Transcript of a2-l02 ========== _0:08_: We're a bit tighter in this room than where we are in the other _0:12_: room, so we will, well, we'll all be friends. _0:17_: I think we're alternating. We're more or less alternating between _0:22_: this room and the boys room from from day-to-day. So keep track _0:27_: of the application to where you are _0:34_: after the confusion, technological confusion of the _0:37_: beginning of last time didn't get all the way through chapter _0:41_: one. So what I'm going to do is quickly touch on the last bits _0:45_: of chapter one. _0:47_: I'm going to go over them quite quickly, _0:52_: not talking them in as much detail as they as they would _0:56_: would deserve, because as I said last time, there are sections _1:00_: that you'll want to go back to in in coming weeks when it when _1:05_: the the point of you know why do we fight about time, why do we _1:09_: make a fuss about clocks becomes a little clearer. So I'm _1:13_: introducing these ideas to you, what you to have them in your _1:18_: head at this point. But the the texture of them will will arrive _1:22_: later, I think _1:26_: so, so quite promptly I I I expect to go on to chapter 2 in _1:31_: this section. So, so _1:35_: I'm just warning you that this will feel a bit rushed because I _1:39_: I expect you to be going back to this later. _1:43_: The last thing we did more or less last time was talk about _1:47_: this quick question of measuring times. And _1:51_: rather counterintuitively, I said that the only _1:55_: observer of the three involved whose time we are interested in _1:59_: right now, we put up with answering the question what is _2:03_: the time of the event in this frame? The only observer the _2:07_: relevant is the observer who was stationary in our frame and Co _2:12_: located with the event. _2:14_: OK, the driver has a can describe a time to that event _2:20_: because they were Co located with the event within the _2:23_: sneezing _2:25_: and they were stationary in that frame. They were sitting _2:28_: stationary in the car. So there are two frames here just to _2:31_: drive this point home, 2 frames here, the motorway and the car. _2:34_: They are both perfectly good frames. _2:37_: Different people are stationary in them and and different _2:40_: people. And there are two people Co located with the event. _2:44_: The policeman and the driver are both Co located with the event, _2:48_: even though they're in different frames. OK, so we're imagining _2:51_: the sneeze, the driver and the people all in the same the same _2:54_: spot of the same location and location. Even though you know, _2:58_: because it's a car driving past, they're not literally in the _3:01_: same spot. But for the purposes of this, they are the same _3:04_: sport. _3:06_: I will watch up. You signing somewhere else? _3:12_: Um, _3:14_: watching this happen is not _3:17_: a way in which we measured the time of that event. _3:20_: Partly because if we see that event happen, things like we've _3:25_: got to wait for the light to get to our eye, so there's an extra _3:29_: correction would have to apply. But also because as woke become _3:33_: clear, the question of what is the time, what is the time? _3:37_: Becomes a complicated question _3:40_: and we are simply avoiding that question. You know in a good way _3:44_: by saying the only time that matters is a time of person _3:47_: collocated with an event. So I'm seeing this again and again and _3:50_: again just to drive it home that the time at which only happens _3:53_: at the time of an observer Co located with the event. _3:59_: So you'll forget that and you get confused. But I've said to _4:02_: you several times, so bank those up and listen to them in your _4:05_: head, _4:07_: intended to come, _4:09_: so that how we measure time, _4:11_: we make a big fuss about it. _4:13_: How do we measure distance? How do you measure lengths? And this _4:17_: also is something that will _4:20_: become _4:22_: a bit more complicated _4:24_: that you think that you expect. _4:27_: If I wanted to measure the length of this bench here, _4:34_: then there's a variety of where they could do it. _4:36_: I could get a a tape measure _4:41_: or he'll get better stick and lay it out. And there's also the _4:44_: ways I can think of doing it. _4:46_: But the way we are, you will think of of measuring. That _4:50_: is if I get me and a lot of friends line it up along the _4:54_: front here in previous years I've made this an audience _4:57_: participation but _4:60_: activation front bench you if this is a a coordinate frame, it _5:04_: is room, it's a coordinate frame. _5:08_: Then this observer here has you know, you know your coordinates, _5:11_: that you're this far from this wall, this far from this wall, _5:14_: this far from the ground. You know the same. _5:19_: Everyone knows their coordinates in the room, _5:23_: and there's another observer at the other end of the bench _5:26_: who knows their coordinates. And you know and the timings are _5:29_: one. _5:30_: And the way we measure the length of the bench is we _5:34_: arranged beforehand that everyone will walk. It will will _5:39_: look at the bench at a certain time _5:42_: and everyone I said tape ever looks at the bench and the two _5:45_: people who are at the end knew it down. I was at the end of the _5:47_: bench _5:48_: and then we subtract the coordinates. _5:51_: OK and the length of the bench is. _5:56_: This was every coordinates mine, this was average coordinates, _6:00_: but that seems a very long winded way of doing