We've reached week five. Now also, let's do a preview of the major topics of the week. We've labeled it Spacetime Switches. There are actually a number of different topics we're covering, but the idea of space time switches comes from the Lorentz transformation, which we'll be talking about, enables us to switch between different frames of reference very easily. But before that, we'll have the quotations of the week. We'll do that in a minute. We'll talk just briefly about convenient units for the speed of light. The concept of a light year and the fact that, if we measure distances in light years. A light year is a distance, a distance light travels in the air as some of you may know. If we measure velocities in light years per year, then see the speed of light is simply one. By definition, it's one light year per year. It's the distance it travels in one year. And so, a couple of other tips there will make things a little easier for us calculationaly when we do things. And then we're going to spend a little time looking at a case of time dilation and length contraction to build on the ideas we were working with last week. We introduced and derived last week to get some more familiarity with them, to struggle with them a little bit. Try to get a deeper understanding of it and we're calling this Star Tours, part one. The idea is we're going to send. In this case, Bob will go on a trip to a nearby star, five light years away. They nearest star to Earth actually is about 4.2 light years away. We mentioned that in one of the early problem sets, but I think we mentioned in terms of the distance not in light years, but just in how long light would take to get there is about 4.2, 4.1 to 4.2 years. Anyway, so we're just going to imagine Bob taking a trip there and we're going to analyze this from Alice's perspective as she watches Bob take the trip to the nearby star and she's on Earth. So analyze it from both perspective and vast perspective, we'll try to make sense of both of their perspectives and then we'll sort of hit a wall, hit a puzzle and that will be something that really doesn't make sense we'll get to. And so, we'll have to hold that side for a minute and because we won't be able to answer it yet, and that's really what the next part here is. In order to answer it, we're going to derive the Lorentz transformation. Lorentz transformation, just like the Galilean transformation allowed us to switch between different frames of reference in a non-relativistic manner. The Lorentz transformation also derived by Einstein, but typically called the Lorentz transformation now. Allows us to switch between different frames of reference when relativistic speeds are involved and it actually is equivalent to the Galilean transformation for slow speeds, so it subsumes the Galilean transformation. So this will probably be the most algebra we do in the entire course, it will take us a while to get through it. Several video lectures, but we'll work our way through it and then get these transformation equations. And then we'll spend a little time exploring those transformation equations, trying to understand them. See what they're telling us. See if they make sense from what we know so far and then we're going to use those transformation equations, they're very general and useful in all kinds of ways. But we're going to use them to revisit this whole idea of leading clocks lag, because this will turn out to be the key to understanding our Star Tours conundrum that we end up with there. So, we're going to revisit leading clocks lag and do it quantitatively. Find out how exactly much do leading clocks lag. Remember, when you have a series of clocks moving by you, you're in one frame of reference, you see two or more clocks moving in another frame of reference past you. Then the leading clock as it's moving past you in that series of clocks or two clocks, lags behind the rear clock and we did that qualitatively before. Now we'd like to figure out exactly how much does it lag behind that clock and that's going to be the key, as we discover to figure out this problem we run into. That's Star Tours, part two here and then we'll say a few words about the speed of light being the ultimate speed limit and why that might be so. What would happen, if you could travel at the speed of light. And then finally, talk about combining velocities. We did a little bit of this with, so we have the Galilean transformation idea where if you have a car and you have a basketball shooting machine that we talked about and then a tennis ball out of the basketball, that type of thing. In our everyday experience, those types of things just add. You add the velocities or if the velocities are opposite of each other, you subtract the velocities. Well, a similar idea in terms of the special theory of relativity, but it's a little more complicated. Because if the speed of light is an ultimate speed limit, what if you have something traveling at 0.9c. Say, Bob on his spaceship traveling at 0.9c and then he shoots out maybe an escape pod or something, traveling at 0.5c away from him. So he's traveling at 0.9c, nine-tenths the speed of light. He shoots out of an escape pod at 0.5c. So, that's 0.5c with respect to him traveling away. In classical physics we say, you just add the velocities, 0.9c plus 0.5c. Alice watching it over here, as Bob goes by and shoots off the escape pod. Alice would say, presumably, 0.9c plus 0.5c, 1.4c is the velocity of the escape pod as she sees it. But in actual fact, you will never see anything go past the speed of light. So combining velocities here will show us the new formula for doing that such that no matter how fast Bob shoots out that space pod or whatever, Alice will never see it go faster than the speed of light. Actually, it will never get up to the speed of light, but it will never exceed the speed of light there. So, that's sort of a rundown of where we're heading this week. Let's do the quotations of the week. Two short ones, this time. First one, Einstein. It's not that I'm so smart, it's just that I stay with problems longer. It's not that I'm so smart, it's just that I stay with problems longer. Now I said Einstein, quotation of Einstein. In actual fact, Einstein probably did not say this. It's one of those things that somebody invented at some point and it sounds good. It sounds like Einstein could have said it, it's certainly inspirational. And therefore, you see it all over the place. In actual fact, there's something he could have said, because he certainly did stay with problems longer. He certainly was very, very smart. Hard to measure those types of things at a certain level, but great scientists also have this tenacity about them and he was tenacious when he got on to a problem. We saw that in the Special Theory of Relativity, it was about ten years of thinking about that. Other things as well, but ten years from about 1995, 1996 when he started in the university to year 1905. I should have said, 1896 if I said 1996 to 1905. Ten years and then actually the next ten years after that he spent a large part of time working on his general theory of relativity and took about ten years to work on that, as well as a number of other things as well. So that tenacity, that idea that I'm going to stay with this problem. Now, it's not always a benefit. Because if you go off in the wrong direction, then you may be going off in the wrong direction for a long time. In fact, many physicists who were contemporaries of Einstein during the second half of his life felt that he had gone off in the wrong direction in terms of the physics of the day, which had gone in much more quantum mechanical direction and Einstein had some real problems with that. And so really for the last half of his life from about 1925 on or so, he was out of the mainstream of physics. He's certainly revered by many people and physicists, but just did not really contribute anything major at the time from about 1925 til he died in the 1950s. So again, it's a good quality to have. No matter how smart you are, however, you want to measure that, but just staying with the problem longer. That struggle for understanding that we talked about before. So even though Einstein probably didn't say it, it certainly captures one aspect of his scientific personality and the second quotation similar to the first. In this one is something he said, one should not pursue goals that are easily achieved. One must develop an instinct for what one can just barely achieve through one's greatest efforts. And so there's that incite into want to tackle problems that are challenging for you, but you also have to have some insights sometimes is this just too hard of a problem and scientists have to have that as well. They have to understand given our current capabilities, our current understanding. My current abilities maybe, that's just something it's not good for me to tackle. Leave it for somebody else or leave it for 20 years from now and maybe we'll be able to come back, and tackle that problem again. On the other hand, sometimes the really hard problems like that, the only way you really do crack those nuts as it were is for somebody to take it on or a group of people really to take it on and to stay with that problem until it gets solved. So that's overview of the week where we're heading, quotations of the week. And again, we're going to be building on the things we've been doing the last couple weeks now with the key concepts of the special theory of relativity and seeing what some of those implications are for our situations not only with counting the stars maybe, but also combining the velocities and ultimate speed limits and the like.