 Greetings and welcome to the Introduction to Astronomy. In this lecture we are going to talk about Special Relativity and do note that this is an enrichment lecture. It is not something that is covered directly in our textbook. So, we still want to take a look at it a little bit. We've mentioned a little bit about Special Relativity before. So, Special Relativity was put forth by Albert Einstein in 1905, about a decade before his general theory of relativity. And it was a new description of motion. Remember that general relativity did gravity? This one talks about motion. And we know that Newton's laws of motion work in almost every situation, but not quite. They cannot explain motions at high speeds. And high speeds getting close to the speed of light, we need Special Relativity. So, what was a little bit of the comings of this? Well, first of all, back in the 1800s, it was considered that light needed a medium through which to travel. And this was called the ether. And in fact, an experiment was done in 1887 by Michelson and Morley to measure a light beam traveling through the ether in different directions and seeing how its speed was affected. And here we see the setup there as a light beam would be split so that if some of it would go in one direction, perpendicular to the ether, some would go parallel to it. And there should be a difference in the light travel times for those two. No difference was found, meaning that there was no ether. And we now know that light does not need a medium through which to travel. So, since the laws of physics are exactly the same, there's no way to tell the difference between the reference frames. Everything is going to be... There's no way to tell the difference between those two. So, what the second one is that the speed of light is a constant and has the same value for all observers. That is the speed of light 300,000 kilometers per second. And that does refer to the speed of light in a vacuum. So, not just the speed of light, but the speed of light in a vacuum. So, it does not matter if the observer is moving, then the speed of light will still be... So, the speed of light, since the speed of light is the same, but velocities will add differently. Normally, we can add velocities together. So, if you're moving and something is thrown, you add the two velocities together to get the net velocity. When you get close to the speed of light, it does not matter. A light beam shining ahead of a fast-moving car or spaceship is still traveling at exactly the speed of light. You cannot add in the motion of that craft. So, if you had a spaceship moving at half the speed of light, that light would still be moving ahead at just the speed of light. Not the speed, not one and a half times the speed of light. You can never exceed that speed. So, when you get close to light speed, there are different ways of adding velocities. Now, some of the consequences here, when we look at special relativity, are simultaneous events depend on the observer, whether two things are simultaneous. So, observer A may see the two flashes simultaneously occurring, but that does not mean that there is simultaneity there. Because observer B here, observer B, this light will reach her first, and this light will reach later. So, it depends on the observer as to whether things occur simultaneously. So, if there's a burst of light, one observer can see them at exactly the same time, and another one can see them not occurring at exactly the same time. We also have time dilation. Now, we mentioned this before when we talked about general relativity, but clocks slow down as one moves faster. And if you really want to know the conversion factor, it's this one that tells you as how fast you're going. And as you get closer and closer to the speed of light, this gets bigger and bigger, and it gets bigger and bigger very fast. And you can never exceed the speed of light, because if you exceeded the speed of light, then under the square root here would be negative. And of course, that would become imaginary, and there is no solution there. So, we have observed this. This is actually observed here on Earth. How do we observe it? Well, muons. These are elementary particles that are produced in the upper atmosphere when cosmic rays interact with atoms. Muons do not live long enough to make it down to the ground. They decay very quickly. However, because they are moving so fast at close to the speed of light, their internal clocks are slowed down, and they can actually survive the trip down to the surface of Earth. We also can have length contraction, so time changes, but so do lengths. And objects moving at very high speeds will appear shortened in the direction of motion. So, something moving at a very high speed, you will see it as foreshortened there, and it will appear shorter because of the high speed of travel. So, again, that affects things as well. So, there are some very interesting things, such as the time dilation and the length contraction, that will increase as you get close to the speed of light. Now, at our speeds, it makes no difference. None of these will be noticeable. Now, causality. Well, causality, sometimes it can one thing cause another. Well, it depends on where you are within the cone here, within the light cone. So, in the light cone, space is represented by the x-axis, and time by the y-axis. We are at point A, that is the current location is at the origin. Travel is possible within the shaded region, so something happening at A can affect something at point B. It is possible to travel there at less than the speed of light. Travel is impossible outside that shaded region. So, A could cause B, but there is no way A could cause C because it would evolve faster than light travel, which is impossible under special relativity. Now, we can look at one other example of this, and that's what's called the ladder paradox. A ladder paradox says a rapidly moving ladder would be shortened and would fit into a smaller garage. So, if you had a ladder moving at a very high speed, it would appear shortened, and you could, for that instant, have it completely within the ladder. However, since motion is relative, you can also consider a stationary ladder and a moving garage. Well, what would happen there? Well, now the garage is shortened, and what happens? So, does the ladder fit or doesn't it? Because if the garage is shortened, then there's no way the ladder is going to fit inside this. So, what is going on here? Well, we can take a look at what the resolution to this paradox might be. And what we see is that, here, I said it would not fit, but here we can see the example that you have two cases of this happening. If you have the ladder moving, yes, the ladder is foreshortened and you have, for an instant, that it is within this object. And you can have both doors closed. So, it's how the doors are open, both doors are closed, and it is within there. Now, in the other point of view, where this is moving, remember that things do not occur simultaneously to all observers. So, here we have simultaneity, and, therefore, the doors do not open and shut at the same time. So, one door is shut here, and that lets the ladder in, this door opens, and then this door finally shuts. So, under this, the ladder is never completely within the garage, but it does completely apply to what we've seen before. It really is just a matter of simultaneous events. What things are simultaneous in one reference system are not going to be simultaneously in the other. In the second case here, we never have the two garage doors closed at the same time as we do in the first. It is not a simultaneous event there. So, there is no paradox. It does not fit in. It doesn't have any issue being in there because it still fits since one of the doors is open under this reference frame. So, there are some other paradoxes that you can consider, too, and they're usually something similar to this to be able to explain how things actually work under special relativity. So, let's go ahead and finish up with our summary. And special relativity, given by Einstein, describes motion at speeds near the speed of light. This causes things like time dilation and length contraction, as well as issues with causality that have to be considered. Paradoxes like the latter paradox occur because the simultaneity depends on your reference frame. And that kind of fixes the paradox because there are two different reference frames. 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.