Transcript of a2-l01 ========== _0:12_: Hi, I'm Norman Green _0:14_: and this, in case anyone having a little panic, is _0:19_: the relative gravitation strand of astronomy too _0:23_: good? You're there, we are. _0:26_: Now there's a couple of this first lecture is all a little _0:30_: bit weird because there's a bit of predatory stuff we've got to _0:33_: get through about how I organise the course. And the the topics _0:37_: I, I, I'm sort of gallop through in this first lecture seem a bit _0:41_: disconnected and that's this are sort of disconnected. But they _0:44_: are important important ideas that you've got to to get under _0:48_: your under your skin really more or less over the rest of the of _0:52_: the course. So you will come back to this material again and _0:55_: again over the course of of these 15 lectures, _0:59_: but we'll only really get properly going in the next _1:02_: lecture _1:03_: tomorrow. _1:06_: So with that said, _1:11_: that's the that's the wrong computer. _1:17_: With that said, there are some things I want to make sure to _1:20_: say _1:22_: which are. _1:24_: Um, _1:29_: if you look in the middle _1:32_: middle of the relevant page, you'll see that there are. I _1:36_: will show you a picture of the middle _1:39_: um, _1:40_: just so we know what we're talking about. _1:43_: Yeah, _1:45_: you will see that there are. _1:48_: The number of number of resources _1:51_: under _1:54_: under section 10 Medical section 10, _1:59_: including the lecture notes _2:01_: and I'd like to note _2:03_: include _2:05_: Introduction PDF, _2:07_: axioms.pdf. And there are _2:12_: some other versions of those which are the same but in a _2:15_: slightly laid out slightly differently. In a way, which _2:19_: might I I I think I think I aim to be more useful on a tablet. _2:22_: Whichever one that's the same in both of them. Whichever one _2:26_: works better for you, works best for you. _2:29_: And that's a theme, _2:31_: because these notes are fairly comprehensive. There's a lot of _2:35_: text in there _2:37_: and the way that I have ended up delivering these lectures is _2:41_: that the main event is the lecture, _2:44_: right? That's the the the the thing we focus on. _2:48_: But _2:50_: the notes others have Co main event if you like. _2:54_: They are Co equal. With the lecture as the way I'm I'm _2:57_: delivering this stuff to you because relativity makes a lot _2:60_: more sense the second time you do it. _3:03_: And if I do it in a lecture and I do it in the notes, you'd have _3:08_: getting two goals at once. _3:10_: And that's important, because it will only make sense the second _3:13_: time you do it. Now, if you think notes, first, I'm gonna _3:16_: read the notes and then just check what he says in the _3:18_: lecture, that's good. If you think I'm going to sit back and _3:21_: let it wash over me in the lecture and then check what's _3:23_: happening in the notes, that's good too. _3:26_: But you have to decide who you organise it, _3:29_: OK? You have to sort of take charge of your own learning here _3:32_: and work out how do I work out what's going on here? _3:37_: And if someone like Sam Goldman of the of the movie mogul who _3:40_: said half of the money I spend on advertising is wasted, _3:44_: but I don't know which half _3:46_: and half of what I say in the notes is irrelevant to you _3:48_: because you don't need that bit. But the the half that's that _3:51_: that is needed for you is different from for for for all _3:54_: of you. _3:56_: So the it's quite a lot of material here, a lot of pages _3:59_: here. _4:00_: Don't panic, you know it's supposed to memorise everything. _4:04_: OK, now the the notes are there as a resource for you to go _4:07_: revisit what happened to the lecture and make sense of it. _4:10_: Second time, it follows that it's a good idea to look at the _4:14_: notes before the lecture. _4:16_: Now you have to understand everything, but you get an idea _4:19_: of what to commit. This isn't a detective mystery. There are no _4:22_: cliffhangers. _4:24_: Yeah, _4:27_: spoilers are good. If you know what's coming up, then you can _4:30_: know that bit didn't make sense in the notes. I'll really pay _4:33_: attention in the lecture because it'll be explained in a slightly _4:36_: different way. _4:38_: OK, I could go on at this for some length and I will post. You _4:41_: know right now that that these slides are in there because for _4:45_: reasons, but I'll generally post the slides after the _4:49_: after the lectures. The slides unlike you know, some people do. _4:52_: People do have different opinions about how to lecture _4:55_: with slides. I don't like slides very much, so the slides I do _4:58_: are pretty minimal. There really is something for me to stand in _5:01_: front of or a diagram to point to. _5:04_: There's nothing in the slides that isn't in the notes. OK, so _5:07_: don't think Oh my God, if it's to work with those sides as _5:11_: well. _5:12_: OK. So the state-of-the-art of prop, A prop which I put, I mean _5:14_: I don't think the right, I don't think there's much point in _5:17_: putting them up here really but people want them, they feel _5:19_: secure if they've got a copy of the site. _5:22_: So I do OK, but I don't regard, I don't rate the site as