0:00:06.539,0:00:09.958 Space: it's where things happen. 0:00:09.958,0:00:12.575 Time: it's when things happen. 0:00:12.575,0:00:14.324 We can measure where things are 0:00:14.324,0:00:15.658 and when things take place, 0:00:15.658,0:00:17.157 but in modern physics, 0:00:17.157,0:00:18.993 we realize when and where 0:00:18.993,0:00:22.467 are actually part of the same question. 0:00:22.467,0:00:24.679 Because when it comes to understanding the universe, 0:00:24.679,0:00:28.055 we need to replace three-dimensional space plus time 0:00:28.055,0:00:29.847 with a single concept: 0:00:29.847,0:00:33.644 four-dimensional space-time. 0:00:33.644,0:00:35.773 We'll explore and explain space-time 0:00:35.773,0:00:38.273 in this series of animations. 0:00:38.273,0:00:39.234 Animations? 0:00:39.234,0:00:40.317 Yeah. 0:00:40.317,0:00:42.523 Well, we're not very animated are we? 0:00:42.523,0:00:46.859 Sure we are! Look, I can go from here to here. 0:00:46.859,0:00:48.659 Whoa! How'd you get from here to there? 0:00:48.659,0:00:50.024 How fast did you go? 0:00:50.024,0:00:51.689 Did you run? Walk? 0:00:51.689,0:00:53.357 Did you even go in a straight line? 0:00:53.357,0:00:57.108 Ah! To answer that, you'll need to make our cartoon physics 0:00:57.108,0:00:59.543 look more like physics physics. 0:00:59.543,0:01:02.107 You'll need more panels. 0:01:02.107,0:01:05.301 More panels, please! 0:01:05.301,0:01:10.096 Okay, in each panel, Andrew's in a slightly different place. 0:01:10.096,0:01:11.975 So I can see each one records 0:01:11.975,0:01:14.892 where Andrew is at a different time. 0:01:14.892,0:01:18.981 That's great. But it would be easier to see 0:01:18.981,0:01:20.440 what's going on if we could cut out 0:01:20.440,0:01:22.773 all the hundreds of panels and stack them up 0:01:22.773,0:01:26.069 like a flip book. 0:01:26.069,0:01:28.155 Right, now let's flip through the book 0:01:28.155,0:01:30.607 so that we can see one panel after another 0:01:30.607,0:01:34.358 getting through 24 in every second. 0:01:34.358,0:01:36.439 See! I told you it was an animation. 0:01:36.439,0:01:39.376 Now you can see me walking along. 0:01:39.376,0:01:42.046 Drawing all those panels and putting them into a flip book 0:01:42.046,0:01:45.757 is just one way of recording the way I'm moving. 0:01:45.757,0:01:49.773 It's how animation, or even movies, work. 0:01:49.773,0:01:52.346 As it turns out, at my walking speed, 0:01:52.346,0:01:55.691 it takes two seconds to get past each fence post, 0:01:55.691,0:01:58.521 and they're spaced four meters apart. 0:01:58.521,0:02:00.478 So we can calculate my velocity -- 0:02:00.478,0:02:02.482 how fast I'm moving through space - - 0:02:02.482,0:02:05.484 is two meters per second. 0:02:05.484,0:02:08.238 But I could've worked that out from the panels 0:02:08.238,0:02:11.156 without flipping through them. 0:02:11.156,0:02:12.493 From the edge of the flip book, 0:02:12.493,0:02:14.608 you can see all of the copies of the fence posts 0:02:14.608,0:02:16.440 and all of the copies of Andrew 0:02:16.440,0:02:20.124 and he's in a slightly different place in each one. 0:02:20.124,0:02:23.230 Now we can predict everything that will happen to Andrew 0:02:23.230,0:02:26.775 when we flip through 24 pages every second, 0:02:26.775,0:02:28.132 including his speed of motion, 0:02:28.132,0:02:30.343 just by looking. 0:02:30.343,0:02:33.387 No need to flip through at all. 0:02:33.387,0:02:34.638 The edge of this flip book 0:02:34.638,0:02:37.701 is known as a space-time diagram 0:02:37.701,0:02:40.066 of Andrew's journey through, you guessed it, 0:02:40.066,0:02:42.067 space and time. 0:02:42.067,0:02:45.151 We call the line that represents Andrew's journey 0:02:45.151,0:02:47.510 his world line. 0:02:47.510,0:02:49.865 If i jog instead of walking, 0:02:49.865,0:02:54.454 I might be able to get past a fence post every second. 0:02:54.454,0:02:56.037 He's not very athletic. 0:02:56.037,0:02:59.207 Anyway, when we look at this new flip book from the edge, 0:02:59.207,0:03:02.260 we can do the same analysis as before. 0:03:02.260,0:03:03.837 The world line for Andrew jogging 0:03:03.837,0:03:05.297 is more tilted over 0:03:05.297,0:03:07.759 than the world line for Andrew walking. 0:03:07.759,0:03:10.926 We can tell he's going twice as fast as before 0:03:10.926,0:03:14.395 without flipping the panels. 0:03:14.395,0:03:16.638 But here's the clever bit. 0:03:16.638,0:03:20.361 In physics, it's always good to view things from other perspectives. 0:03:20.361,0:03:22.226 After all, the laws of physics 0:03:22.226,0:03:23.861 should be the same for everyone 0:03:23.861,0:03:26.277 or no one will obey them. 0:03:26.277,0:03:29.066 So let's rethink our cartoon 0:03:29.066,0:03:31.652 and have the camera follow Andrew jogging along 0:03:31.652,0:03:35.237 as the fence posts approach and pass behind him. 0:03:35.237,0:03:37.777 Still viewing it as a flip book of panels, 0:03:37.777,0:03:39.777 we don't need to redraw anything. 0:03:39.777,0:03:42.832 We simply move all of the cutout frames slightly 0:03:42.832,0:03:45.110 until Andrew's tilted world line 0:03:45.110,0:03:48.003 becomes completely vertical. 0:03:48.003,0:03:50.695 To see why, let's flip it. 0:03:50.695,0:03:54.424 Yes, now I'm stationery, just jogging on the spot, 0:03:54.424,0:03:56.051 in the center of the panel. 0:03:56.051,0:03:57.552 On the edge of the flip book, 0:03:57.552,0:04:00.361 my world line was going straight upwards. 0:04:00.361,0:04:03.027 The fence posts are coming past me. 0:04:03.027,0:04:06.312 It's now their world lines that are tilted. 0:04:06.312,0:04:09.438 This rearrangement of the panels is known as a 0:04:09.438,0:04:11.649 Galilean transformation, 0:04:11.649,0:04:16.240 and it lets us analyze physics from someeone else's perspective. 0:04:16.240,0:04:18.574 In this case, mine. 0:04:18.574,0:04:21.945 After all, it's always good to see things from other points of view, 0:04:21.945,0:04:24.694 especially when the viewers are moving 0:04:24.694,0:04:26.693 at different speeds. 0:04:26.693,0:04:30.529 So long as the speeds aren't too high. 0:04:30.529,0:04:33.278 If you're a cosmic ray moving at the speed of light, 0:04:33.278,0:04:38.028 our flip book of your point of view falls apart. 0:04:38.028,0:04:39.805 To stop that from happening, 0:04:39.805,0:04:42.140 we'll have to glue panels together. 0:04:42.140,0:04:44.612 Instead of a stack of separate panels, 0:04:44.612,0:04:47.977 we'll need a solid block of space-time, 0:04:47.977,0:04:50.694 which we'll come to in the next animation.