Welcome back everybody, well, we've you talked about special relativity and how the notion of frames of reference led Einstein to his sort of radical revision of our understanding of the nature of space and time, separately and he merged them into a new entity that we call space-time. And if you'll remember the whole idea with special relativity was thinking about inertial frame. Frames of reference that didn't have any acceleration going on. Now, to make the next great step Einstein had to try and include the one force that seems pervasive because it's a force it produces acceleration through, there's an intimate link between forces and accelerations and that force is gravity. We see gravity all around us. It's what keeps our butts in our chairs. It's what keeps the planets in orbit around the sun. And so, Einstein needed to to enlarge his understanding of relativity to be able to include accelerations and particularly to include gravity. And this is why we went from special relativity to general relativity. And while special relativity actually Einstein was able to work out with fairly simple math. General relativity took him a number of years to work out, trying to figure out how to get gravity into the, the picture. So, for the work we are doing, the most important principle that Einstein came up with was the idea of the equivalence principle and that basically states that if you are in a box car where you can't see the outside world. There is no experiment you can do that will tell the difference whether or not that box car is sitting on the earth or whether in space with rock and motors attached to the bottom accelerating at 9.8 meters per second squared. Why is that number important? Well, 9.8 point 0.8 meters per second squared is the acceleration due to gravity. If I take a ball and I drop it, that is how fast it will accelerate towards the floor. And what Einstein recognized that is if you were in this box car and the box car had rocket motors attached to it and the acceleration that those rocket motors produced was 9.8 meters per second squared. If I were to take a ball and let it go, what would happen is, is that the floor would accelerate towards the ball at 9.8 meters per second squared. And what you would see if you are inside the, rocket or inside the box car is you would, what, what appears if the ball was falling. In fact actually it would appear as if you were falling and what would happen is the, the floor of the box car would come sweeping up towards you and, and scoop you up, so to speak. So from your point of view you wouldn't be able to tell whether or not there was rocket motors that were producing the acceleration or whether it was a gravitational field producing the acceleration. So that's the idea of the principle of, of equivalen, equivalence. And it was essential for Einstein to be able to make the link between motion particularly accelerated motion and gravitational fields and the consequences of this are pretty, pretty dramatic. Imagine for example that you are in a rocket and a beam of light comes through a window, while the, your rocket is accelerating at say 9.8 metres per second squared. Well, as you can imagine though, from an outside observer's point of view, the light is just travelling in a straight line. But, from the, your point of view, the floor is accelerating upward and it would look as if the light were being bent downward. From your point of view in the rocket, the light would appear to be deflected. Its path would be deflected. And it's from this that Einstein came to understand that gravitation fields can deflect light. And in, in a even larger sense kind, Einstein came to understand that really in thinking about gravity, the most important thing to think about was the shape of space-time. And that, rather than thinking of space-time as being an empty container into which the events of physics occur. Space-time was in fact a curved manifold, it was a fabric and that fabric could be distorted by large objects that produce gravitational fields, and the motion of other objects would then be forced to be deflected by the curvature of space-time. So Einstein through the principle of equivalence and a whole lot of math, Einstein was able to see that rather than thinking of gravity as being a force, we should think of gravity as being a distortion of the essential fabric of this new quantity called spacetime. And then, if we're interested in the motion of objects, we should think about under a gravitational, quote unquote, force. What we should really be thinking about, is how the motion gets deflected by the shape of space-time. As we say in physics mass tells space-time how to bend or distort and space-times tells mass how to move. Okay, so that's the most important thing we sort of need to understand for general relativity, the basic idea. But, just like what's better for rel, relativity where we saw that depending on how you move relative to someone else, your measurements of space and your measurements of time will be different. If you're close to a gravitation, a large massive object which is producing a lot of distortion of space-time. Your measurements of space and your measurements of time will be different from someone who is far away from that object. So, for example if your at the bottom of a building looking up to your friend who say, on the fifth floor. Time is actually going slower for you because you are closer to the, the mass of objects and space-time is more distorted for you at the bottom of the building than it would be for your friend further up. So in some sense, people are close to a, a gravitational object, time has slowed down for them relative to the outside world. So, that's what we need essentially to understand, take the next step and understand black holes and that's where we'll go next. [BLANK_AUDIO]