a very _5:25_: important part of the resource. OK _5:28_: they're they're prop for me. _5:33_: The E360 I I think that means this is being recorded. _5:37_: I don't know where it goes after this echo through a bit of a _5:40_: novel thing I'm not very sure what happens. I trust it works _5:44_: and for the first couple of lectures I will do record record _5:47_: them myself. And just as a bit of a backup to do we reassure _5:51_: ourselves that doesn't work. Don't rely on that _5:54_: because some people think ohh all the lectures are recorded, _5:57_: just go listen to them afterwards. Doesn't make a lot _5:59_: of sense because being in the lecture concentrating it a part _6:02_: of the of the whole learning. _6:04_: Umm, _6:07_: the other big big big teaching resource is the exercises. _6:12_: Each of the chapters in the notes has a block of exercises _6:16_: which are pretty cute, _6:18_: clearly linked to specific parts of the notes. _6:22_: And relativity is something you only understand when you do the _6:26_: exercises. _6:28_: You cannot just sit back and and I think yeah, yeah, yeah, got _6:31_: that. _6:32_: You think you understood it when you sit in the lecture, but you _6:35_: didn't. _6:38_: Very probably not. OK, it's when you you you you're forced to _6:41_: rethink it and and it forced to buy ahead in the table a bit _6:45_: going through the exercises. That's where you understand it. _6:48_: You go ohh, it's simple really _6:50_: OK And that is also why it's in next semester that are released _6:54_: the solutions and notes to the exercises, not the semester, _6:59_: because OK is quite handy to check you've got the answer _7:03_: right, but it is more useful, you know, controlling that to _7:06_: bang your head on the table a bit. It's the it's the impact _7:10_: that get the learning in. OK, _7:13_: umm _7:16_: but boom. _7:17_: Um. OK, _7:23_: other _7:26_: Where are we? _7:29_: I although it's terrifically all fashioned, _7:32_: like the idea of aims and objectives, I think internally _7:35_: learning outcomes are one fashion later and they're out of _7:38_: fashion. _7:39_: For me. The aims and objectives are very simple and are very _7:42_: useful. Structuring notion _7:45_: definitions differ, but for me the aims are the point. _7:51_: They're why you're learning this _7:53_: and why I'm teaching it. And there are things like _7:56_: understand, _7:58_: appreciate the the other things you'll remember _8:02_: after you've done the exam in two years. You'll remember the _8:05_: aims you because that that that is why you're doing this course. _8:09_: And so if the exam were understand things, you went, _8:12_: Yeah, then we'd all be a lot happier. _8:15_: That'd be a nice exam, _8:17_: but it doesn't really work in assessment terms. So _8:21_: as well as the aims, there are the objectives, _8:25_: and the objectives are party tricks, _8:27_: the things you can do, _8:29_: things that you can be assessed on. _8:33_: They're not terribly exciting necessarily, but the best way of _8:36_: achieving the objectives. _8:38_: It's achieved the aims. If you understand something that the _8:41_: the objects would become pretty easy, OK, but they are the other _8:44_: other other nice concrete things which you can do. There are _8:47_: things like provide descriptions of such and such, _8:51_: describe as different an exam answer, blah blah blah and so _8:57_: on. _8:58_: So that's a very good distinction. I tend to associate _9:01_: exercises with objectives. When I'm making up the exam, I look _9:05_: at the list of objectives. _9:08_: So that's it's not a one to one mapping, but there is a _9:11_: correlation between what I think is what the objectives of what I _9:15_: think is fair game in the exam. _9:18_: Things which are clearly not objectives after the exam ask me _9:20_: questions. But that's the that's the basic answer I'll give you _9:23_: whenever you ask me that question _9:25_: every time and moving on very rapidly. _9:30_: Umm, _9:32_: so. And my timetable for this lecture to this lecture is _9:37_: timetables in a way that other ones aren't so much. It's _9:41_: already all short. So _9:44_: and we'll just press on. _9:47_: So the _9:49_: this market here because it's just backing up the the the _9:53_: market made that a lot of this is for you to work out what you _9:57_: need to read. _9:58_: So there's there's more material than you might like _10:01_: but that's because I'm sort of forcing you to to just to think. _10:04_: You will probably have look look at all the words in all the _10:07_: notes, but you your your study only says selected bits as there _10:11_: are signpost aims and objectives are signposts. At the end of _10:14_: each section, I tend to have a couple of key points, which is _10:17_: also signposts is what you should have picked up from that. _10:20_: You're very standard things. _10:23_: So that's sort of the other thing I've got to remember. _10:26_: Remember I was asked to say to you is there is no lab this _10:29_: afternoon. I think you know that because I think you were told _10:33_: that on Moodle. But to see you tracking up to Garscube, just _10:36_: remember, no love this afternoon, OK? They start. I'm _10:39_: not sure when they start. I don't have to do that, so I _10:42_: