 Greetings and welcome to the Introduction to Astronomy. In this lecture we are going to talk about general relativity. This is how we understand gravity to work. We've previously talked about Newton's law of gravity, and we'll see a little bit about why that is incorrect, although it does work in most situations. So what is general relativity? Well, first of all it was put forth by Albert Einstein about a hundred years ago, and it was a new description of the working of gravity. Now as I said, we previously studied Newton's gravity, and it works in almost every situation. However, what it cannot do is explain motion near strong sources of gravity. That is general relativity, and that's what we're going to talk a little bit about in this lesson. It also cannot explain motion at high speeds. Those near the speed of light, that is what is called special relativity, and I will look at that in a future lecture. What it does is instead of describing gravity as a force between two objects, gravity is a bending of space and time. So massive objects will deform space and time, and then objects move in the shortest path they can in that deformed space-time. So first of all one of the first things, we start off with the postulate of general relativity, which is the equivalence principle. Essentially what was proposed that is that if you are in a sealed room, you can't look out, there is no experiment that you can do that will determine the difference between these two things. One is an object in space far away from any sources of gravity, or a freely falling object. You cannot tell the difference between these two. Are you free falling through Earth in this closed room towards the ground? Or are you out in space far away from the gravity? There is no experiment that you can do that will tell the difference between these two while you are in that state. Obviously in one situation, yeah, you're eventually going to hit the ground and that will be when things change. But the equivalence principle says that while you're falling or out in space, there is no experiment that we can do. Or you can also look at this as an object being accelerated as compared to an object in a gravitational field that has that same acceleration. So if you are accelerating, then you cannot tell the difference. Anything you do, such as dropping a ball, it will do exactly the same thing whether you are accelerating or whether you were falling in under a gravitational force. So we know that the force will change as we accelerate. So if you are not moving in an elevator here where it's just staying still, or if it were moving at a constant speed, you would register your normal weight. If the elevator is accelerating down, you're going to weigh lighter than normal. If it's accelerating up, you will weigh more than normal. And if the elevator cable should break, you would know no weight at that time. You would be in a state of free fall. And you would not be able to tell the difference here until you hit the ground. You would not be able to do any kind of experiment that could tell you whether you were in an elevator or if you were out in space far away from any gravitational force. Now we can also look at this as two people here jumping down this bottomless pit. Now they throw the ball back and forth, and to them it looks like they're throwing it right directly to each other. However, to an outside observer, an outside observer sees it as a curve. That you throw it, one person throws it here, the other person catches it at a much lower place. And again, that is all relative to who is doing the observing. So it makes the difference as to who is doing the observing as to exactly what we see. What does it mean for light? Well, what do we want to look at? Does light travel in a straight line? We would think that it does, but let's look at a thought experiment here. And we have this rocket in deep space. So the light beam will travel straight across and strike point B directly across on the other side of the craft. Now the same rocket, exactly the same rocket in Earth orbit. Now it is being accelerated and it's following a curved path under Earth's gravity. Where does the light beam strike? Well, there are two options to think about here. Does it follow a straight line? Which means it would go straight through and strike at some other point here. That would be light following a straight line would be point B prime. Or is the equivalence principle correct? Which would say you can't tell the difference and you would see it traveling this direction. And that would be point C. It can't do both. One of these is wrong here. So one of these must be wrong. And we're going to find that it is the equivalence principle that is correct. So that light instead of following a straight path would follow a curved path as under gravity. Just like the spacecraft does. So let's look at what we mean by spacetime. So spacetime, an event occurs, can be specified using four dimensions. That's three spatial dimensions and one time dimension. And we graph that here with distance here in one dimension just looking at distance eastward on the x-axis, time on the y-axis. So what we get is between points A and B, we are traveling eastward at some rate. And we could figure that out if we wanted to by the slope of that line. The steeper that line is, the slower you're moving. The flatter that line is, the faster you're moving. And that means you could set a limit to how fast, how flat this line could be by the speed of light. Now between B and C, you stopped moving. So you were stopped for whatever reason. You stayed at the same distance eastward. But time, of course, continues to go forward even while you're stopped. And between C and D, you went eastward. But now it's a steeper line. So you were going at a slower rate, the closer you go up towards vertical, the slower at which you are moving. Now we can also look at spacetime using a two-dimensional diagram. And here we see points like A, B, and C. So A is where you are. B is a point you can get to because you're traveling within this cone. This cone is set by the speed of light. You cannot travel outside of that cone. So if you stop moving, you keep going forward in time. And that's it. So