So we've come to Week 7 now, and this may have been a week that many of you are looking forward to. Because we are going to get into some of the famous paradoxes that arise from the special theory of relativity. And actual fact, the not so much paradoxes, as pseudo paradoxes because they're well understood within the theory itself and around some of the edges, there can be some debate over exactly how things work or the proper interpretation of things. But also, there are many experimental results that demonstrate that the theory is on very solid ground here that the results you get are actually true. So there are pseudo paradoxes in the sense that we can explain them and there is nothing paradoxical about the explanation itself except it's out of the realm of our ordinary experience. And that's what makes it seem paradoxical or a little bid weird. So of course, we'll have the quotes of the week in just a minute. But we're going to start off this week going back to a problem we looked at last week, the whole thing about cause and effect, if you can have faster than light travel, and how that reverses cause and effect. So we're going to take what we've been doing recently with space time diagrams and apply it to that situation. Try to get some more insight on that. And then a famous paradox is so called pole and the barn paradox where we'll have Elsa I think, in this case. We'll have her running very fast, speeds up significant fraction the speed of light with the long pole, and Bob will be over there with his barn. And the barn will be shorter than the pole, but Bob will say, no problem Alice, you'll be able to fit the pole inside the barn and I'll be able to close the doors. And the pole will be completely inside the barn or close the door we'll take a pictures to show them it is completely inside the barn. Meanwhile, Alice takes a look at the barn and says no way is my pole going to fit in there. My pole is definitely longer than the barn. So, length contraction comes into that, the analysis of this problem, and also the relativity of simultaneity. So we'll look at the famous pole and the barn paradox there, or sometimes the pole in the barn paradox. Then, the topic how objects undergo length contraction. This actually is one of those things that is still debated among physicist. We're going to look at one version of it to get some insight into it. And as many things we've done here, we'll discover that a key part of this is simultaneity and synchronization of clocks, going all the way back to some of the original insights of Einstein from his two basic principles. Speed of lightning concept and the principle of relativity. And then we'll take some of those insights and actually apply to another paradox, the so-called spaceships on a rope paradox or situation. I guess we could officially label that a paradox. And this is another one of those things that when it first came out you'd ask a lot of physicists. And they would get it wrong, until they really thought through exactly what was going on. We'll try to figure out what is this spaceships on a rope paradox. It's essentially two spaceships that accelerate at exactly the same velocity all the time, so their distance between the spaceships always remains constant. And there's a rope that attaches between them at tension. And so the question is will the rope break or not? And a special to your relativity indicates that will, but would seem like it shouldn't. And so again, that's what makes it paradoxical, and we'll look at that. And then finally the most famous paradox of all, the twin paradox called the twin paradox because you can imagine you have two identical twins, you send one of them of on a spaceship at a very high velocity, perhaps to a nearby star, then they make the return trip. Time dilation says that the twin who goes away and comes back again, and the special theory of relativity says, that twin who made the trip will come back and will age less than the twin who stays home. And yet, it seemed to be a symmetrical situation, because couldn't you put yourself in the case of the twin who actually makes the trip. They see, the other twin, going back away from them in the other direction and then coming back in. So it seems to be a symmetrical situation, so how do you get this asymmetry in the ages involved? Of course a special theory of relativity says time dilation works from one frame to another frame, and then also in the opposite direction. So we'll have to do a careful analysis, to see exactly what's going on with the twin paradox. So that's our schedule for the week. Couple quotes of the week. Here's one actually from 1933, is when he said this. He said, the years of anxious searching in the dark, for a truth that one feels but cannot express, the intense desire, and the alternatives of confidence and misgiving, until one achieves clarity and and understanding, can be understood only by those who experience them. And really, you see this is 1933, so 20-25 years or 28 after his miracle year, but in the years preceding his miracle year, as we talked about how he felt sort of a physic tension and could not get over these theoretical puzzles and assymetries as he called them. And finally, had the breakthrough insight in 1905 about that. And then after that, up until about 1915, spent a good part of the next ten years working out the general theory of relativity, very difficult task. And then in his later years, worked on a so called unified field theory, and ultimately was fruitless in those efforts, but just the idea that sort of trying and trying and trying, hitting dead end and dead end and dead end and getting up again and taking different route and seeing where enlightenment might come. So that's what he's talking about, the alternative is a confidence you think you're in the right track, and then also you hit a dead end the misgiving that comes until when sees clarity and understanding. So, talking about that experience. And the second quote is, what I see in nature is a magnificent structure that we can comprehend only very imperfectly and that must feel a thinking person with a feeling of humility. So the interesting contrast between some of Einstein's quotes and this one, where it's really emphasizing the humility that enters the how we can understand the wonderful, the magical, mysterious reality of nature. And yet also, we have the power to do so, and somebody like Einstein in particular, to gain great insight into exactly how the world works in that marvelous structure of reality. So again, nature, magnificent structure that we can comprehend only very imperfectly even in our best efforts like the special theory of relativity, or the general theory of relativity. And therefore fills a thinking person with a feeling of humility.