don't _10:44_: OK _10:45_: any questions about the other sorts of organisational things? _10:49_: Have I forgotten anything obvious? _10:51_: Nope. _10:53_: OK, so _10:55_: onward to the physics bit. _10:58_: I have on the next slide _10:60_: put all of the physics you will learn in the next 10 weeks _11:04_: because we do 10 weeks of special activity and five weeks _11:08_: on general activity. _11:10_: So all the physics you'll learn in the next 10 weeks, _11:14_: That's it. _11:16_: It's two sentences. _11:20_: There's _11:21_: on a national reference reference, performance of _11:24_: physical experiments. It's called the principle and the _11:26_: speed of light. The same constant value measured in any _11:29_: inertial frame. _11:30_: That's it. _11:32_: Why many 10 weeks talking about that? Because those are easy to _11:37_: state, _11:38_: and those are the physical, the thing, the physical statements _11:42_: you didn't know before. But the consequences of these are _11:46_: intricate, and even understanding what those words _11:49_: mean is a bit subtle, _11:52_: and so there's not a lot of volume to learn in this course. _11:55_: You don't memorise stuff. I have a rotten memory, so I don't _11:59_: think it's fair to think to play you to memorise stuff. When I _12:03_: can't, I can't. _12:06_: So demonstrating that you understand these things is the _12:08_: point of the objectives. _12:11_: So there's not a lot to learn. And _12:14_: this is not this is this. What is and isn't a mathematical _12:18_: course. _12:20_: The maths we we use in this course is addition, subtraction, _12:24_: multiplication, division, square roots. _12:28_: Later on we use differentiation, _12:31_: but it's all school physics. It's all school maths. _12:35_: There is no funky maths in this _12:39_: course. _12:41_: But in a different sense this is a mathematical course, because _12:45_: the way we start things with there's there's no seat of the _12:49_: pants intuitive. You know you'll get you know get this picture _12:53_: and you'll understand. It doesn't there. There's no see _12:56_: the fans intuitiveness in this in this course it's all about _12:60_: this axiomatic approach. This is the fundamental the fundamental _13:03_: insight which is expressed in logical form of feeling, _13:07_: mathematical style of thinking. And then you move proceed _13:10_: carefully and thoughtfully forward in a mathematical style. _13:14_: So although the the arithmetic use is very simple, _13:18_: the style is quite abstract and that is and and and that's I _13:21_: think the first course you've done. Where that's true _13:26_: First, your first year courses have tended to be more _13:28_: physically _13:29_: unless you know apart from say the pure pure maths courses that _13:33_: you've done. _13:34_: So that will be a bit of a jolt. OK. _13:38_: Also, you have done a bit of special relativity before, I _13:42_: think in physics one is. That's right, yeah, OK. And that's I _13:46_: think 2 lectures and I'm sure the word Lorentz transformation _13:50_: was mentioned and events and stuff. But that's just two _13:54_: lectures. How can I spin it out to 10 lectures? _13:59_: Because I want you to actually understand it, _14:03_: and you can't do that without good without sort of going round _14:06_: and round several times and and getting a bit confused. So this _14:09_: is quite a thorough version of of special activity _14:13_: that's. But these are the only _14:15_: physical statements, only statements about the world. The _14:19_: only thing about the world that could be otherwise that I'm _14:22_: going to make all the until a bit later. All the rest is _14:25_: deduction. _14:29_: So _14:31_: as I said, this first lecture is, _14:36_: you know, dotting around a bit what what happens next is _14:39_: Chapter 2, which I think is what we'll get through in one _14:42_: lecture, is going through those axioms and think, what do they _14:46_: actually mean? What do those words mean? _14:50_: Chapter three and four, which I think is. I think it's 3 _14:53_: lectures basically, Roughly is but the field direct _14:56_: consequences of those actions. OK, given those axioms, what _14:60_: follows, _15:01_: and there's quite a lot of followers pretty directly before _15:04_: you get into anything, any, any, anything calculational. And _15:08_: that's interesting. Those axioms, although they look very _15:11_: simple, are full of physical content. _15:15_: Chapter 5 is where we go onto the main apparatus. _15:18_: The the main. The main, Yeah, the main international tool. Or _15:22_: relatively how you how, given a A-frame, you're sending A-frame _15:27_: that's moving past you. How do you say this event that happened _15:31_: here happened in those coordinates, the moving frame, _15:34_: blah blah. Those words will mean more in a short while _15:39_: after that. That's that. That's sort of the the, the, the, the _15:43_: the first pillar of the whole thing. After that we talk about _15:48_: and and that we I think we'll spend 3 lectures on that. OK. _15:54_: The kinematic dynamics is how do you describe motion, what how do _15:57_: you talk about momentum and energy and conservation of _16:01_: things in a relativistic context. You're familiar with _16:04_: these things