it. But it's _6:03_: very precise. It's very and it's precise enough that we can _6:07_: really think, think through what what happens here. _6:11_: It's over. It's over complicated for this further set of _6:13_: situation where the bench is just sitting there. There are _6:16_: all sorts of other ways we could do that. _6:19_: What about the case where the bench wasn't just sitting there, _6:22_: it was flying through the room. _6:25_: OK, so it is zooming along _6:28_: at some relatively speed. _6:30_: How then _6:31_: do we measure the length? What is the length of the bench in _6:36_: that sense? _6:38_: And there's a variety of ways you could think of doing that. _6:41_: But the way that hangs together, and the way that it is _6:44_: productive for relativity is this we do basically the same as _6:47_: we did before. _6:50_: So imagine you're all sitting where you are _6:54_: and the bench is moving, moving past you. _6:57_: OK, so you're standing clear. _7:00_: And as before we say, OK, everyone, _7:04_: get you synchronise your watches. _7:06_: At a certain time we're going to look in front of our, in front _7:09_: of our noses _7:11_: and as this bench, you fly through the room, _7:14_: everyone goes _7:16_: do, do I see a bench in front of me? _7:19_: And depending on where the bench is, some foot wouldn't. _7:23_: Some thought would _7:25_: so we see that the first person who spotted where we saw the _7:28_: bench in front of them and we see the last person who saw the _7:32_: bench in front of them and we surprised those coordinates _7:36_: and that's the length of the bench in this frame _7:39_: seemed over complicated. _7:42_: But the point that the crucial thing is at the same time, _7:47_: OK, so we prearranged what time the observation were going to be _7:51_: made. Everyone made an observation just in front of _7:54_: their nose. Do I see the bench or do I not and we collected the _7:58_: data afterwards _8:01_: and that the the the reason why we're doing it that way is _8:03_: because it makes it clear where time comes into it. _8:07_: Everyone made the observation at the same time in the with their _8:11_: synchronised watches and everyone in the in the room _8:16_: has synchronised watches, _8:18_: OK and and we can talk about the the, the, the process of of _8:22_: doing that. It's interesting, but _8:26_: play parenthesis _8:29_: and that and that of the very other other options you might _8:32_: think of. That is the way we measure the length. _8:35_: What we'll discover is that gets a bit more that that that that _8:38_: has interesting consequences when it comes to _8:42_: thing moving at Russia 6 speed. So I'm not going to explore _8:46_: those consequences right now. I'm going to explore them _8:49_: shortly in probably chapter three or more Lecture 3, _8:52_: but this is the picture I want you to have in mind. _8:58_: We have among the people standing on a platform that we _9:01_: could hear an awful lot of trains going through stations. _9:05_: People are standing on a station platform. They've marked off _9:10_: the coordinates along the platform. So there's the origin _9:13_: of the X axis is at one end of the platform, and there's a grid _9:17_: on the platform. There are two observers are stationary. _9:20_: They're standing on the platform and the train goes past at a _9:24_: certain time. The same time _9:26_: they observe where the train is, you know, where trained and the _9:29_: and the two extremes 2. At the end of the train, subtract the _9:32_: coordinates and that's the length. That's what we are _9:35_: taking to be the length of the train in the in that in that _9:38_: frame. _9:40_: We're going to explore that more in a bit, but I want to log that _9:43_: with you right now as what we mean we have, we have a we we do _9:46_: we we mean a very specific thing. We'll talk about _9:48_: measuring a length. _9:51_: Any questions about that? _9:56_: And _10:00_: and and and and sneak preview. The reason why we are making a _10:05_: fuss about this _10:07_: is because it turns out that the question of of of simultaneous _10:11_: is what is what turns out to be more complicated than we _10:15_: thought. We're measuring the end of this, of this train end to _10:20_: this bench, whatever at two points for just simultaneous in _10:24_: our frame. _10:25_: It turns out that isn't A-frame dependent thing. That that is a _10:29_: is A-frame dependent thing. It's not a frame independent thing. _10:32_: Different frames _10:35_: have different notions of what is simultaneous _10:38_: and that's where a lot of the there's a lot of stuff about _10:41_: length contraction possibly comes from. _10:47_: So that's a picture of a, I think an engine change odometer _10:52_: that I I talked to the the _10:55_: observers and their _10:57_: distance measuring sticks. I think that was a sort of _10:60_: imperial distance measure in _11:02_: available now. The other thing I want to talk about is clocks. _11:08_: Clocks are nice and simple things. Of course you have one _11:11_: on your phone, on your wrist, or on the wall. _11:16_: We're going to abstract the notion of a clock. A clock is a _11:20_: thing which tells you the time and nice and complicated way. _11:24_: What is the time? It's a _11:27_: um, _11:29_: this is where you know the whole thing can start to go off rails _11:32_: and people get off go. What is time and all that stuff? Time. _11:36_: Time is a distance. Time is a distance through time. We're _11:39_: going to be very simple minded about what? What time is it? _11:43_: