# What theorems did Emmy Noether discover?

## What theorems did Emmy Noether discover?

In 1918 she proved two theorems that were basic for both general relativity and elementary particle physics. One is still known as “Noether’s Theorem.” During the 1920s Noether did foundational work on abstract algebra, working in group theory, ring theory, group representations, and number theory.

What is Emmy Noether’s theorem?

Noether’s theorem proclaims that every such symmetry has an associated conservation law, and vice versa — for every conservation law, there’s an associated symmetry. Conservation of energy is tied to the fact that physics is the same today as it was yesterday.

### How is Noether’s theorem used today?

Every time scientists use a symmetry or a conservation law, from the quantum physics of atoms to the flow of matter on the scale of the cosmos, Noether’s theorem is present. Conservation of energy comes from time-shift symmetry: You can repeat an experiment at different times, and the result is the same.

Who was the first person to prove Noether’s theorem?

Noether’s theorem. The theorem was proven by mathematician Emmy Noether in 1915 and published in 1918, although a special case was proven by E. Cosserat & F. Cosserat in 1909. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function ),…

#### What kind of symmetries does Noether’s theorem apply to?

This theorem only applies to continuous and smooth symmetries over physical space . Noether’s theorem is used in theoretical physics and the calculus of variations.

When did Noether’s theorem apply to Hamiltonian mechanics?

A generalization of the formulations on constants of motion in Lagrangian and Hamiltonian mechanics (developed in 1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian alone (e.g., systems with a Rayleigh dissipation function ).

## Are there natural quantum counterparts of Noether’s theorem?

There are natural quantum counterparts of this theorem, expressed in the Ward–Takahashi identities. Generalizations of Noether’s theorem to superspaces also exist. If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time.