 Greetings and welcome to the Introduction to Astronomy. In this lecture, we are going to discuss general relativity, which is how Einstein explains how gravity works. And it will be very important as we will be coming up in coming lectures looking at black holes, and we really need general relativity to be able to understand what is going on around a black hole. So let's go ahead and get started here. What we have, first of all, is let's take a look at general relativity. What is it? Well, it was put forth by Albert Einstein in 1916, over 100 years ago. And it was a new description of how gravity works. Isaac Newton described gravity as a force between two objects, so that each object, one object here and another object here, that there would be a force pulling on this object and a force pulling on this object. And as you recall, those were equal and opposite forces. And that was a way of explaining how orbits worked. However, while it works in almost every situation, there are some cases where Newton's description of gravity does not work. So it can, for example, it cannot explain motion near strong sources of gravity, which is where we need general relativity, which is what we are talking about today. It also cannot explain motion at very high speeds, and that means those near the speed of light, in which case we need special relativity, which I am not going to go into in this lecture. So let's look at what it does do and what it does describe gravity. Instead of being a force between two objects, it describes it as a bending of space and time. So space and time are bent, and then objects move around in this bent space time. So what does this mean? Well, Einstein gave us a postulate to start this out. And that postulate is what we call the equivalence principle. And essentially what the equivalence principle says is that there is no, if you are in a sealed room, no experiment can be done to determine the difference between these two things. And that means that if you are in a sealed room unable to see out, then you could be a weightless object in space, or you could be an object being accelerated, sorry, between a weightless object in space or a freely falling object. So there is no way to tell the difference between those two. And that's kind of what is pictured in here, is that if you have two people in free fall in this bottomless well, that they can throw a ball back and forth. And to them it looks like they can throw it right back and forth to each other as they fall. Whereas in reality the path of it is not a straight line but is actually curved. So it is curved down here and then curved again. But by the time the young lady here throws it to the gentleman over here, by the time he catches it she will have fallen as well. So they will still be exactly facing opposite each other, meaning that they can just play catch. And not it will not be any different if they were there, but they could do the same thing if they were out in space, away from a gravitational field. Now the other example is that is an object accelerated by a force compared to an object in a gravitational field. And what that means is that if you were in a rocket being accelerated, there is no experiment that you can do that would tell the difference between that rocket being accelerated at a constant rate out in space as compared to that rocket sitting on the surface of the earth unmoving. And again this is in a sealed room so you cannot look outside and see that you are moving. You can only do things with objects. And the example would be if you were to drop the ball while you were on the earth it would naturally hit the ground. However if you were out in space and the rocket was accelerating you could again release that ball and instead of it falling to the ground under gravity the floor would come up and strike it. But the result is exactly the same and that's what Einstein's equivalence principle is suggesting that there is no way to tell the difference between these two states. Now the important thing is what this means for light. So let's take a look at what it means for light. Does light travel in a straight line? We tend to think of light as traveling in a straight line but this is not always the case. If we imagine a rocket sitting here on earth the light beam should travel straight across the craft and strike the other side so you would expect if you're shining a flashlight that it will go straight across and strike the other side at the same level. Now that makes perfect sense to us I hope but let's imagine the same rocket accelerating through space. Well in this case the light would hit at a lower level and that is because we have the light is now going to move a little bit because if this rocket is traveling through space the rocket is moving upward now so in the time that it takes the light to travel from the person across to the wall the rocket will have moved up a small amount and therefore the light beam will hit further down in this case than it would have in the first case. However the equivalence principle says that we cannot distinguish between these two situations. So we should not be getting a difference whether the rocket is sitting on earth or is accelerating through space. These two should be according to Einstein equal. That exactly the same thing is going to happen in either case. So by having two here, two different values here, two different occurrences something is wrong and what that means is that gravity must be able to bend light just as it bends or causes other objects to move and that is quite different than what Newton told us. Newton said that gravity was a force between objects with mass. If light has no mass then gravity should not be bending it. So let's take a little closer look at what some of this does and what do we mean first of all? How can light be bent by gravity? How can this possibly work? It does not make sense under Newton. If you recall Newton gave us the force is equal to the gravitational constant times the product of the masses divided by the distance between them squared. If one of these masses was light and it had zero value then of course the force is going to be zero. But what happens according to Einstein is that the space and time around a massive object are deformed, so not nice and straight and flat and the light will follow the shortest path available through that deformed space time. Because of this light does not travel a straight line path as it otherwise would. In terms of the mass of an object the amount of distortion depends on how much the object is, how massive the object is. Now we can try to understand space time with the use of a little diagram here as you're traveling in one direction say traveling east at a certain time. So as you travel there you travel and you're traveling at a constant rate here so that as you travel a distance eastward a constant amount of time is taking. At point B what happened? All of a sudden the line is going straight upward. Well in this case now the distance is no longer changing but time still continues to run on. So essentially between B and C maybe the driver stopped. So maybe they stopped for lunch or a break for a certain amount of time and you could figure out how much that is here maybe about 20 or 30 minutes and then they picked up again later on as they continued to travel eastward. So all that means is kind of a way to understand what we mean by space and time. In this case we're looking at it two dimensionally. In reality we'd want to look at this with four dimensions three space dimensions and one time dimension. So in order to really understand it we need to do a little bit more but this gives us a rough idea of how what we mean by space time they are actually intertwined together and you can't remove them you can't look at just the spatial dimensions you have to look at time as well. So let's look at what that means in terms of how