It's. It's _11:45_: how far from in time from something you have moved. And a _11:50_: useful image, I think is this thing and this thing is it's _11:56_: called _11:58_: Ohh God, what is _12:01_: And _12:03_: a tough real log. _12:05_: If you are on a sailing boat and you want to know how far you've _12:09_: sailed, then one way you can do that is to a propeller behind _12:13_: you. _12:15_: And as it pulled through the water it turns and you discover _12:18_: how much water you've you've moved through and you can use _12:21_: that to navigate your position if you have GPS or whatever. And _12:25_: that's a picture of old fashioned taffrail log, and I _12:28_: think it is useful to have in mind the idea of a clock as a _12:31_: taffrail log. It a clock tells you how much time you have gone _12:35_: through. _12:38_: And again, this sounds as if I'm making things over complicated. _12:40_: You know how How is that a complicated notion? _12:43_: It's. It turns out to be important, and it turns out that _12:47_: we have to be precise about it _12:50_: because at the _12:53_: the question of how much time have I moved through? _12:55_: Is very straightforward from the point of view of being a clock. _12:60_: It gets more complicated when you want to step back and talk _13:02_: about things moving around at speed. _13:05_: So again I want to lodge that thought in your head I _13:11_: in in the next chapter and one after that we'll we'll we'll _13:13_: start to use that _13:16_: and and see why we have to be so precise about that. So I'm I I'm _13:20_: this this this whole first chapter is a whole a whole bunch _13:23_: of of of sneak previews _13:26_: and you may see mention of the clock hypothesis. The clock _13:29_: hypothesis sounds grand is just clocks are unison simple the the _13:33_: they they don't they don't malfunction you we we assume _13:36_: that clocks are working that they don't get suddenly break _13:39_: when you got when they got high speed or with their accelerators _13:43_: That's obviously not true all clocks but the the the clocks we _13:46_: imagine our heads for the purposes of this of this whole _13:49_: study are uncomplicated and and and people are careful enough _13:53_: about this whole area people need to see that _13:57_: OK _13:59_: I think almost you're getting good progress here _14:03_: then one of the one of the last points is as you saw that same _14:12_: are we in the right place. _14:14_: No we are not _14:19_: and I was all I was saying _14:22_: Yeah _14:24_: that we can talk of _14:27_: frames yes see X&Y and a _14:32_: observer _14:34_: stationary in that frame _14:37_: with an order order there and coordinates X&Y. _14:41_: And we could talk of _14:45_: another frame, _14:48_: it's primed with coordinates X prime, Y primed and Z prime and _14:52_: T primed. And we presume there will be observer, one or more _14:57_: observers stationary _14:59_: in that frame _15:00_: and that frame _15:02_: is moving at speed V in _15:06_: with respect to the frame S along the X axis. _15:14_: And that is that's a setup we're going to, we're going to see _15:17_: that diagram again and again and again in one other variant. OK. _15:21_: So get used to it. _15:23_: That setup is called standard configuration. _15:27_: So when I say 2 frames are in standard configuration, that's _15:30_: the picture that jumps into your head, _15:34_: plus _15:35_: the constraint that at time zero _15:42_: time t = 0. That's the time on the watch of the observer in S _15:49_: the _15:53_: the origin of the moving frame. _15:57_: At the origin of the _15:59_: stationary frame, _16:03_: the origin of the _16:04_: moving frame is there as well. So sorry that that makes our _16:08_: over complicated. The origins coincide at time t = 0 we we we _16:12_: set the clocks and set the the coordinate systems so that the _16:16_: origins are the same. At time t = 0. So at time t = 0, T prime _16:20_: is equal to 0 as well and the true origins are at the same _16:23_: place. _16:25_: OK, so that that, that the, the, the, the setup, that everything, _16:31_: all the equations we end up using not too many of them and _16:35_: presume. OK. And so _16:38_: and _16:43_: there is _16:45_: basically there's approximately in round numbers, there's _16:49_: approximately 1 relativity question and it comes to the _16:52_: exam. _16:54_: It's Here's a puddle _16:57_: cast into standard configuration. _16:59_: Here are some coordinates you know extract from from from the _17:03_: the some the corners of the various events. Identify the _17:06_: events. Work out what they're they're those coordinates are in _17:10_: the other frame. _17:12_: That's what so many of the exercises about is basically _17:14_: what the what the all of the exam questions are about. You'll _17:17_: see that again and again and again _17:19_: and and and it sounds, you know, why is that important? You you _17:23_: might ask him. We would. Do we have to worry about the _17:26_: coordinates of this event in of in two different frames? _17:30_: Specific that specific problem? No. But that's the the tool that _17:34_: we use, that the mental tool we use to work out things like the _17:40_: the the way that Russia's momentum works, relativistic _17:43_: force, Russia energy and and so on. So that that toy problem in _17:47_: a sense is the one that drives all the all the all the other _17:51_: things. _17:52_: So step one of all of those _17:56_: that variance of that more same puzzle is draw diagram, put it _18:01_: inside configuration. _18:03_: OK. So again, you'll