depending on how fast you're moving, you can get closer and closer to the edge of the cone. The edge of the cone is the speed of light. So C would be inaccessible. You cannot get to point C because it would require faster than light travel. So again, it would get more complicated. We'd actually need one more dimension of space to add to this to get a complete picture of what it would look like. Now, how can light be bent by gravity? So what happens is that spacetime, space and time around a massive object, are deformed. So let's look at an example of a rubber sheet here that is relatively flat here across this opening. And an ant traveling there would travel in a straight line. So the ant is confined to the surface of the sheet and would travel then in a straight line. But if you put some kind of massive object there, in this case a paperweight, then the space and time are deformed. So we see how space and time kind of dip down where the paperweight exists and then come back out. This causes us to not follow a straight line path. A straight line path would then not be possible because it would involve moving out of space altogether. Your space is confined by that two-dimensional sheet. So the ant traveling would now have to travel down and back up. That would be the shortest path that can take while remaining on the space of the rubber sheet. How much of this distortion occurs depends on the mass. The more massive object will cause more distortion. If you put a very small object there, the distortion would be much less. If you put a very massive object there, the distortion would be much more. So we will see this distortion in space when we look at much more massive objects. Now how can we test general relativity? Well, we have a couple of tests that have been done. One, an early one, was one that we had a problem with before general relativity, and that was the orbit of Mercury. The perihelion position slowly changes. Now that's actually predicted by Newton. However, Newton was off, not by a lot, but by 43 arc seconds per century. Is that a lot? That's a very small amount, but it was a measurable amount, and it was consistent. So we knew that this was not correct, that there was something wrong with Newton's measurements. Could have been that there was another planet there, but searches for that were unsuccessful. And general relativity, when it came out, was able to explain the orbit of Mercury precisely, and explain the exact amount of deviation of its perihelion, closest position to the Sun, as it changed. We also have the deflection of starlight. So we already talked about how light could be deflected. And this was done in 1919 during a solar eclipse. That allows the Sun to be blocked out, and we could see the stars around it. So we took pictures of these, and we could take pictures there, and we could take pictures at previous times of the same star field, and look for deviation of those stars close to the Sun. Under general relativity, we should get far more deviation than we would get under Newton's gravity. And we find that the shifts are what is predicted by general relativity. We also looked at gravitational waves. We'll look at these in more detail in another lecture. But these were predicted by general relativity over 100 years ago, but it took about 100 years, a century, for us to be able to have the technology to be able to detect the incredibly small motions caused by gravitational waves rippling through space. How about time? We've looked a little bit about what happens to space. What happens to time under general relativity? Time will slow down in the presence of a gravitational force. And that means a clock on the ground will run slower than a clock in orbit. Or if you're in a building, if you're on the second, third, fourth, fifth floor, the higher up you are, then the faster your clock will run. Now, it's not going to be a very measurable over that kind of distance, but from orbit it's actually measurable. We also have a gravitational redshift. What happens to light escaping from a massive object? Normally, when something tries to escape from an object, when we launch something, it slows down. So it would slow down, under gravity, pulling it back. But light can't slow down. But it has to lose energy. Therefore, its wavelength will be stretched. And it must always travel at the speed of light, so that speed cannot change, but its wavelength can. So what can be sent out as blue light can end up escaping a very massive object as red light. And depending on the strength of gravity, this could be even more significant. So all this about general relativity. Why is it important? Why does it matter to you? I mean, we think of it as applying very extreme astronomical conditions. However, you use it every day. We have GPS satellites in orbit. That's what we use to determine our position here on Earth. They're traveling at high speeds, and the clocks slow down because of special relativity. Again, we'll talk about that later on. But just for now, that's what happens when things are traveling at high speeds. However, they're also high above Earth. Gravity is weaker, and therefore the clocks speed up. That's general relativity. So the difference ends up being 38 microseconds per day. Again, it does not sound like a whole lot, but if this is not taken into account in just one day, your GPS would be off by 7 miles. And that means you're not going to get to your location if you're depending on your GPS to get you there if the general relativistic and special relativity calculations are not taken into account in calculating this and using those satellites. So let's go ahead and finish up with our summary. And what we've looked at this time, we talked about general relativity, which describes gravity as a bending of space and time. We talked about many of the tests that have been done, and each so far has confirmed the predictions of general relativity. And we mentioned an example in GPS satellites which use both general and special relativity to locate you through your phone. So that concludes this lecture on general relativity. We'll be back again next time for another topic in astronomy. So until then, have a great day, everyone, and I will see you in class.