Translational symmetry → momentum conservation

15:10further with the new quantum revolution and trying to put that into this same language. Okay. Okay. And turns out it gets even deeper when you go into quantum mechanics. In quantum mechanics for example um you know everything is a wave function, >> right? >> Whatever whatever that means. But [laughter] what gets even weirder is that wave function is a complex number. >> Okay? It's a complex number which means it has a magnitude and it has a phase. It has a phase with respect to like uh some kind of zero some zero that you arbitrarily choose. That complex number has it's like a clock hand, right? It's

15:51got a length and it's got an angle. Well, according to quantum mechanics, what are the observables? The observables are probabilities of outcomes of experiments. And that comes from taking the magnitude of this complex number. The magnitude meaning only the length. So the the the phase actually doesn't matter when it comes to things that we can see. Right? Which means if I if I take an electron for example and I change the phase everywhere for that electron all over the universe, right? Cuz this wave function is everywhere. >> That's not going to change the outcome of my experiment. If I add a phase or I subtract a phase, if everywhere I'm just like making the clock go a little bit, a

16:32little bit, >> that's not going to change whatever thing I observe. Okay? And it turns out that that symmetry has to do with the conservation of charge. The fact that I can't create a positive or a negative charge anywhere. >> It's crazy, right? So, this is getting real interesting. >> Oh, interesting. >> This is getting really, really interesting. Okay, please continue. Right, cuz it's now it's again now from that foundation I'm extrapolating to a variety of other things we've talked about before that are making even more sense understanding this like correlation or this relationship. >> Yeah, it's I mean physics is is is