from physics. One, _16:07_: What do these ideas look like in a realistic context? _16:10_: And and and and that sort of thing. That's very important. If _16:12_: you do particle physics for example, _16:15_: and then chapter 8:00 and 9:00, the last five lectures is _16:17_: general relativity. We cannot go into the maths of general _16:20_: relativity because that is actually quite hard _16:23_: and that's that's an honours masters course. But what we can _16:27_: do is give an account of general relativity which is has much _16:31_: more textured, is much more substantial because we'll spend _16:35_: 10 weeks, 10 lectures, sorry, and thinking through the _16:38_: terminology and thought processes of special activity. _16:42_: So there's a lot more substance we can say about generativity. _16:46_: So it's it's beyond a popular account, _16:50_: but we we can't get to the free technical account so we can get _16:54_: to that intermediate range there _16:58_: and that's and that's five lectures, _17:02_: OK. _17:03_: And _17:04_: so I'm not gonna be, I'm, I'm gonna gallop through these now _17:08_: really. But that's OK because I want to have said these things _17:13_: to you at one point, _17:16_: even though _17:18_: I it doesn't sort of matter that I'm going to go through rather _17:21_: too quickly because we're coming back to them again and again and _17:24_: again in later weeks. So I'm sort of logging these in your _17:27_: head _17:28_: just just now, but you'll come back to these, you'll come back _17:31_: to the notes for these bits again and again, and we will _17:34_: talk over them again and again. _17:40_: OK, _17:42_: key thing. Number one, what is an event? _17:46_: An event is _17:48_: that _17:49_: that happened there. It happened, you know, two metres _17:52_: from the, from that door, from that, from that wall, 1 1/2 _17:55_: metres from the floor, _17:57_: 4 metres from there. And it happened _17:60_: 10 seconds ago _18:01_: for the four numbers attached to it, _18:05_: 3 spatial coordinates and a time coordinate. _18:08_: But notice that I said it happened from that wall. That _18:13_: war, that war someone in the street _18:17_: would give, would give different physical coordinates to that _18:20_: event. _18:22_: OK, obviously. _18:24_: So the event is in some sense absolute. There's no, there's no _18:28_: question that event happened, but the numbers you used to _18:31_: describe it are relative. So the first one that you're going to _18:35_: use that word a lot, that's the first time it comes in there. _18:39_: They are basis dependent. They are coordinate frame dependent. _18:44_: So my coordinate system in this room start for the order over _18:47_: there say blah blah blah you you you can imagine 3 axes. _18:51_: Someone standing in the street has a different coordinate _18:54_: system. My watch I I said it happened 1010 seconds ago from _18:58_: when it was. Someone might say it happened at rib and 11 1/2 _19:01_: hours from midnight. _19:03_: So the zero of position and the zero of time is up to you. It's _19:09_: up to the definition of the coordinate. _19:14_: Another sort of event is. _19:19_: I caught it. _19:21_: I didn't miss it. I caught it. So how did I catch it? I I _19:25_: caught it because my hand and the eraser were in the same _19:29_: place at the same time _19:33_: and it doesn't matter what coordinates you give to that _19:37_: quote was brought to this room quarters relative to the to _19:40_: buyers Rd. _19:42_: They were in the same place at the same time, _19:45_: and there's nothing relative about that. There's no point of _19:48_: view _19:49_: in which I didn't catch it. If two cars collide, _19:53_: then metal is bent _19:56_: and there's no point of view in which that metal isn't bent you _19:59_: there's no way you can be moving in which you you look at it in a _20:02_: funny way and and and they didn't. They missed each other. _20:05_: So two things which happened which collide which are which _20:08_: are at the same place at the same time are there. Absolutely, _20:11_: there's nothing there. So why is he saying why is he saying this _20:14_: again and again? Why is he making a fuss of this? It sounds _20:17_: it's obvious, it's obvious, but it remains obvious if you like, _20:20_: even when there's a lot of other things that you thought were _20:23_: obvious aren't obvious anymore. So it doesn't need saying. _20:28_: That that remains true. _20:33_: So which of the following events? _20:36_: Who says supernova explosion was an event _20:39_: behind? _20:40_: Who say it wasn't? _20:43_: Who's the A concert with an event? _20:46_: Who said it wasn't? _20:49_: Who see the whole country clapping its hands at once? Was _20:52_: an event _20:54_: not _20:58_: a collision between 2 particles in the LHC. Is that an event? _21:02_: No, _21:04_: I agree with with, with most of you, even when you you, you, _21:08_: you, you disagree with each other because a concert, _21:13_: OK, that is a sort of an event in the sense that it happens at _21:16_: A at a place and a time. _21:18_: You know you know it. It said that on a ticket you'll be here _21:22_: at this time and they will start. But it also has a _21:25_: duration, _21:27_: and from that sense it's not an event _21:29_: because it's. It's