see this lots and lots of times I'm _18:06_: seeing it now to say it's important make sure you're _18:08_: you're more or less have that more or less right way up in _18:11_: your head. _18:13_: OK. _18:17_: Yeah. _18:18_: Um, _18:20_: what's the definition of that? _18:23_: I'm also going to mention, _18:26_: as I said, I I hope I made clear last time the notes and the _18:31_: lectures are the same material, just delivered in different _18:36_: ways. _18:39_: I hope the lecture is a bit more vivid than the notes, but the _18:42_: the notes are more, you know, more careful than the the the _18:46_: the the the precise wording is quite carefully thought through _18:49_: and revise from year to year based on what people have found _18:53_: puzzling. _18:54_: So there's a sort of fast and slow stream of the material, but _18:58_: another source of material is books. _19:02_: The library has books. Wonderful thing. _19:06_: The web has stuff stuff on it, _19:09_: not always equally good, but I will mention a couple of books _19:14_: which are on the which, some of which are on short loan in the _19:19_: library and are available for as ebooks. _19:23_: So if you go I I see that there's a link in the middle to _19:27_: the A book list which in the notes to a booklist which it was _19:30_: actually turns out to be out of date last year's. But on the _19:33_: Moodle you'll find a link to the book list books at the library _19:37_: or something. It's called and that's a link to recommended _19:40_: books and including electronic texts. _19:44_: The Colonoscopy is the A2 course recommended book. It talks _19:48_: relativity. It's not wrong. I don't find it terribly exciting _19:52_: the way it talks relativity. And there are and it makes some _19:56_: slightly _19:58_: aspect notational changes, but still worth reading to get a _20:02_: different way of of making sense of this. _20:06_: Tyron Wheeler is an excellent book. It's a book though you _20:15_: it's worthwhile looking looking through that. It's a book you _20:18_: read all of the more or less. I think it's a great book but a _20:22_: bit of a proposition _20:26_: that book Rindler if you're getting if stuck in puddles and _20:30_: but deep subtleties here you know what is time and and so on _20:34_: then I might well you say go and have a look at that I might in _20:38_: the notes points will bits of of of renderer could render is very _20:42_: careful about things like that _20:45_: it's a book that goes on to well beyond this course but for for _20:49_: deep things that that that's useful. The book called French, _20:54_: which is very old fashioned but in portable, quite a good way _20:58_: and I think quite different from from me. There's a long way of _21:02_: saying read other things. _21:05_: Don't know, _21:08_: I think. I think the way I teach relativity is the best way, _21:12_: but that's the way it makes more sense to me and I am not you. _21:17_: I hope you will agree that the way I teach relativity is a good _21:20_: way, but other views are possible _21:24_: so I don't I I encourage you to to to to find other ways of _21:27_: thinking it through. Be aware though, there are some there. _21:31_: There's more than one routine, not all of them are completely _21:34_: compatible, and there are a few rotational differences, so just _21:38_: be a bit alert to that when reading other other sources. _21:45_: OK, that's the end of last week's lecture _21:49_: a while ago into Chapter 2. Are there any questions? _21:56_: Everyone has _21:57_: any worries, _21:59_: he thoughts. _22:02_: OK, I'll take that as a I mean, my essay isn't terribly good, _22:06_: but I don't think I would put hand up. I'll show, I'll show _22:09_: it. I don't mind audience participation within limits. _22:14_: OK, _22:22_: so _22:26_: I mentioned _22:28_: and the last time that the entire physical physical content _22:32_: of this course is comes into two axioms. _22:36_: And by physical content by I mean things about our universe _22:41_: that could be otherwise. _22:45_: The mathematical statements are, and we admit, a bit of the _22:48_: philosophy of mathematics here. Mathematical statements are true _22:53_: if the things that the _22:57_: are based on are true. So there's a there's a logic to _23:00_: maths. You can't. If you agree with this statement, then this _23:04_: deduction from it, you can't disagree with. So those are _23:07_: mathematical statements. _23:09_: Physical statements are things about our universe that could be _23:12_: otherwise. _23:14_: So gravity, you know, _23:17_: if he goes me, for example, you can imagine a universe where _23:20_: that wasn't true. And before Newton, Aristotle did imagine a _23:22_: universe where that wasn't true and everyone went, oh, that's _23:25_: fair enough. That's clearly how it works. _23:28_: So Newton saying _23:30_: using first law in second and third law, we're making a _23:32_: statement about the world. He using a statement. This is about _23:35_: how our universe is, _23:37_: although it could be otherwise. _23:39_: And the two axioms are _23:42_: relatively interesting because the the the physical content of _23:45_: it is so tiny _23:47_: it is a large chunk of _23:51_: of relatively going to learn. For the first five chapters, C _23:54_: consist of just these two bits of physical information. _23:58_: And that's amazing. I mean, relatively is is weird _24:01_: and the most so parenthesis and most physical theories version _24:06_: one of them when they were first produced by by Newton or Galileo _24:11_: or Maxwell