Conservation Laws and Symmetry (Noether’s Theorem)

Today, when I was studying a mechanics textbook, I found something interesting. It was mentioned that symmetries and conservation laws are closely related. As an example, energy conservation corresponds to the time-translation symmetry in time (which means the laws of physics do not change according to time). The conservation of momentum corresponds to the space-translation symmetry, while the conservation of angular momentum has the rotational symmetry as its corresponding symmetry.

For detailed explanation of Noether’s Theorem, you might want to look at this post:

Emmy Noether was a female German mathematician Emmy Noether, and her life story is quite interesting. Here is a New York Times article about Emmy Noether:


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