a sequence of events. It's sequence of of of _21:32_: notes if you're like, which are all in the individual event. So _21:35_: an event has no duration. _21:37_: So the start of the concert is unequivocally an event, _21:41_: but the the concept as a thing because it really and similarly _21:45_: the whole kind of clapping hands at once. Well, yes, that does _21:49_: that sort of has a, _21:51_: you know, I definitely I I sort of definite time, but it's also _21:55_: spread out in space _21:58_: because it's the whole country, it's it's doing it once. There's _22:02_: not happening at a place you can't see what is the place at _22:05_: which the whole country does this. OK, if you stand _22:08_: sufficiently far back, OK, it happened in the UK, but if _22:12_: you're in the UK then because it was spread out in space, it _22:15_: didn't happen at a place and that means and we'll go on to _22:19_: this next time. I think that means it didn't happen at a _22:22_: time. _22:25_: It seemed obvious that if everyone claps that they would _22:28_: see everyone claps their hands at once. That seems obviously. _22:31_: Well, I know what that means. _22:33_: Turns out you don't. _22:35_: If something is extended in space, the question of what _22:37_: tended to happen at becomes much more complicated and we'll come _22:41_: to that, I hope in a moment. _22:43_: It certainly will come to that again and again and again over _22:45_: the next few weeks. _22:46_: So, _22:48_: and there's no issue about the .4, if those things were in the _22:51_: same place at the same time, they decided that that that _22:54_: happened at a place in the time, _22:56_: you know and and the story. _23:00_: So yeah, _23:02_: and _23:06_: what is it? _23:10_: So next, how do we locate these events? _23:16_: I've alluded to this, _23:18_: but what we do is we have reference frames and we have _23:23_: observers, and these two _23:26_: fridges being something very specific, our reference frame. _23:30_: They're not exotic, but we do have a very specific meaning _23:35_: when we talk about these. In this context, our reference _23:37_: frame is a coordinate system. _23:40_: It's an origin and a set of axes in space and in time. So it is _23:45_: saying that is the zero of my coordinate system and I'm _23:49_: measuring all times from midnight. _23:52_: I've defined A coordinate system _23:54_: feel straight forward. _23:57_: Someone else could have a different coordinate system, as _23:60_: I've said. _24:01_: So there's nothing. There's a coordinate system. Is a. There _24:04_: are infinite many, many coordinate systems. _24:06_: OK, everyone gets gets a coordinate system. Everyone gets _24:09_: lots of coordinate systems. OK, there's coordinates from makes _24:12_: more sense to you. Is the one in which you where you're standing _24:14_: still at the minute. OK, _24:16_: but there's nothing special about that. And that is the _24:19_: thing about relativity. There's nothing special about the _24:22_: coordinate system that you that you choose _24:25_: within certain limits, _24:28_: because there are different observers, _24:31_: and observers are, well, observers. _24:34_: Again, not an exotic notion, but the when we're talking about an _24:39_: observer in special activity, we mean someone _24:43_: with a notebook _24:44_: who is very short sighted _24:48_: notebook and a watch and very shortsighted and and they will _24:50_: pay attention to things that happen in front of their nose _24:54_: and they will write down where they are when that happens. So _24:58_: OK I OK, it happened at 11:40 and I'm at this position in in _25:03_: the quarter. They write that down and and and make a note _25:07_: that that's their job. _25:10_: If, if, if if it happened over there, they're not interested. _25:13_: OK, _25:14_: so observers are in a coordinate system. _25:18_: They know where they are in the coordinate system, in space, and _25:21_: in time. Well, they've all got to you. They know they're all _25:24_: written on on the ground and they and they know what spot _25:26_: they're sending on. And they've all got to watch. They're where _25:29_: they are and what time it is, and they only pay attention to _25:31_: things in front of their noses, _25:34_: OK? They ignore things which happened elsewhere. If you want _25:37_: to to to work out where an event happened, you've got to have _25:41_: lots of friends. _25:43_: OK, so if I want, if there was a firecracker went off in the _25:46_: middle of the room, _25:48_: the only person I'd be interested in Who, who, who? I _25:52_: would ask where did that happen and when? If the person, _25:55_: unfortunate person, who's sort of sitting on top of it when it _25:59_: when it went off, everyone else ignored it but that person. I _26:03_: asked Where are you? What time do you go off? No one else even _26:06_: sought? OK, hold on to that thought. _26:09_: So observers are very limited people _26:15_: and what this is illustrating _26:19_: come back to is 2 reference frames. _26:22_: A reference stream S _26:26_: which has an X&AY _26:28_: and someone standing stationary in that reference frame with the _26:32_: watch _26:33_: and as someone in different reference frame it's frame which _26:37_: is a different ex prime axis, a different