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. | + | '''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. |
| + | This, this theorem by [[Amalie Emmi Noether|Amalie Noether]] allows physicists to extract important information by considering various transformations which leave the laws unchanged.<ref name="WhomadeGod">{{cite book | ||
| + | |author=Edgar Anrews | ||
| + | |title= Who made God? Searching for a theory of everything. | ||
| + | |publisher= EP Books | ||
| + | |location= Carlisle, PA, USA | ||
| + | |year= 2010 | ||
| + | |pages=149 | ||
| + | |isbn=978-0-85234-707-2 | ||
| + | |url=https://books.google.com/books?id=p5LkPwAACAAJ&dq=Andrews+Who+made&hl=en&sa=X&ei=ahTXUYX9A4qF4gTLoYGgCQ&ved=0CCsQ6AEwAA | ||
| + | |quote= }}</ref> | ||
| + | |||
| + | ==See also== | ||
| + | [http://math.ucr.edu/home/baez/noether.html Noether's Theorem in a Nutshell] | ||
| + | == References == | ||
| + | <references/> | ||
| + | |||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
| + | [[Category:Physics]] | ||
Latest revision as of 05:01, January 9, 2019
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. This, this theorem by Amalie Noether allows physicists to extract important information by considering various transformations which leave the laws unchanged.[1]
See also
References
- ↑ Edgar Anrews (2010). Who made God? Searching for a theory of everything.. Carlisle, PA, USA: EP Books, 149. ISBN 978-0-85234-707-2.