we can distort space and time around it. And again we are looking at a smaller number of dimensions because we can't easily picture three dimensions of space and one dimension of time. But what we mean by this is that what Einstein tells us is that the mass will distort the shape of the space time around it. So seen in the image here here we have the Earth and in this flat two dimensional space time if you imagine putting the Earth on top of that or putting a ball or a heavy object on a sheet that was held tightly it would deform the space and time around it it would deform that space. So what we find is that objects will follow the shortest path in the distorted space time. So instead of things traveling straight as they would far away from the object when something is coming close to the Earth it gets bent a little bit bypassing through that distorted space. And the more massive the object the more the space and time will be distorted so the greater this amount of change in direction will be. So a light ray far away from the Earth would travel straight a light ray passing very close to the Earth would actually be bent. Now if we replace the Earth by say the Sun then the bending would be even larger. If we replaced it by a black hole then it would be even more extreme bending. So we would get a very significant bending this amount of deviation down here would get larger and larger. So Einstein made some very interesting postulates here and his theory comes up with some very interesting ideas but what we want to know is can we test these? So any good scientific theory needs to be able to be tested and we want to look at some first and next at some of the tests of general relativity that have been done. Now one of those is the orbit of Mercury. So one of the problems that Newton's theory had is that it could not predict the orbit of Mercury properly. In fact it could not predict what we call the perihelion or closest approach. It slowly changes so it would be here one approach and then it moves a little bit the next one and it's a little bit different the next one. It's constantly changing over time. Now general relativity predicts this and so does Newton's law of gravitation. So in both of them predict what we call the procession of the orbit of Mercury. However Newton's value is off by a very small amount. 43 arc seconds per century. So every hundred years it would be off by 43 arc seconds. Remember that the full moon is 1,800 arc seconds across. So we are talking about a very small change. However it was measurable and definitely could be noted even back in the early 1900s. So we knew that something was wrong. One of the things that was thought was that maybe there was another planet orbiting inside Mercury's orbit that had never been detected. But that is no longer needed once general relativity came about. It gave the correct value for how Mercury's orbit would change. And it was very important for Mercury because Mercury was the closest planet to the sun. So it was most affected by the general relativistic effects. Now one of the other things that was tested was the deflection of starlight. The orbit of Mercury was important. However if we think about it that was something that was known so we want to look at predictions. We really like theories that make predictions. And one of the predictions that general relativity makes is that starlight will bend. So during a 1919 eclipse the idea was to go and observe stars that were close to the sun during an eclipse and then look at them again a few months later when the sun was no longer near them. So the prediction would be by Einstein that the deflected path means that the light coming this direction passing close to the sun is going to change its path. And it's going to make it look like it appears to come from another direction. And that will change the apparent path of the star on the sky. And that was a prediction that was made by Einstein's theory in 1916 and several years later it was actually detected and the shifts were found and have now been found to be really what has been predicted by general relativity. Now general relativity again looks not just at space but at time as well. So what happens with time in general relativity? A couple things that we see is that time will slow down in the presence of a strong gravitational force meaning that a clock on the ground will run slower than a clock in orbit. This can be tested as well. So this is something we can do with very accurate atomic clocks having a clock here on the ground of the Earth and measuring it, putting another clock up in orbit and then comparing the two we find that the clock on the ground will run slower than the clock up in orbit. One of the other things that occurs is the gravitational redshift. So light escaping from a mass of objects cannot slow down. Normally when we try to escape from the Earth we lose energy, things lose energy they will move slower and slower. They may be going fast enough to escape but they are not going to actually they are going to change their energy they are going to lose energy which means they slow down. However light cannot slow down light always travels at the same speed which we know is the speed of light but it must lose this energy. So what that means is that its wavelength gets stretched. So the speed cannot change but the wavelength can and that means as we're trying to escape that light starting out here as blue light from a strong gravitational force can be shifted through the spectrum through green, through yellow, into orange and red by the time it gets to a distant object. The higher the gravitational force here the more the shift will occur. So light traveling trying to escape from the sun has a minor shift, minor gravitational redshift. Light trying to escape from a neutron star or from near the surface of a black hole will get a much stronger redshift. Now all of this can seem very far fetched. You know what does it actually mean to you that there is general relativity? So what we find is that it really think of it only applying in extreme conditions but you use it every day. And the big combination, the big point of this is the GPS satellites. These are what you use to determine your position so when you pull out your smartphone and try to navigate to a location it is using the signals from GPS satellites to locate where you are and follow you as you travel. Well, these satellites are doing two things. They first of all are traveling at high speeds which causes the clocks to slow down. That's part of special relativity which we have not talked about a lot but they are also high above the earth where gravity is weaker so the clocks speed up and that is a general relativistic effect. So the two do not exactly cancel though and in fact the combined difference is 38 microseconds or 38 millions of a second every day. Now that may not seem like a whole lot but in terms of determining positions here on earth that could be seven miles in a day. So if the effects of special and general relativity were not taken into account your GPS would very quickly become useless. Those changes and those shiftings actually do occur and if we were not able to correct for them GPS would not work. So let's finish up here as we do with our summary and what we find is that remember general relativity given to us by Einstein in 1916 gives us, describes gravity as a bending of space and time as compared to Newton's force between two objects. Many of tests have been done and each of these has been able to confirm the predictions of general relativity. And as an example the GPS satellites use both general and special relativity to locate you through your phone. So to find out where you are and to be able to allow you to travel to various places using GPS on your phone general and special relativity do need to be taken into account. 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.