Instruction :
What is Noether's theorem and how does it relate symmetries to conserved quantities?

Response:
Emmy Noether proposed a theorem that states that for every symmetry in physics, there is a conserved quantity. For example, for the symmetry that the laws of physics are unchanged by a translation in space, a rotation in space, or an offset in time, the corresponding conserved quantities are linear momentum, angular momentum, and the conservation of energy.