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Theorem

Noether's Theorem

NUR-ter, German [ˈnøːtɐ]; named for Emmy Noether
Also Known As Noether's First Theorem
Mathematical Physics

Noether's theorem states that every continuous symmetry of a physical system's action corresponds to a conserved quantity: rotational symmetry yields conservation of angular momentum, translational symmetry yields conservation of momentum, and time-translation symmetry yields conservation of energy. Emmy Noether proved it in 1918, and it has become one of the most cited results connecting mathematics to physics. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Statement
For every continuous symmetry of the action of a physical system, there is a corresponding conservation law. 1
Proof Year
1918 1
Classification
Statement Form
Existence Theorem 1
FAQs

What problem led Emmy Noether to the theorem linking symmetry and conservation?

It grew out of a special relativity problem she worked on at Göttingen at the invitation of Hilbert and Klein.

Hilbert was working on physics, in particular on ideas on the theory of relativity close to those of Albert Einstein, and decided he needed the help of an expert on invariant theory. He and Klein invited Noether to Göttingen, and one of the problems she took up there came from special relativity. She proved that to every infinitesimal transformation of the Lorentz group there corresponds a conservation theorem. This result is sometimes referred to as Noether's theorem, and it establishes a relationship between symmetries in physics and conservation principles.
Connections

Has Statement Form

Existence Theorem, Concepts

In Branch

Mathematical Physics, Branches of Mathematics
Source Wikipedia: Noether's Theorem

Named After

Emmy Noether, Mathematicians

Proved By

Emmy Noether, Mathematicians
Source Wikipedia: Noether's Theorem
Sources
1. Wikipedia: Noether's Theorem
Wikimedia Foundation
  • Introduction
    If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time.
  • History
    Emmy Noether in 1918
  • In Category: Theorems
  • In Branch: Mathematical Physics
  • Proved By: Emmy Noether
  • In Group: Classical Mechanics and Dynamics, Lead section
    formulation is quite general and has been applied across classical mechanics, high energy physics, and recently statistical
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