== | ||
| + | [http://math.ucr.edu/home/baez/noether.html Noether's Theorem in a Nutshell] | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
[[Category:Physics]] | [[Category:Physics]] | ||
Revision as of 12:59, October 1, 2011
Noether's theorem is a mathematical theorem that relates symmetries of a Hamiltonian or Lagrangian system to conserved quantities. The theorem states that for every continuous symmetry there is a conservation law. For example, the invariance of time translation (i.e, the laws of physics do not change with time) leads to the conservation of energy. The invariance of spatial translation (i.e, the laws of physics are the same everywhere) leads to conservation of momentum.
