6 - 1 - Week 5 Introduction (10-23, High-Def)

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  We've reached week five, now also, let's do a preview of the, the major topics of the week. We're, 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 will 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, the distance light travels in a year as some of you may, may know. if we measure velocities in light years per year, then C, the speed of light is simple one by definition. It's one light year per year, it's the distance it travels in one year. And so, that and a couple other tips there will make things a little easier for us calculationally 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 within the struggle a little bit. Try to get a deeper understanding of it. And recalling this Star Tours part 1, the idea is we're going to send in this case, Bob will go on a trip to a nearby star, 5 light years away the, the nearest star to earth actually is about 4.2 light years away. We mentioned that in one of the one of the early problem sets. But I think we mention, mentioned in terms of the distance not in light years, but just in how long light would take to, to get there is about 4.2, 4.1 and 4.2 years. Anyway so, we're just going to imagine Bob taking a trip there. And we're going to analyze it from Alice's perspective as she watches Bob take the trip to the nearby star and she's on earth, so will analyze it from her perspective and Bob's perspective. We'll try to make sense of both their perspectives, and then we'll sort of hit  a wall, hit a puzzle in that there will be something that really doesn't make sense. We'll get to, and so we'll have to hold that aside 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 frame 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 actuallly is equivalent to the Galilean transformation for slow speeds, so, it subsumes the Galilean Trnasforation. 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,uh and, get these transformation equations. And then we'll spend a little time exploring those transformation equations, trying understanding them, seeing what they are telling us, seeing if they make sense from what we know so far. And then we're going to use those transformation equations, they, they're very general, 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 exactly how much do leading clocks lag when you have, remember 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, to figure out that problem  we run into, that's Star Tours, part two here. And then we'll say a few words about the ultimate speed limit speed of light being an ultimate speed limit, and why that might be so. What would happen if we could travel at the, the speed of light. And then finally, talk about combining velocities. We did a little bit of this with the Galilean transformation idea where if you know 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 to 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 0.9 C, say Bob on his space shift travel at 0.9 C. And then he shoots out maybe an escape pod, or something, traveling at 0.5 C away from him. So he's traveling at 0.9 C, 9 10th of the speed of light. He shoots out an escape pod, at 0.5 C, that's 0.5 C with respect to him travelling away. In classical physics, we say you just add the velocities 0.9 C plus 0.5 C. Alice watching it over here as Bob goes by and shoots off the escape pod, Alice would say presumably 0.9 C plus 0.5C, 1.4 C is the velocity of this escape pod as she sees it. But in actual fact you'll never see anything go past the speed of light. And so combining velocities here, show us the new formula for doing that. Such that no matter you know 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. Okay, 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, it's something he could have said, because he certainly did stay with problems longer. He certainly was very, very smart, you know 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 onto a problem, we saw that in the special theory of relativity. It was about 10 years of thinking about that, other things as well, but 10 years from About 1995, 1996, when he started in the university to year 1905, 19, yeah, 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, as well. So that, that tenacity, that idea that I'm going to stay with this problem, now it's not always a benefit. Because if you, you know, go off in the wrong direction 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 a much more quantum mechanical direction. And Einstein had some real problems with, with that. And, and so, really for the last half of his life, from about 1925 around or so, he was he was out of the mainstream of physics. He's certainly revered by many people and physicists, but just did not really contirbute anything major at the time
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