1 00:00:06,539 --> 00:00:09,958 Space: it's where things happen. 2 00:00:09,958 --> 00:00:12,575 Time: it's when things happen. 3 00:00:12,575 --> 00:00:14,324 We can measure where things are 4 00:00:14,324 --> 00:00:15,658 and when things take place, 5 00:00:15,658 --> 00:00:17,157 but in modern physics, 6 00:00:17,157 --> 00:00:18,993 we realize when and where 7 00:00:18,993 --> 00:00:22,467 are actually part of the same question. 8 00:00:22,467 --> 00:00:24,679 Because when it comes to understanding the universe, 9 00:00:24,679 --> 00:00:28,055 we need to replace three-dimensional space plus time 10 00:00:28,055 --> 00:00:29,847 with a single concept: 11 00:00:29,847 --> 00:00:33,644 four-dimensional space-time. 12 00:00:33,644 --> 00:00:35,773 We'll explore and explain space-time 13 00:00:35,773 --> 00:00:38,273 in this series of animations. 14 00:00:38,273 --> 00:00:39,234 Animations? 15 00:00:39,234 --> 00:00:40,317 Yeah. 16 00:00:40,317 --> 00:00:42,523 Well, we're not very animated are we? 17 00:00:42,523 --> 00:00:46,859 Sure we are! Look, I can go from here to here. 18 00:00:46,859 --> 00:00:48,659 Whoa! How'd you get from here to there? 19 00:00:48,659 --> 00:00:50,024 How fast did you go? 20 00:00:50,024 --> 00:00:51,689 Did you run? Walk? 21 00:00:51,689 --> 00:00:53,357 Did you even go in a straight line? 22 00:00:53,357 --> 00:00:57,108 Ah! To answer that, you'll need to make our cartoon physics 23 00:00:57,108 --> 00:00:59,543 look more like physics physics. 24 00:00:59,543 --> 00:01:02,107 You'll need more panels. 25 00:01:02,107 --> 00:01:05,301 More panels, please! 26 00:01:05,301 --> 00:01:10,096 Okay, in each panel, Andrew's in a slightly different place. 27 00:01:10,096 --> 00:01:11,975 So I can see each one records 28 00:01:11,975 --> 00:01:14,892 where Andrew is at a different time. 29 00:01:14,892 --> 00:01:18,981 That's great. But it would be easier to see 30 00:01:18,981 --> 00:01:20,440 what's going on if we could cut out 31 00:01:20,440 --> 00:01:22,773 all the hundreds of panels and stack them up 32 00:01:22,773 --> 00:01:26,069 like a flip book. 33 00:01:26,069 --> 00:01:28,155 Right, now let's flip through the book 34 00:01:28,155 --> 00:01:30,607 so that we can see one panel after another 35 00:01:30,607 --> 00:01:34,358 getting through 24 in every second. 36 00:01:34,358 --> 00:01:36,439 See! I told you it was an animation. 37 00:01:36,439 --> 00:01:39,376 Now you can see me walking along. 38 00:01:39,376 --> 00:01:42,046 Drawing all those panels and putting them into a flip book 39 00:01:42,046 --> 00:01:45,757 is just one way of recording the way I'm moving. 40 00:01:45,757 --> 00:01:49,773 It's how animation, or even movies, work. 41 00:01:49,773 --> 00:01:52,346 As it turns out, at my walking speed, 42 00:01:52,346 --> 00:01:55,691 it takes two seconds to get past each fence post, 43 00:01:55,691 --> 00:01:58,521 and they're spaced four meters apart. 44 00:01:58,521 --> 00:02:00,478 So we can calculate my velocity -- 45 00:02:00,478 --> 00:02:02,482 how fast I'm moving through space - - 46 00:02:02,482 --> 00:02:05,484 is two meters per second. 47 00:02:05,484 --> 00:02:08,238 But I could've worked that out from the panels 48 00:02:08,238 --> 00:02:11,156 without flipping through them. 49 00:02:11,156 --> 00:02:12,493 From the edge of the flip book, 50 00:02:12,493 --> 00:02:14,608 you can see all of the copies of the fence posts 51 00:02:14,608 --> 00:02:16,440 and all of the copies of Andrew 52 00:02:16,440 --> 00:02:20,124 and he's in a slightly different place in each one. 53 00:02:20,124 --> 00:02:23,230 Now we can predict everything that will happen to Andrew 54 00:02:23,230 --> 00:02:26,775 when we flip through 24 pages every second, 55 00:02:26,775 --> 00:02:28,132 including his speed of motion, 56 00:02:28,132 --> 00:02:30,343 just by looking. 