Gauge symmetry → electric charge conservation

21:02>> The girth, one would say. >> Exactly. The girth of that bone is way bigger. And that's where he scaled in. He's like, if I wanted a super dog or whatever, Clifford the big red dog, that guy's bones would be would be really thick because it needs to hold up the weight of the dog, right? I don't know why he chose dog, but anyways, maybe he had affinity to dog. Do dogs? Who knows? >> Look, I have three dogs, so I also have >> I love dogs. So, yeah. Yeah, I I get it. I get it. [laughter] If if he had cats, he would not be my favorite. >> Nothing against cats. Nothing. I'm sure there's there's cat lovers in the audience. I'm just not a cat person. Um, okay. Here's another broken symmetry, right? Um, we can think about

21:44motion. >> Okay. >> Okay. What if I what if I what if I put my experiment right I'm doing some experiment and then I put my experiment on a spaceship that is moving at a constant velocity actually according to Galilean relativity and later Einstein's relativity my experiment on that moving spaceship that's going at the on a in a straight line at constant velocity is going to have exactly the same results as my experiment that's on the ground that stationary, whatever that means. Because turns out if if I can't tell in my spaceship, I can't do any experiment that tells me if I'm moving and somebody

22:24else is stationary and so on and so forth, right? If both of our experiments are exactly the same, I can't tell who's moving and who's stationary. All I can say is somebody is moving relative to me. That was the big, you know, light bulb of Einstein to say that that's actually true. What are the consequences of that? Right? That's something called a Lorent transformation. So that's that's a symmetry of the universe. The fact that I can boost myself into a reference frame where I'm moving in a constant velocity, but my laws of physics won't change. On the other hand, you can think, okay, what about if I'm rotating at a constant angular velocity? Is that a symmetry?

23:04What that means is if I'm in a spaceship yes >> that's that's just let's say stationary, whatever that means, and I do an experiment and then I put myself on a rotating reference frame, for example, the Earth. >> Yes. >> Right. But take out gravity. Somehow I'm rotating, but there's no gravity. >> Would the experiment be the same? The answer is no. >> No. >> The answer is no. And I mean, you have you been to Griffith Observatory? >> Yes. >> Have you seen the big pendulum from the from the ceiling down? That's called Focal's pendulum. That's a great example