Symmetries and Conservation Laws

[Lukeblackhill]

I've been caught by a quite interesting statement of Berkeley physics Course Vol.1 (Chap. 5), that says "In the physical world there exist a number of conservation laws, some exact and some approximate. A conservation law is usually the consequence of some underlying symmetry in the universe.".

I made a quick search on internet and found that a good thing to understand best this relationship between symmetries in a physical system and conservation laws, is the understanding of the so called "Noether's Theorem". I'd like to know if anyone has a better suggestion. My specific desire is to be able to identify which symmetry causes that particular conservation and why (for ex. I know the homogeneity of space is the cause of the conservation of linear momentum, but I haven't think about why).

Thank you!
Luke.

 

[anorlunda]

Noether's Theorem is indeed remarkable. There are some pretty good writeups on Wikipedia.

https://en.wikipedia.org/wiki/Noether's_theorem that describes how to derive it.
https://en.wikipedia.org/wiki/Conservation_law#Exact_laws shows which symmetries go with which conservations.

 

[lightarrow]

... for ex. I know the homogeneity of space is the cause of the conservation of linear momentum

That's a quite common "myth": actually the "homogeneity of space" has nothing to do with momentum conservation. This law comes instead from the "translations invariance of the system's Lagrangian" . If you are an high school student, this can be a good reason to study physics at university: probably you cannot completely understand the meaning of this (as others) invariance without a good knowledge of physics and mathematics.

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lightarrow