Y prime axis and they _26:40_: have a different watch and they were great. So if something _26:44_: happens, an event happens and this second reference frame as _26:48_: prime is moving with respect to the first one _26:51_: at a speed V. _26:53_: So at all times the location of the origin of this _26:58_: reference frame is at X _27:01_: in it. At X in the _27:05_: South frame equals Vt simply because it's moving at a _27:09_: constant speed VS There's a bit of school maths for you, _27:12_: multiplication distance speed times time. You remember that _27:16_: bit, _27:19_: So what that is showing is _27:22_: I'd rather elaborate way of showing a moving reference frame _27:27_: S prime is moving in the frame S at a speed VS the origin is at _27:31_: space at at a coordinate X at the origin. That point there is _27:36_: it. Coordinate X prime equals 0 and coordinate X equals Vt _27:42_: a point there is a cordon. X prime equals whatever _27:46_: and it coordinate. X equals whatever plus Vt _27:49_: keeps it. Nothing exotic there. OK, we'll get on to exotic _27:53_: later, but there's nothing exotic there. OK, _27:57_: but those two observers only pay attention to things locally. _28:03_: Now I've said there's there's possibly have lots and lots of _28:05_: different inertial frames and a different reference frames. _28:08_: Everyone gets a, gets a reference frame, gets a _28:10_: coordinate frame. _28:11_: But some of them are special. _28:14_: Some of them you can. _28:19_: In some of them you can take it that you are not moving. _28:23_: Now I'm standing here, I'm. I'm not having any difficulty _28:26_: standing here. I'm not being thrown about because the _28:28_: building isn't shaking. This is a good thing. _28:32_: If I were in a train _28:34_: and the training was just bowling along the track in a _28:37_: nice calm fashion, then it could also, I could stand on the train _28:41_: with the difficulty I could juggle _28:43_: or a great cup of tea, whatever. Whether difficulty, because as _28:47_: far as I'm concerned I can regard that steadily moving _28:50_: train as being stationary _28:52_: and it is stationary, that there's there's no, there's no _28:54_: experiment I can do _28:55_: that would tell me that that's steadily moving train isn't _28:59_: stationary. I can look out of a window and see the landscape go _29:02_: by, but all that tells me is I'm moving with respect to the _29:05_: landscape. It doesn't mean I'm absolutely moving. I'm _29:08_: absolutely moving. _29:10_: OK, it might sugar, but so it might be that there there are _29:13_: some vibration in the in this, but that's just OK that's OK _29:17_: vibrating _29:20_: and that's not that it's tricky to tell you moving. It's not _29:24_: that no one knows how to _29:27_: tell you movie. One of those axioms was you cannot tell _29:31_: you're moving at a constant speed _29:34_: and a matter of of deep physical principle, there is no physical _29:37_: experiment you could do that would tell you if you're moving _29:40_: at a constant speed _29:42_: that you are actually the one moving as opposed to the rest of _29:46_: the world moving past you. And you've seen this is happening to _29:50_: image and saying in a train station, in a tree, in a train, _29:54_: in a station, you're you're gazing blankly into space and _29:57_: the train next to you is moving _30:00_: and you don't know if you're if you're trained to start off _30:03_: smoothly, whether it's that train to move at the station or _30:05_: your train, you can't tell. _30:07_: And there's nothing with specially processed experiments. _30:10_: You could because if you had a little pendulum and you as _30:13_: you're trade accelerated, you could do that little pendulum _30:16_: would, would, would, would put to one side and in a way you can _30:19_: imagine or or or or a ball on the table would roll off. So you _30:23_: can tell you're accelerating _30:26_: absolutely. And there's no doubt that you're accelerating. If you _30:30_: are sitting in a train and it's accelerating at a station, you _30:33_: can feel you're being pushed the small of your back. You can tell _30:37_: you're accelerating unequivocally and absolutely, _30:41_: but once you're not accelerating, _30:44_: your frame is as good as anyone. Your your idea of stillness is _30:47_: as good as anyone else, and that's to repeat myself. That's _30:51_: not _30:52_: a curiosity. That's a fundamental physical principle _30:54_: that there are a lot of things and it's not, and it's called _30:57_: the principled relativity. It's not Einstein's principle of _31:00_: relativity, It's Galileo's principle of relativity. Because _31:03_: he _31:04_: spelled out quite like that. But it was. It was. Galilean physics _31:09_: rests on that as a notion. _31:14_: And so that means that those frames which are not _31:17_: accelerating have a special status. _31:20_: They are the ones that we're going to make all our _31:22_: measurements in. _31:25_: The other one will give a special name to namely inertial _31:27_: reference frames, because they are inertial _31:30_: and in our show in the sense that Newton's second law, _31:34_: Newton's laws work in the actual frame. _31:38_: If you _31:40_: So you're floating out in space and we'll come back to this _31:43_: