WEBVTT 00:00:06.539 --> 00:00:09.958 Space: it's where things happen. 00:00:09.958 --> 00:00:12.575 Time: it's when things happen. 00:00:12.575 --> 00:00:14.324 We can measure where things are 00:00:14.324 --> 00:00:15.658 and when things take place, 00:00:15.658 --> 00:00:17.157 but in modern physics, 00:00:17.157 --> 00:00:18.993 we realize when and where 00:00:18.993 --> 00:00:22.467 are actually part of the same question. 00:00:22.467 --> 00:00:24.679 Because when it comes to understanding the universe, 00:00:24.679 --> 00:00:28.055 we need to replace three-dimensional space plus time 00:00:28.055 --> 00:00:29.847 with a single concept: 00:00:29.847 --> 00:00:33.644 four-dimensional space-time. 00:00:33.644 --> 00:00:35.773 We'll explore and explain space-time 00:00:35.773 --> 00:00:38.273 in this series of animations. 00:00:38.273 --> 00:00:39.234 Animations? 00:00:39.234 --> 00:00:40.317 Yeah. 00:00:40.317 --> 00:00:42.523 Well, we're not very animated are we? 00:00:42.523 --> 00:00:46.859 Sure we are! Look, I can go from here to here. 00:00:46.859 --> 00:00:48.659 Whoa! How'd you get from here to there? 00:00:48.659 --> 00:00:50.024 How fast did you go? 00:00:50.024 --> 00:00:51.689 Did you run? Walk? 00:00:51.689 --> 00:00:53.357 Did you even go in a straight line? 00:00:53.357 --> 00:00:57.108 Ah! To answer that, you'll need to make our cartoon physics 00:00:57.108 --> 00:00:59.543 look more like physics physics. 00:00:59.543 --> 00:01:02.107 You'll need more panels. 00:01:02.107 --> 00:01:05.301 More panels, please! 00:01:05.301 --> 00:01:10.096 Okay, in each panel, Andrew's in a slightly different place. 00:01:10.096 --> 00:01:11.975 So I can see each one records 00:01:11.975 --> 00:01:14.892 where Andrew is at a different time. 00:01:14.892 --> 00:01:18.981 That's great. But it would be easier to see 00:01:18.981 --> 00:01:20.440 what's going on if we could cut out 00:01:20.440 --> 00:01:22.773 all the hundreds of panels and stack them up 00:01:22.773 --> 00:01:26.069 like a flip book. 00:01:26.069 --> 00:01:28.155 Right, now let's flip through the book 00:01:28.155 --> 00:01:30.607 so that we can see one panel after another 00:01:30.607 --> 00:01:34.358 getting through 24 in every second. 00:01:34.358 --> 00:01:36.439 See! I told you it was an animation. 00:01:36.439 --> 00:01:39.376 Now you can see me walking along. 00:01:39.376 --> 00:01:42.046 Drawing all those panels and putting them into a flip book 00:01:42.046 --> 00:01:45.757 is just one way of recording the way I'm moving. 00:01:45.757 --> 00:01:49.773 It's how animation, or even movies, work. 00:01:49.773 --> 00:01:52.346 As it turns out, at my walking speed, 00:01:52.346 --> 00:01:55.691 it takes two seconds to get past each fence post, 00:01:55.691 --> 00:01:58.521 and they're spaced four meters apart. 00:01:58.521 --> 00:02:00.478 So we can calculate my velocity -- 00:02:00.478 --> 00:02:02.482 how fast I'm moving through space - - 00:02:02.482 --> 00:02:05.484 is two meters per second. 00:02:05.484 --> 00:02:08.238 But I could've worked that out from the panels 00:02:08.238 --> 00:02:11.156 without flipping through them. 00:02:11.156 --> 00:02:12.493 From the edge of the flip book, 00:02:12.493 --> 00:02:14.608 you can see all of the copies of the fence posts 00:02:14.608 --> 00:02:16.440 and all of the copies of Andrew 00:02:16.440 --> 00:02:20.124 and he's in a slightly different place in each one. 00:02:20.124 --> 00:02:23.230 Now we can predict everything that will happen to Andrew 00:02:23.230 --> 00:02:26.775 when we flip through 24 pages every second, 00:02:26.775 --> 00:02:28.132 including his speed of motion, 00:02:28.132 --> 00:02:30.343 just by looking. 