Noether’s theorem explained (conservation and symmetry)

12:15process. >> It is it is and and and it's been shown to be true. There's so many experiments that show that you know this is the laws of physics. there's no special point in space and time or direction in space and time that like yield different laws of physics right um Emmy not in no's theorem what she actually showed was if we take if we take the um assumption that physics is the same after these translations that then something must be conserved >> every single time that we have this symmetry that's something that we can tackle in a later episode and actually prove no theorem. It's a beautiful proof um and it's quite intuitive. But at the

12:56end of the day, what ends up happening is any symmetry is associated with a conservation law. So for example, the fact that I can translate in space, meaning I do an experiment here, then I do an experiment somewhere else and the physics laws are exactly the same, that leads to a conservation of momentum. >> Okay? >> Yes. Yes. >> In any situation, >> right? If I do an experiment today and then I do it tomorrow and the and and the week after and the month after and all of the laws of physics are the same, that leads to a conservation of energy. Okay? If I do an experiment here and I change the rotation where I rotate my entire experimental apparatus and I do it again and the laws of physics are the same,

13:37that leads to the conservation of angular momentum. >> Right? It's a deep deep notion that we have. Okay, this was in the early 1900s where Amy Noter came up with this. >> I've never understood it intuitively because we've talked about all three of the we've talked about conservation of angular momentum quite a bit. We've talked about the conservation of energy uh and and the conserv conservation of momentum and have never understood it intuitively in this context of if you're doing your experiment here today and there tomorrow there like it >> there is no difference which means there Yeah, according to me. >> Yeah, >> that's it's that's actually very I just

14:19had a light bulb go off in my head. Apologies. >> It's so deep, dude, to think about, right? That like really like >> these laws that we have, these rules that these numbers are never going to change in any given setup has to do with the fact that the universe wants to conserve the laws of physics >> regardless of these transformations. >> Right. >> Right. It's it's a very deep statement to make. Okay. And that's something that Emmy noter came up with with not theorem. >> Now she did that for classical mechanics. This is before the quantum revolution and things like that. And Hermon while was one of her colleagues at Goting. He thought this was one of the craziest things he's ever heard,

15:00right? The fact that you can connect like an action on the physical laws to a conservation of the physical laws themselves. and he started um going