or whoever. _24:13_: Yeah, I'm largely an intelligible and if you go back _24:16_: to the original papers you know you they don't make sense. You _24:18_: know because folks since then have gone. I know that's a _24:21_: really weird weird way of explaining it. He had a much _24:24_: better way of explaining it that that turns out to be a much more _24:27_: productive way of doing so. So the original version of _24:29_: Microsoft equations which underlie all of electromagnetism _24:32_: are unintelligible. You can't read that paper unless you're a _24:35_: historian in physics basically because it just doesn't make _24:37_: sense. Why would you even think of it that way? _24:41_: Relativity is, _24:43_: I think, almost unique in the Einstein 1905 paper is still _24:47_: basically readable, _24:49_: and that's 120 years ago. _24:55_: Einstein's version. One overactivity will basically _24:59_: that it you know that's it done _25:01_: and that's that's very strange. I mean that and and and and that _25:04_: in a way what made Einstein weirdly good that you got the _25:07_: right answer from the very beginning _25:11_: and all this stuff but trains as well everyone talks about trains _25:14_: through relativity because it's a very convenient. It's a great _25:18_: example to use. Actually did that first in a popular book _25:21_: talking about relativity. _25:23_: It's enough enough _25:27_: fandom, _25:29_: SO2 axioms and the consequences. _25:35_: Objectives, power, blah. And _25:38_: I want to see _25:40_: that we're talking about Einstein, Special relativity. _25:44_: The principle of relativity, which is actually one, was not _25:48_: Einstein's, but Galileo's, _25:50_: and in the notes I quote a passage from _25:57_: and from from Galileo's account which Book Awards and which is a _26:02_: long party. We describes imagining _26:06_: being below decks in a ship with all sorts of stuff. _26:13_: Both. You could roll, roll around small animals, whatever, _26:17_: and and they all do their thing _26:21_: and if the if the boat then starts sailing out so it's _26:24_: moving _26:26_: at a constant speed, _26:28_: everything works as before, _26:30_: Agario said. Ohh, that's actually quite significant. _26:33_: That's telling something about the world that you can't tell _26:36_: you're moving _26:38_: and that is the the the the that that Galileo is relatively _26:42_: principle is _26:45_: axiom one. You're like of Einstein's special relativity _26:49_: that you can't tell you're moving. And so if we say the the _26:53_: if we see that same thing and we pinned down your intuitions in _26:60_: the the, the, the, the terminology we're just starting _27:02_: to use here. _27:04_: We're saying that if you are, _27:07_: if you if you describe physics, _27:10_: describe a physical process like someone throwing the ball _27:15_: using the coordinates _27:17_: of some understanding on on the harbour, _27:20_: the ship goes past someone on the board could be throwing a _27:24_: ball from hand to hand and it's uses laws work perfectly well. _27:28_: You know things weren't going to parabola blah blah blah blah _27:31_: blah. You know how to do that sort of stuff. So you could _27:35_: describe it perfectly successfully using the X _27:38_: coordinate along the harbour or or the train platform and the _27:41_: time when you watch _27:44_: and the person in the porch or on the train platform or on the _27:47_: train _27:48_: throwing the ball from hand to hand could do exactly the same _27:52_: thing. They could also describe what's happening using Newton's _27:56_: laws and, but they would be using the coordinates X prime, _28:01_: which are the coordinates attached to the boat. _28:04_: And both of these are good descriptions and it's very easy _28:07_: if you know one of these _28:09_: to to work out the other one. Because _28:13_: for this boat instant configuration, _28:17_: because the frame is moving at speed V along the X axis _28:23_: at any for any event, the ex prime coordinate of that event _28:29_: see the observer clapping the hands. _28:33_: The ex prime coordinate of that is the X coordinate of that _28:36_: minus the distance that the thing has travelled. This sounds _28:40_: insultingly obvious. OK, I'm. I'm not telling you anything _28:43_: sophisticated here. I'm telling you something you are very _28:46_: familiar with. _28:47_: I'll say that a lot, A lot of times as well. _28:51_: A lot of one of the ways people get confused about relativity is _28:54_: they they hear something like that said and they think, Oh my _28:57_: God, that much more complicated than I thought. _29:01_: It's not what we're doing, What I'm doing there in describing _29:04_: something you do understand that you understood when you were in _29:08_: school. _29:09_: But I'm using the terminology of this rather elaborate _29:13_: terminology of changes of frames and stack configuration to do _29:17_: it. So what I'm doing is I'm, I'm letting you translate, I _29:20_: mean you already understand, into slightly different _29:24_: conceptual rotation. OK, so I'm not telling you anything funky _29:28_: there. _29:29_: OK. _29:31_: And this transformation of coordinates _29:35_: is known as the Galilean transformations. Galileo didn't _29:37_: call that, and no one called it that until after people talked a _29:40_: little bit relativity. In fact, they had to give a name to that _29:43_: perfectly obvious thing, that perfectly obvious transmission _29:46_: coordinates. OK, so I talk about the Guardian transformation. I _29:49_: just mean