system
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human
Why does time symmetry imply conservation of energy?

I've been getting into relativity and QM and i was just wondering why Noether's theorem says that symmetry accross time implies energy is conserved? I get that symmetry across space conserves momentum, and symmetry of rotation conserves angular momentum (and i think symmetry of phase is what causes conservation of charge?? Please correct me on that), but why does time relate to energy? Is it to do with work done? Please help!
gpt
A way to think about it is that in relativity energy is the time component of the 4d momentum vector.

 So energy is conserved with time translation symmetry for the same reason momentum is conserved with space translation symmetry.