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6 - 17 - Week 5 Introduction (10-23, Low-Def)

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  [BLANK_AUDIO]. We've reached Week 5 now, so let's do a, a preview of the, the major topics of the week, where we've labeled it Spacetime Switches. there are actually a number of different topics we're covering but the, the idea of Spacetime 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, 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 lightyear. And the fact that if we measure distances in lightyears, a lightyear is a distance, the distance light travels in a year, as some of you may, may know. if we measure velocities in lightyears per year, then c, the speed of light, is simply one. By definition, it's one lightyear per year. It's the distance it travels in, in one year. And so, that and a couple of other tips that will make it 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, and derived last week, you get some more familiarity with them, just struggle with them a little bit. Try to get a deeper understanding of it and we're calling this Star Tours part 1. That is we're going to send, in this case, Bob will go on a trip to a nearby star, five light, lightyears away. The nearest star to earth is actually about 4.2 light years away. We mentioned that in one of the one of the early problem sets. But I think we mentioned, mentioned in terms of the distance not in lightyears, but just in how long light would take to, to get there, it's about 4.2, 4.1, 4.2 years. Anyways, 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 store, and she's on Earth.  So analyze it from her perspective, and Bob's perspective, we'll try to make sense of both their perspectives. And then we'll, 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 frames of reference. in a non-relativistic manner, the Lorentz transformation also derived by, 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, it subsumes the Galilean Tranformation. 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, and then get these transformation equations. Then we'll spend a little time exploring those transformation equations. Trying to understand them, seeing what they are telling us, see if they make sense from what we know so far. And then we're going to use those transformation equations. The, they're very general. They're useful in all kinds of ways but we're going to use them 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, 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 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 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 this, this problem we run into, that Star Tours part 2 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 you could travel at the, the speed of light. And then finally talk about combining velocities, we did a little bit of this with sort of the Galilean Transformation idea where if you know, if you have a car and you have a basketball shooting machine that, that we talked about, and then a tennis ball out, out of the basketball that type of thing. In our every day experience, those types of things just add, you add the velocities, or if the velocities are opposite 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 travelling at 0.9c, say Bob on his spaceship travelling at 0.9c. And then he shoots out maybe an escape pod or something, travelling at 0.5c away from him. So, he's travelling at 0.9c. 9 10th the speed of light. He shoots out of the escape pod at 0.5c, so that's 0.5c with respect to him travelling away. in classical physics we'd say oh, you just add the velocities. It's 0.9c plus 0.5c, Alice watching it over here. As Bob goes by and shoots off the, 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 actually in fact you will never see anything go past the speed of light. And so, combining velocities here, and show us the new form for doing that, such that no matter you know, how fast Bob shoots out that, 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 will never exceed the speed of light there. Okay. So that's sort of a rundown of where we're heading this week. Let's do the, 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, I said Einstein quotation-wise, 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 [UNKNOWN]. 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 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, or [INAUDIBLE] 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. It took about 10 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 or 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, in much more quantum mechanical direction and Einstein had some real problems with, with that. And, and so really for the last half of

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Jul 23, 2017
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