that the obvious thing _29:52_: and that is the guardian transformation written out _29:56_: again. It looks like I'm making a meal of this, _30:01_: the X coord X prime coordinate. So the coordinate of this event _30:05_: in the moving frame is. Is that the why part? Prank coordinates, _30:08_: how high up it was? Blah, blah, they're the same time as the _30:12_: same the speed of the ball being thrown. _30:15_: If I threw a ball from the back of the ship to the front or the _30:19_: back of the train to the front, then it speed in the train and _30:23_: its speed as viewed by the station platform are going to be _30:26_: different. _30:28_: Not surprisingly and and the different by that amount you _30:31_: know the, the, the, the, the, the, the, the speed on the train _30:34_: is the speed on the platform minus the speed of the of of the _30:37_: train. Not a big surprise. _30:40_: Nice and simple. Too simple even did writing down _30:46_: sue relative principle. Is is actually one _30:50_: quick question. _30:52_: Suppose I have a fancy new cosmological theory that says _30:55_: the special point in the universe. See halfway between _30:58_: here and Andromeda. _31:01_: And the gravity should constant G changes depending on how far _31:05_: you are _31:07_: from that point there. So there's a sort of a sort of, I _31:10_: don't know what you call it, but that that my wonderful wonderful _31:14_: idea. This solves dark matter. I I see if the graphic content _31:17_: varies according to distance from the special point _31:21_: to that idea of a chance of being right, _31:27_: who is the chance being right? _31:29_: Who didn't have a chance to be right? _31:32_: Who had put the hands up yet? _31:34_: How about we chat between you and I _31:39_: whichever way you think that could be. Why? _32:14_: OK, _32:17_: how many folk would say that idea? Yeah, is a is a gore. _32:23_: How may we see it? Couldn't work work. _32:26_: OK, _32:29_: that the reason it can't work _32:32_: because if that worked it would violate the relativity _32:36_: principle. _32:38_: So that Richard principle that that that that that axiom you _32:41_: can't tell you're moving had already done some work. _32:44_: Why did it violate the right principle? Because if _32:49_: if you if that theory were true, then what you could do is _32:53_: measure. Measure G, Measure big. Not very easy. You could measure _32:57_: big and and find a value for it and then you sort of think what _33:01_: was a wonder about a bit and you measure again. I think I didn't _33:06_: get right the first time. You measure it again and it's _33:09_: changed. _33:12_: You know, Either you made a mistake in your measurement or _33:15_: you've got closer to this, this magical point in half. In other _33:18_: words, you'll be able to tell you we're moving _33:22_: so, so, so there are two principle, says _33:27_: Ohh. There are multiple ways of of reframing the relativity _33:30_: principle, and one of the books I point to in the in the _33:33_: biography is a book about the relativity principle about, you _33:37_: know, how you can think about this and what and what its _33:40_: consequences are. Just that one axiom. _33:44_: So it's already doing work just by by saying that because it _33:48_: effectively says all coordinate frames are equal, you can't pick _33:52_: one that's special, and you can't pick one that's absolutely _33:55_: moving. _33:57_: So it's useful to think back on that and think _34:01_: and I think that's that's a very that looks rather silly question _34:04_: but it's very productive question. _34:07_: We've got two things puzzle about and if you make sure you _34:11_: understand why they're principle is it's getting there _34:15_: and the other thing that I'll that's important is the idea of. _34:22_: Ohh go this is not I'm gonna get through all through all the _34:25_: changing have to have to go faster and is _34:33_: I, I, I I said that we can analyse physics in one frame and _34:37_: and and equally well in another we'll get different numbers _34:42_: the the velocity of the ball of the throwing ball will be _34:44_: different in in in in these two cases but it would be the _34:47_: there'll be the same you know but there'll be the same _34:50_: physics. It would be the same equation. _34:52_: For example, the constant acceleration equations are just _34:57_: X prime equals _35:01_: UT plus half a t ^2 _35:05_: as you don't recall, _35:08_: and _35:10_: the executive square _35:13_: even apply the _35:18_: the _35:20_: gully and transmission to that _35:24_: I will get. _35:26_: So that's X = X X prime equals X _35:32_: -, b T and we end up with. What is it? _35:38_: And the X _35:42_: goes P minus _35:46_: then we say that X = X prime plus _35:51_: PT equal to UT primed plus _35:57_: half _35:58_: a T primed squared. Because remember the the T prime equals _36:03_: T was one of the other. _36:08_: You need to go in transmission or X prime is equal to U -, v _36:15_: she primed plus _36:17_: half a _36:18_: T prime squared. _36:21_: So what I've done there _36:24_: is I have changed frame, _36:27_: I change coordinates using the Galilean transformation _36:31_: equations. I've gone from the description of this accelerated _36:35_: motion _36:36_: in the platform frame _36:39_: or the harbour frame whatever, to the description of the same _36:42_: motion in the _36:45_: train frame and I've got an equation which is different _36:50_: because it has a different speed. Here I have the same _36:52_: form. _36:53_: In other words, the explanation of