57 00:02:30,343 --> 00:02:33,387 No need to flip through at all. 58 00:02:33,387 --> 00:02:34,638 The edge of this flip book 59 00:02:34,638 --> 00:02:37,701 is known as a space-time diagram 60 00:02:37,701 --> 00:02:40,066 of Andrew's journey through, you guessed it, 61 00:02:40,066 --> 00:02:42,067 space and time. 62 00:02:42,067 --> 00:02:45,151 We call the line that represents Andrew's journey 63 00:02:45,151 --> 00:02:47,510 his world line. 64 00:02:47,510 --> 00:02:49,865 If i jog instead of walking, 65 00:02:49,865 --> 00:02:54,454 I might be able to get past a fence post every second. 66 00:02:54,454 --> 00:02:56,037 He's not very athletic. 67 00:02:56,037 --> 00:02:59,207 Anyway, when we look at this new flip book from the edge, 68 00:02:59,207 --> 00:03:02,260 we can do the same analysis as before. 69 00:03:02,260 --> 00:03:03,837 The world line for Andrew jogging 70 00:03:03,837 --> 00:03:05,297 is more tilted over 71 00:03:05,297 --> 00:03:07,759 than the world line for Andrew walking. 72 00:03:07,759 --> 00:03:10,926 We can tell he's going twice as fast as before 73 00:03:10,926 --> 00:03:14,395 without flipping the panels. 74 00:03:14,395 --> 00:03:16,638 But here's the clever bit. 75 00:03:16,638 --> 00:03:20,361 In physics, it's always good to view things from other perspectives. 76 00:03:20,361 --> 00:03:22,226 After all, the laws of physics 77 00:03:22,226 --> 00:03:23,861 should be the same for everyone 78 00:03:23,861 --> 00:03:26,277 or no one will obey them. 79 00:03:26,277 --> 00:03:29,066 So let's rethink our cartoon 80 00:03:29,066 --> 00:03:31,652 and have the camera follow Andrew jogging along 81 00:03:31,652 --> 00:03:35,237 as the fence posts approach and pass behind him. 82 00:03:35,237 --> 00:03:37,777 Still viewing it as a flip book of panels, 83 00:03:37,777 --> 00:03:39,777 we don't need to redraw anything. 84 00:03:39,777 --> 00:03:42,832 We simply move all of the cutout frames slightly 85 00:03:42,832 --> 00:03:45,110 until Andrew's tilted world line 86 00:03:45,110 --> 00:03:48,003 becomes completely vertical. 87 00:03:48,003 --> 00:03:50,695 To see why, let's flip it. 88 00:03:50,695 --> 00:03:54,424 Yes, now I'm stationery, just jogging on the spot, 89 00:03:54,424 --> 00:03:56,051 in the center of the panel. 90 00:03:56,051 --> 00:03:57,552 On the edge of the flip book, 91 00:03:57,552 --> 00:04:00,361 my world line was going straight upwards. 92 00:04:00,361 --> 00:04:03,027 The fence posts are coming past me. 93 00:04:03,027 --> 00:04:06,312 It's now their world lines that are tilted. 94 00:04:06,312 --> 00:04:09,438 This rearrangement of the panels is known as a 95 00:04:09,438 --> 00:04:11,649 Galilean transformation, 96 00:04:11,649 --> 00:04:16,240 and it lets us analyze physics from someeone else's perspective. 97 00:04:16,240 --> 00:04:18,574 In this case, mine. 98 00:04:18,574 --> 00:04:21,945 After all, it's always good to see things from other points of view, 99 00:04:21,945 --> 00:04:24,694 especially when the viewers are moving 100 00:04:24,694 --> 00:04:26,693 at different speeds. 101 00:04:26,693 --> 00:04:30,529 So long as the speeds aren't too high. 102 00:04:30,529 --> 00:04:33,278 If you're a cosmic ray moving at the speed of light, 103 00:04:33,278 --> 00:04:38,028 our flip book of your point of view falls apart. 104 00:04:38,028 --> 00:04:39,805 To stop that from happening, 105 00:04:39,805 --> 00:04:42,140 we'll have to glue panels together. 106 00:04:42,140 --> 00:04:44,612 Instead of a stack of separate panels, 107 00:04:44,612 --> 00:04:47,977 we'll need a solid block of space-time, 108 00:04:47,977 --> 00:04:50,694 which we'll come to in the next animation.