00:02:30.343 --> 00:02:33.387 No need to flip through at all. 00:02:33.387 --> 00:02:34.638 The edge of this flip book 00:02:34.638 --> 00:02:37.701 is known as a space-time diagram 00:02:37.701 --> 00:02:40.066 of Andrew's journey through, you guessed it, 00:02:40.066 --> 00:02:42.067 space and time. 00:02:42.067 --> 00:02:45.151 We call the line that represents Andrew's journey 00:02:45.151 --> 00:02:47.510 his world line. 00:02:47.510 --> 00:02:49.865 If i jog instead of walking, 00:02:49.865 --> 00:02:54.454 I might be able to get past a fence post every second. 00:02:54.454 --> 00:02:56.037 He's not very athletic. 00:02:56.037 --> 00:02:59.207 Anyway, when we look at this new flip book from the edge, 00:02:59.207 --> 00:03:02.260 we can do the same analysis as before. 00:03:02.260 --> 00:03:03.837 The world line for Andrew jogging 00:03:03.837 --> 00:03:05.297 is more tilted over 00:03:05.297 --> 00:03:07.759 than the world line for Andrew walking. 00:03:07.759 --> 00:03:10.926 We can tell he's going twice as fast as before 00:03:10.926 --> 00:03:14.395 without flipping the panels. 00:03:14.395 --> 00:03:16.638 But here's the clever bit. 00:03:16.638 --> 00:03:20.361 In physics, it's always good to view things from other perspectives. 00:03:20.361 --> 00:03:22.226 After all, the laws of physics 00:03:22.226 --> 00:03:23.861 should be the same for everyone 00:03:23.861 --> 00:03:26.277 or no one will obey them. 00:03:26.277 --> 00:03:29.066 So let's rethink our cartoon 00:03:29.066 --> 00:03:31.652 and have the camera follow Andrew jogging along 00:03:31.652 --> 00:03:35.237 as the fence posts approach and pass behind him. 00:03:35.237 --> 00:03:37.777 Still viewing it as a flip book of panels, 00:03:37.777 --> 00:03:39.777 we don't need to redraw anything. 00:03:39.777 --> 00:03:42.832 We simply move all of the cutout frames slightly 00:03:42.832 --> 00:03:45.110 until Andrew's tilted world line 00:03:45.110 --> 00:03:48.003 becomes completely vertical. 00:03:48.003 --> 00:03:50.695 To see why, let's flip it. 00:03:50.695 --> 00:03:54.424 Yes, now I'm stationery, just jogging on the spot, 00:03:54.424 --> 00:03:56.051 in the center of the panel. 00:03:56.051 --> 00:03:57.552 On the edge of the flip book, 00:03:57.552 --> 00:04:00.361 my world line was going straight upwards. 00:04:00.361 --> 00:04:03.027 The fence posts are coming past me. 00:04:03.027 --> 00:04:06.312 It's now their world lines that are tilted. 00:04:06.312 --> 00:04:09.438 This rearrangement of the panels is known as a 00:04:09.438 --> 00:04:11.649 Galilean transformation, 00:04:11.649 --> 00:04:16.240 and it lets us analyze physics from someeone else's perspective. 00:04:16.240 --> 00:04:18.574 In this case, mine. 00:04:18.574 --> 00:04:21.945 After all, it's always good to see things from other points of view, 00:04:21.945 --> 00:04:24.694 especially when the viewers are moving 00:04:24.694 --> 00:04:26.693 at different speeds. 00:04:26.693 --> 00:04:30.529 So long as the speeds aren't too high. 00:04:30.529 --> 00:04:33.278 If you're a cosmic ray moving at the speed of light, 00:04:33.278 --> 00:04:38.028 our flip book of your point of view falls apart. 00:04:38.028 --> 00:04:39.805 To stop that from happening, 00:04:39.805 --> 00:04:42.140 we'll have to glue panels together. 00:04:42.140 --> 00:04:44.612 Instead of a stack of separate panels, 00:04:44.612 --> 00:04:47.977 we'll need a solid block of space-time, 00:04:47.977 --> 00:04:50.694 which we'll come to in the next animation.