the acceleration acceleration _36:58_: equations work just as well in the 2 frames. It's as if I just _37:02_: swapped added primes to everything _37:05_: and that looks what you're going. You know what the why _37:09_: that surprising. _37:11_: It's not surprising because you you've been you have you intuit _37:15_: quite a lot of the principle. But the point being that the is _37:19_: important here is that the description of of the physics _37:22_: that's happening as described by an equation in the platform _37:26_: frame _37:27_: and the description of the physics that's happening as _37:30_: described in the _37:32_: train frame _37:34_: are the same. _37:35_: The equation has the same form, the number of different, because _37:40_: the velocity has picked about a term from the speed of the _37:45_: frames. _37:46_: But the form of the equation is the same, and that turned out to _37:50_: be a. That's your first look at a deeply important principle if _37:55_: you're going to do general activity in 4th, 4th or 5th _37:59_: year. If you stick with this area, _38:02_: then that becomes _38:04_: the the the principle that guides essentially all of _38:07_: general relativity, The fact that that the form of the _38:10_: equations has to say the same in different frames. _38:14_: The court is basically we are seeing the coordinates you've _38:16_: picked. The coordinates you pick don't matter, _38:19_: they're just a calculation or two. _38:24_: So the next thing that's interesting here is _38:30_: you've heard of Maxwell's equations. Is that right? Yep. _38:35_: Is that is that, is that right or is that wrong? I saw some _38:38_: notes there, but there were. I'm not, I'm not. I'm not going to _38:41_: ask you questions about them but you've heard of them and you _38:45_: you very good and they they describe electromagnetism. So _38:49_: they they unify all of the the electric and magnetic laws that _38:53_: were developed through the century and that's a way of of _38:56_: of writing them down. I'm not going to you know that that's _39:00_: math beyond portable point but they are they are nice macro _39:04_: creations are great. They were developed during the next _39:07_: century and they were found very quickly to be, OK, that's the _39:11_: answer. That's that's how electromagnetism works. _39:17_: But the problem _39:19_: which is that the speed of light, _39:22_: it's sort of built into those equations _39:25_: and people discovered that if you do _39:31_: the Galilean transformation _39:33_: on macro equations and that's a mathematical quite intricate _39:37_: thing to do. But that's not the point. If you do this _39:40_: transformation _39:42_: that what you get afterwards _39:44_: is microaggressions. _39:46_: In other words, what that appear to be saying was the macro _39:50_: equation that didn't work when you were moving. _39:54_: But what that means is that you can tell if you're moving _39:58_: because if that were true. _40:00_: Then you could just do an electrical experiment. The _40:03_: experiment and if maximum equations work then you're _40:05_: stationary. If they don't work, then you know you're moving and _40:08_: that breaks. Breaks the relative. France _40:11_: and folk were disturbed by this because that's clearly _40:16_: not right, because a radio still works when you're moving _40:22_: light still works removing that electronically radiation. _40:27_: So there was a big problem _40:29_: at the end of the next century, _40:32_: and this was highlighted in the very first sentence of of of _40:36_: Einstein's 1905 paper. _40:39_: It is known that Maxwell's equations, as usually understood _40:42_: at the present time, making five would apply to moving bodies, _40:46_: least asymmetries who should not appear to be inherent in the _40:49_: phenomena. That's a long way of saying they break _40:52_: the IT looks like Maxwell tweeted don't work is the _40:55_: problem. _40:58_: So at this point there are were four possibilities. _41:02_: Either _41:03_: Maximilian is wrong, _41:05_: perhaps _41:06_: could try. It didn't work. _41:08_: One possibility. _41:10_: Perhaps the relativity principle is wrong. Perhaps you can tell _41:14_: you're moving in some circumstances. But that seems _41:17_: very that's not comfortable motion because that seems so, _41:20_: so, so fundamental to our idea of how the universe works, _41:25_: pops the Galilean transformation is wrong. _41:28_: Perhaps the the the this _41:30_: thing here, perhaps that perhaps there's more to it than that. _41:34_: Perhaps there's some new physics happening here, _41:37_: and the answer you will not be surprised to discover it. _41:40_: Migrations are right. _41:42_: The relativity principle is right. Is the Galilean _41:45_: transformation. That's wrong. _41:48_: And special activity is the new physics that comes out of this. _41:51_: So this, it turns out, is this bit that's wrong or assumption _41:55_: that that was how you went from one frame to another. That's the _41:58_: bit that broke _42:02_: you know to everyone surprise and horror and and it it _42:05_: although it's relativity was adopted as the answer and it was _42:10_: agreed organically the right answer in a remarkably short _42:14_: time. It was about a decade it took for basically everybody to _42:18_: to be on board with saying ohh right that that solves the _42:22_: problem. There were holdouts were a long time and there's an _42:26_: interesting story to talk about about the whole thoughts, but _42:30_: the the acceptance of what was in fact faced with _42:39_: