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I am reading through my professor's notes and I am unsure as to what the intimate relationship between the symmetry property of a physical system and the conservation laws of energy, momentum, and angular moment are related to each other.

Like, I can see the latter two being related to conservation of energy, but how do they relate to symmetry property for a physical system?

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Energy conservation is a consequence of a system’s invariance under time translations. Momentum conservation is a consequence of a system’s invariance under spatial translations. Angular momentum conservation is a consequence of of system’s invariance under rotations.

These relationships are all examples of Noether’s Theorem, named after the celebrated female mathematician Emmy Noether, “the most important woman in the history of mathematics”.

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