Welcome back everyone. So, we now want to talk about black holes, which are some of the most interesting objects in the universe, and the most interesting physics that we understand. However to get there we first have to do a little preliminary work. And we want to talk about the theory of relativity. And now everyone knows, the theory of relativity was the, you know, the brainchild of Albert Einstein. And so to understand why relativity is important and what it's trying to teach us about the world, we first have to think about a very important concept called frames of reference, because this is what Einstein had to work with. Einstein had to sort of puzzle out how it is that physics might change as we move from one platform of doing physics from the next. And by platform I mean, like, I'm standing still on a planet and I'm looking out at space or what if I'm on a rocket ship zooming along at very high speed. Do the laws of physics, or does physics what I see in the universe change based on where I am and how I'm moving? Because, of course, what we want in physics is we want to understand general, universal principles. And what Einstein was really after was, which laws or which aspects of physics don't change as you're moving from one frame of reference to the other. So let's imagine a rocket traveling through space with a speed of V of R, we'll call it. Now, to an observer on the rocket, the, the, ship isn't moving at all, right? You all notice, when you're driving in a car, and, the windows are completely blackened and you have perfect shock absorbers, you wouldn't even know that, you were moving, right? So to you, sitting in the rocket ship, there's no motion at all. But for a person at rest watching the rocket ship go by, they would see the rocket move at V sub R. Now imagine that inside the rocket ship, you have a little pellet gun and you fire that pellet fire the pellet gun and the pellet leaves the the, the muzzle of the pellet gun at a speed v sub b, okay. So from the perspective of the person on the ground, the rocket's moving with v r, the pellet is moving with V sub b, and what you'd was is that, that person on the ground would see the pellet moving at v sub r. VR plus VB. Okay. So they would see, their, their observations would say, the speed of the pellet is the speed of the rocket plus the speed of the pellet out of the muzzle. From your perspective, inside the space ship, the speed of the pellet would just be the V sub B So that is a, what we expect to be a very general rule about the frames of reference, obs, observers see themselves at rest, and see everything moving relative to them, and to observers and two different frames of reference, will disagree about the speed, but they, if they understand, if we know the relative speed of the platform, or the spaceship, then they would be able to figure out what is the correct the correct speed, but it turns out that what Einstein found is that things are more complicated. Than this and that's what we'll go to next.