later on. If you leave something where you just let go something, _31:47_: it'll stay. For it is if you give something a push, it will _31:50_: move in a constant, a constant speed until it hits something. _31:53_: Yeah, just like you see the issues. If you are moving along _31:57_: on a on a smoothly moving train, and you roll a ball across the _32:02_: the, the, the, the the table, it'll move in a straight line _32:06_: at constant speed until it hit something. _32:09_: Different laws work while the train is accelerating. If you _32:12_: try and roll the ball across the table and go rule it like that, _32:16_: there's a mysterious extra force _32:19_: which appears which breaks Newton's laws, _32:22_: doesn't break news laws. It's called inertia. And if you are _32:26_: on a roundabout, on a children's roundabout, you throw a ball to _32:30_: someone across the other than their own about, then it goes _32:34_: off to one side. _32:36_: Is there a mysterious force that reflects it? No, it's just that _32:39_: you're in a rotating reference. _32:42_: Centripetal force, central centrifugal force. It's not a _32:46_: force, it's a it's a _32:48_: an illusion caused by being a non inertial frame. So the point _32:52_: of a national frame is that nuisance laws work in it. So you _32:55_: understand the physics of national frames, _32:59_: Physics. No, natural frames is harder. Physical natural frames _33:02_: easy. And we will always stick to natural frames, especially _33:04_: activity. We will do the same thing. We get a general _33:07_: activity, but we have to change our definition of what a natural _33:09_: frame is. And that's exciting. But that's 10 lectures _33:15_: and _33:18_: I I I am _33:21_: I don't feel I have to go to go through this as a as a quick _33:24_: way. I have a quick question. We'll have more of these _33:26_: questions and other lectures and have a think about these when _33:29_: you're, when you're mulling over the the, the you know which of _33:32_: these countries national frames _33:36_: and _33:39_: we can talk about that at some point _33:42_: and blah blah. _33:47_: So how do we measure times? _33:50_: It's really easy. How to make, you know, we know how to measure _33:53_: distances. We just draw things on the ground and and and and _33:56_: you know, with _33:58_: a greater things in the ground and walk away. We are in the _34:01_: reference frame. _34:03_: How do we talk about time? Well, look at our watch. How hard can _34:06_: it be? _34:10_: But when it turns out we have to be a little more specific than _34:13_: that, a little more precise than that, and this remark in _34:17_: Einstein's remark. It comes from I think the 1905 paper _34:21_: because you know the the paper which introduced, you know, _34:24_: banks especially activity in its more of its final form to the _34:27_: world, all our judgments in which types apart our judgments _34:31_: of simultaneous events and that were simultaneous is a key one. _34:36_: If I see the train arrived at 7:00, what I mean is the point _34:40_: of view of the small hand on my watch at 7 _34:43_: and the arrival of the train are simultaneous. _34:46_: Simultaneous in the sense they happen at the same place at the _34:48_: same time, _34:50_: so my watch doesn't have to be right. _34:54_: But when I see _34:57_: my, it happened at seven of my watch. What I mean is the train _35:01_: was here in front of my nose and so was my watch and they were _35:04_: both doing that thing in front of my nose at the and therefore _35:08_: they are. They are simultaneous, absolute and absolute. Sense _35:11_: there were simultaneity gets more complicated if you're _35:14_: talking about things which are separate from each other, as we _35:17_: will discover. _35:20_: But in the same way the if you if you have two cars crashing _35:23_: because they are metal bending because they're the same at the _35:26_: same time, that's absolutely simultaneous. This is absolutely _35:29_: simultaneous. You can hold on to this notion, _35:32_: and the reason why I'm banging on about the reason why I think _35:35_: was banging on about is because that turns out to be a _35:37_: clarifying way of thinking about time. _35:40_: The timer event is _35:43_: what happened on what happened on the clock which was at the _35:47_: same place at the same time. _35:50_: OK, and again, you think this sounds like it's like excess _35:54_: precision. Why does this matter? _35:57_: This is the this is the the list of things I'm kicking off in _35:60_: this first lecture, which will come back with the significance _36:02_: of which we'll come back to next time. So we're gonna see a lot _36:05_: of pictures of this. These are our true observers. _36:08_: Well, and and we we always have multiple observers because what _36:11_: we're interested in the whole point of things like the _36:13_: transformation, are _36:15_: someone in that frame in that when that coordinate system says _36:18_: this happened at this place and this time _36:20_: I'm in this _36:22_: cordon system with respect to which that coordinate system is _36:25_: moving, what is the position and time of that event in my _36:28_: reference frame? _36:29_: That sounds, I think why would one care? But that _36:36_: that's the sort of boiled