As far as I know (and I don't know much), Noether's theorem claims that time translation invariance of the laws of physics leads to the conservation of energy. The way I understand it is that if we imagine a universe where all the laws of physics always require time as one of the inputs, then energy in this universe is not conserved.
But the laws of physics do not necessarily only describe energy, do they? There's at least linear/angular momentum, and maybe other things as well. So why is it that only energy is not conserved in the above universe? What makes time translation invariance specific to energy?
Best Answer
That is incomplete, but not incorrect. As you noticed, there are other conservation laws, and in fact they also come from symmetries. What Noether's theorem states is that for every continuous symmetry of a physical system there is a corresponding conservation law. For example, translation symmetry leads to the conservation of linear momentum, and rotational symmetry leads to the conservation of angular momentum.
It it worth pointing out that energy is not conserved in our Universe, because the Universe is in expansion (hence, it gets bigger, and time translation symmetry does not apply). At local scales this is negligible, but it is relevant at large scales.