 Greetings and welcome to the Introduction to Astronomy. In this video we are going to discuss special relativity, one of Einstein's theories that talks about motion and how he modified Newton's thoughts of motion from centuries before to better fit with the actual reality. So some of our best ideas of how things move are based on Einstein's special and general theories of relativity and in this video we are going to look specifically at special relativity. Now what does special relativity look at? Well it is depends on motion. So it is really looking at a new description of motion. General relativity is a new description of gravity and this changes motion. Now Newton's laws of motion that we've looked at previously work in almost every situation we have. So they are very good to use, there is nothing wrong with them except in very extreme cases that we don't hit in everyday life. For example they cannot explain motions at high speeds those near the speed of light. This is something that Newton's laws cannot predict correctly. This is where special relativity was put forth by Einstein in 1905 to be able to explain. What was some of the earlier work that even predates Einstein in this? And what we can see is that long ago it was thought that light like sound in all other waves needed a medium through which to travel and this was called the ether. Now the ether was not known, was tried to be detected and in fact the Michelson-Morley experiment in 1887 at Case Western Reserve University was going to try to measure the ether by using the setup shown here, a number of different light beams and then splitters to be able to travel them in different directions. So they were going to look at the travel times for light beams traveling in different directions through the ether and what that should mean is that you should find a difference when you're going with the ether whereas going against it you should get some kind of difference in those and you should be able to see that in interference in the light beams and nothing was detected. They found no evidence of any difference meaning was there no ether and we of course we now know that light does not need a medium to travel through but back at this point we did not know that we did not yet realize that. So what did Einstein give us with special relativity? Well he gave us a couple of postulates and those postulates are first of all is that there is no absolute frame of reference, there is no universal frame of universal rest point that we can refer everything to. Really what it means is that we cannot tell who is moving if the motion is uniform. So if you're accelerating you can tell that you're moving but if you're just moving at a constant speed it is very difficult and in fact impossible to be able to tell the difference. You may notice this sometimes when you're driving if you've ever noticed that you're stopped at a light and this car next to you is slowly inching backwards and wonder what's going on and then if you tap your break a little bit you realize that it was not the other car but you that were slowly inching forward because it was such a slow speed and such a slow change you didn't notice the acceleration and you're you could not tell who is actually doing the moving. The other thing is that the laws of physics are the same in each reference frame so whether I'm in the black reference frame or the blue one here the laws of physics have to be exactly the same and also the other postulate states that the speed of light is a constant so there is some constant value for the speed of light and that is three times ten to the fifth per second. So there is a very specific speed and it is the same value for every single observer. It doesn't matter whether they're moving. Now what that means is normally when a person here is moving you would add their speed or subtract their speed from the object that they're that's that they're measuring. So if you're in a car and you throw a ball forward the velocity of the ball is the velocity with which you threw the ball forward plus the velocity of the car. Now that doesn't work when we use light. If you shine a light beam forward off a fast moving rocket ship it still travels at 300,000 kilometers per second. It does not go any faster it doesn't matter in fact if the if the rocket is moving at half the speed of light and it's still traveling forward at just three times ten to the fifth kilometers per second. So no matter how fast the object is going the velocities will add will never the velocities will not add the same as they do with lower velocities. So we get a different way of adding velocities when we get close to the speed of light. We can't just add those velocities together directly as we do in everyday life. Now what are some of the consequences of special relativity? Well let's take a look at what we have here. What do we mean by simultaneous events? Well if we think about those that's something that occurs at the same time. But what does that really mean? It really means that for somebody sitting here not moving and watching these three that they might see events A, B, and C happen in a certain progression. So what they would see is all of these happening at the same time. So if they're all on the x-axis here this is a space time diagram. So space is in this direction and time measured in the other direction. And what we would then see is you know what is possible and what is not possible. But an observer that is not moving would see these occurring at the same time. And if we look at this animation we would see that the first one shows that they all observe at the same time. But to people moving at very high speeds may see event C occur first then B and then A. And someone else would see A first then B and then C. So what we mean by simultaneity really depends on the observer and your motion. There are no absolute simultaneous events. So one person may see things happen at the same time but someone else will not. Now we also get a couple of interesting effects that occur when you get close to the speed of light. One is time dilation. The faster you move the slower clocks run. So that's what this graph shows. At rest you get exactly one rate at which the clocks would normally run. So one would be the rate at which they ordinarily run here on earth. We can see that as you get closer and closer to the speed of light which would be right here this number grows. So as you get close here now clocks are running half as fast when you get to about 86 or so percent of the speed of light. And it goes faster and faster and faster as you get closer and closer to light speed. So the closer you get to the speed of light the more your clocks will show will slow down. Now we can actually observe this with muons that are produced in the upper earth's