down question you have to answer in _36:40_: order to do things like talking about _36:44_: Doppler shift about about I think the general relativity _36:47_: that that that that it all boils down to that sort of question _36:50_: even though it ended up being quite an abstract question. And _36:53_: that in a in a way is why I I I said this was quite a _36:56_: mathematical course because the idea that you take a complicated _36:59_: thing you boil it down to the simplest thing it could possibly _37:02_: be that still has the property and you analyse the hell out of _37:05_: that. That's quite mathematical approach to this. You can _37:08_: understand the rest by building up from that, but you tear down _37:11_: in order to build up. _37:14_: OK. _37:16_: I can see some folk going, oh, this is a great some folk going, _37:19_: oh, there's gonna be terrible, but it's gonna be great. Yeah, _37:22_: it's, it's, it's it's a a tremendous intellectual _37:25_: experience. The point is that there are multiple observers, _37:28_: OK? And each of them knows where they are because they've got one _37:31_: of these little spheres things which let them work out where _37:34_: reference to the the, the, the, the origin of their frame they _37:38_: are so they can put mark in the ground and attach a coordinated _37:41_: position, Gordon, to that. And they've all got to watch, _37:46_: which they can look at with their short sight. _37:49_: OK, we'll see these people again and again. _37:55_: So imagine you're standing on a bridge over a motorway _38:01_: looking police officer standing beside the road so that you're _38:03_: looking down and they're standing beside the road _38:07_: and a car driver goes past them and sneezes. _38:15_: Who would watch? Do you consult to find out the time of this _38:18_: sneeze in your frame? _38:22_: And this is all happening? Artistic speed? So so. And _38:25_: let's, you know, hold on to our intuitions. Who says it's your _38:29_: watch? _38:31_: Who said the police officers watch? _38:34_: Who said the driver's watch? _38:37_: Who hasn't put the hand up yet? _38:40_: OK, I'll try again. Everyone had to put their hand up. I don't _38:43_: care what your answer is, _38:46_: but I want to see if everyone had at least once. Just don't _38:50_: you have a punted make a guess. _38:52_: Who says it's your it's your your own watch. _38:55_: Who's this police officer watch? Who says the drivers watch? _38:59_: Talk to your neighbour. _39:01_: Tell them why you're right. _39:25_: Normally Adeem, _39:28_: normally Odin to give you more time to to to to talk it over _39:31_: than that. But folks, folks, normally I didn't give more time _39:35_: to talk over than that. But you know we're going through at the _39:39_: end here. So after discussion, who would say your own watch? _39:43_: Who should the police officers watch? _39:45_: Who would say the driver's watch? _39:49_: It's the peace officers watch. _39:51_: Why? Because the police officer is in your frame. _39:55_: You and the police officer are both in the same frame. They're _39:58_: both standing stationary in the motorway frame. Neither of you _40:01_: are moving. That's the point. _40:05_: Your the driver is moving. _40:09_: OK, so they're not in your frame. They're not observer. _40:11_: You, you, you you. You want to talk to. You only want to talk _40:14_: to observers who are stationary. You are free. _40:17_: Why not you? Why not your watch? Because you're short sighted _40:21_: too. You can't even see this driver _40:24_: and and and and and so the the driver sneeze didn't happen in _40:27_: front of you. _40:28_: Well, the police officer, they were standing about standing _40:31_: there when the sneeze happened and the right were going past _40:34_: sneezed and the and the police looked to their watch. So _40:37_: they're the only person _40:40_: who can see what the time of that event was in the motorway _40:43_: frame. _40:45_: The driver of the car, they know what time it happened. And their _40:48_: friend, they look at their watch _40:50_: and it turns out they'll give a different answer from the police _40:53_: officer. _40:54_: But we don't care, you know, to begin with and measurement terms _40:58_: what they were. And they watch, we care what happened in our _41:01_: frame. And the only people we talk to are the observers in the _41:04_: frame. And the only one observer whose opinion matters is the _41:08_: observer who was next to the event when it happened. Now, the _41:11_: event didn't happen in the motorway frame rather than the _41:14_: car frame. The event didn't happen in the car frame rather _41:17_: than the motor we frame, it happened in all the frames. So _41:20_: this is a good point of which I can say don't get into this way _41:23_: of thinking of it happens in A-frame and event happens. _41:27_: It's a thing in the world. _41:29_: It happens in all frames _41:32_: but different people describe different coordinates to it. _41:36_: Meditate on that and and we have run out of time. So I will have _41:39_: to to go through the last couple of bits of of of this first _41:42_: chapter next time which is tomorrow which and I think we _41:45_: are the Adam Smith building which is the last year that we _41:48_: will swap back and forth between.