Noether's theorem: Difference between revisions

Revision as of 21:54, 7 October 2003

Revision as of 10:47, 27 October 2003

Line 1:

'''Noether's theorem''' is a very crucialcentral result in [[theoretical physics|theoretical]] [[physics]] that expresses the equivalence of two different properties of [[physical law]]s,. It is named after the formermathematician being[[Emmy thatNoether]] of the early [[20th century]].

Two aspects are related, one being the [[invariance]] of the form that the law takes with respect to any (generalized) transformation that preserves the coordinate system (both spatial and temporal aspects taken into consideration) is subject to, and the latterother being a [[conservation law]] of a physical quantity. It is named after the mathematician [[Emmy Noether]] of the early [[20th century]].

Informally, Noether's theorem can be stated as:

Line 5 ⟶ 7:

:''To every [[symmetry]], there corresponds a [[conservation law]]'' and vice versa.

The formal statement of the theorem derives an expression for the physical quantity that is conserved (and hence also defines it), from the condition of invariance alone. For example, :

* the invariance of physical systems with respect to translation (when simply stated, it is just that the laws of physics don't vary with ___location in space) translates into the law of conservation of [[linear momentum]].

* the invariance of physical systems with respect to rotationtranslation gives(when simply stated, it is just that the laws of physics don't vary with ___location in space) translates into the law of conservation of [[angularlinear momentum]];

* invariance with respect to rotation gives law of conservation of [[angular momentum]];

* invariance with respect to time gives the well known [[law of conservation of energy]], et cetera.