atmosphere. There are particles that are produced by cosmic rays striking atmospheric particles and these muons are produced and these muons should not live long enough to make it down to the surface of the earth. However we can detect them at the surface of the earth because they are moving at such a high speed very close to the speed of light that they therefore last a lot longer. Their internal clocks are running slower so they do not decay as fast as they otherwise would. So this is something that can be observed through observations here on earth. Another example would be what we call length contraction so that objects moving would be shortened in the direction of their motion. So here shown on the side of a building we have an object here that looks circular but if you travel at a slow speed it would be slightly squashed and here and here they will look shorter and shorter so the faster an object goes the more it is going to be shortened in the direction of its motion. One other that I did not mention in the text here is that the mass will also increase. The faster things go the mass will increase as well and we saw that on our previous slide with the time dilation. The mass would also increase so our mass as we travel faster and faster gets very very large. Now one thing that we see for any of these effects is that they are extremely small and essentially negligible for any velocities that we are normally used to. We can't even travel at a tenth of the speed of light so we are looking at things here which really means that we can use the physics and the motion that Newton gave us just as well. It is only when we get to very very high speeds that we need to worry about Einstein's special relativity. Now let's look a little bit about what we mean by causality and what we are looking at here. What we look at is an example of a light cone. We have space on the x-axis, time on the y-axis and our location is always at the origin. So it shows what was possible in the past and what is not possible. So where could we have been while the light shaded areas are areas where it is possible to travel. So from A you can go to here, you can go here, but you cannot travel in this direction. That would require traveling faster than the speed of light. The blue lines would show light speed. So if you are traveling at the speed of light you could just follow along this blue line. But you could not normally be able to, you could not travel any faster. So travel is impossible within the dark shaded regions. There is no way to get into these regions from where we are right now without traveling faster than light. So in essence A can cause B because A can get to B, but A cannot cause C. There is no way anything happening at A could cause C because it would require faster than light travel. Now let's finish this up by looking at an example of a paradox that comes from special relativity. And this one is called the ladder paradox. And the idea is that if we think about a rapidly moving ladder, it would be shortened. Remember we talked about how something moving in the direction of its motion is going to be foreshortened. So a ladder might fit within the garage even though it could not at rest. Say it is a little bit too long. But if it was moving at a high speed, it could instantaneously fit within the garage. You could have both doors shut at the same time and the ladder within it. Now this is a thought experiment. We're ignoring of course any mechanical issues with trying to open and shut the doors very quickly for a ladder trying to come through at light speed. But it's a thought experiment and you can imagine that yes, this would be able to fit within the garage. It should make perfect sense because it is going to be shortened if it's moving fast enough. Again, ignore the ideas to how you could actually physically do this. But the thought experiment should work. However, we have to remember motion is relative. So we also have to look at the option. What if we consider not the ladder to be moving, but the garage to be moving? In that case, what's happening? The ladder is standing still and the garage is going to be shortened. So the ladder should not fit. So what is happening here? Does the ladder fit or does it not? It can't fit. Can it fit and not fit at the same time? Either the ladder is there or it isn't. So either the ladder fits within the garage or the garage is shortened. And therefore, the ladder is now never able to fit completely within the garage. To solve this, we have to come back to the idea of simultaneity. And what that means is that our the question is are the front and the back and the ladder in the garage at the same time. And we have to remember as we looked at previously, simultaneity is relative. So for one observer here, we can see that the garage doors are closed at the same time. So here we have yes, it fits within. And the garage doors are closed at the same time. And therefore the ladder is within them. However, for the observer, other observer, we would not see that we would see one garage door close. And then we would see the other garage door closed afterwards. So here, as the ladder enters, this garage door is still closed while this one is open. And here, now a little while later, this garage door is now closed. And this garage door is now open. So while the results are exactly the same, it's the idea of simultaneity that is different. In this observer, yes, the front and back are closed at the same time. To this observer, they are not, the two will see things differently as we looked at when we talked about simultaneity. So it's not that it's a little bit different in terms of the understanding that we need to be able to look at things that are not common every day, we think of things as being simultaneous for everybody. But when you're moving at very high speeds, especially, simultaneity is different for different observers. So let's finish up here, as we do with our summary. And what we find is, first of all, we talked about special relativity given up to us by Einstein in 1905, and describes motions at speeds near the speed of light. In actuality, it describes motions at all speeds, but it is very important and needs to be used when we get to those very high speeds. This causes things like time dilation and length contraction, as well as causality issues. And we looked at an example, there are other paradoxes as well. But the latter paradox is one good example. And the solution to it comes from the fact that simultaneity actually depends on your reference frame. So if what frame of reference you're using, we'll see exact, we'll see different things as what is simultaneous to one observer is not necessarily simultaneous to another. So that concludes this lecture on special 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.