and in that paper. _42:43_: I think it was on to talk about _42:47_: example of the sort together with unsuccessful attempts to _42:49_: discover any motion of the earth related to the light medium. _42:52_: And this is the idea of the ether, because with one of the _42:56_: ways of making sense of Maxwell equations and undergoing _42:59_: transformation would see our maximum speeds only work in _43:02_: this. There is a reference in an apparent reference frame, sort _43:06_: of which is this idea of the ether, which is the the thing _43:10_: that that electromagnetism wiggles in, in the same way that _43:13_: water we wiggle and water _43:16_: we waves on wiggle in ether and had strange properties. We _43:19_: didn't really make a lot of sense. But there's another long _43:22_: story there. But it was experiments such as the famous _43:24_: Michael Small experiment, which we could, which you may have _43:27_: heard of but we're not going to talk about. We did try to try to _43:30_: actually detect that movement in the ether and failed _43:33_: and failed again. And failed again and everyone was going _43:37_: well. This can't fail. This can be wrong, but that is what is _43:40_: being referred to here _43:44_: and _43:47_: and what _43:49_: Einstein. Einstein then in the paper upgrades this principle, _43:52_: relativity, _43:54_: to not being just a statement about mechanical motion, but to _43:57_: say all the national frames are equivalent for the performance _44:01_: of all physical experiments, _44:03_: so that it absolutely nothing you can do. It's not just that _44:06_: this works from mechanics, but for trains going through _44:09_: stations, it works for all of physics. There's no physical _44:12_: experiments there, no chemistry experiment, no biological _44:14_: experiment, no social experiment that you can do that works _44:17_: differently when you're moving. And that's a very bold _44:20_: statement, is saying we're not talking about Marxism here. _44:23_: We're not talking mechanics here. We are talking about all _44:26_: of physics. _44:31_: Umm, _44:37_: this. This will be a point to to to to to, to, to finish on. _44:41_: So I'm _44:46_: I'm standing here with a friend moving past me in a rocket. So _44:49_: some some huge speed. Let's see. _44:51_: Very high speed. _44:53_: And I observe her watch to be ticking slower than mine. _44:58_: Let's see it's a good it has magically broken because of the _45:01_: rocket. But I unless don't worry how we observe that that watch _45:05_: taking slower because that also the complicated thing. But one _45:09_: way or another observed that what should be moving more _45:12_: slowly than mine, _45:14_: you just I'm going to tick, tick, tick. She's going to tick _45:17_: take, take. _45:19_: No. _45:20_: These windows are too easy. _45:22_: She could look and see my watch, _45:25_: OK, and she would she see my watch moving faster than hers, _45:30_: or slower than hers? _45:33_: Who says you might watch moving faster than hers? _45:36_: Who says you see my watch moving slower than hers? _45:39_: Who had put the hand up yet? _45:43_: I'm not. I'm not taking notes of Hubert the hands up the the _45:45_: reason I was able to put the hand. But I want you to guess _45:48_: when we're another just just to write the company self. So in _45:50_: the last couple of minutes, _45:52_: just talk to your neighbours about what that should be. _46:17_: Why does it bother? _46:30_: Yeah. _46:33_: OK. _46:37_: Think of the question again. _46:40_: Whoops, _46:43_: books. _46:47_: I watched the movie slower than mine. _46:51_: Who would see? She sees my watch moving slower than hers. _46:56_: Who sees? You see my watch moving faster than hers, _46:60_: fairly evenly split. There _47:02_: the answer is _47:05_: that although there's clearly quite quite interesting to _47:08_: analyse _47:09_: and _47:11_: the watch must be moving slower. _47:13_: So I see her watch moving through the main, _47:16_: and she must see my work moving slower than hers, because if she _47:19_: didn't, _47:21_: then _47:22_: one of us would know which one was moving _47:24_: and that we find the right principle. And that makes no _47:27_: sense. I mean, come on, how can my watch moving faster than _47:30_: hers? And how Watch moving faster, faster than mine _47:34_: That's so. So we don't. We have. We haven't even got the second _47:38_: action yet. _47:40_: Already the _47:43_: first. The first action was telling us this extraordinary _47:47_: thing about time _47:49_: that that we can, the two of us can make observations of each _47:52_: other, other clocks, and come to opposite conclusions. But what's _47:55_: happening _47:57_: and this sort of thing is why people go no brothers can't be _47:60_: right. That doesn't make any sense. Oh my God, it does. But _48:03_: you have to be quite careful. But what questions you're _48:06_: asking? Because I said let's not worry about how we measure the _48:09_: measure. How her watch. _48:12_: There's a lot of missing out there. _48:13_: OK _48:15_: and and and so it's it's when we ask the question what do you _48:18_: actually mean by measuring the other person's watch _48:22_: that when you discover you can step through this and you can _48:26_: come to something that does make sense and hangs together and and _48:30_: that's what we're going to be doing in starting in chapter 3. _48:34_: I have the other half of this chapter to go, but I will be, I _48:38_: think displaying myself about taking more. So I'll see you _48:41_: next Wednesday, next Tuesday.