WEBVTT 99:59:59.999 --> 99:59:59.999 we need to replace three dimensional space plus time 99:59:59.999 --> 99:59:59.999 with a single concept: four dimensional spacetime. 99:59:59.999 --> 99:59:59.999 We'll explore and explain spacetime in this series of animations. 99:59:59.999 --> 99:59:59.999 Animations? 99:59:59.999 --> 99:59:59.999 Yeah. 99:59:59.999 --> 99:59:59.999 Well, we're not very animated, are we? 99:59:59.999 --> 99:59:59.999 Sure we are! 99:59:59.999 --> 99:59:59.999 Look! I can go from here to here. 99:59:59.999 --> 99:59:59.999 Whoah! How'd you get from here to there? 99:59:59.999 --> 99:59:59.999 How fast did you go? Did you run? Walk? 99:59:59.999 --> 99:59:59.999 Did you even go in a straight line? 99:59:59.999 --> 99:59:59.999 Ah! To answer that, you'll need to make our cartoon physics 99:59:59.999 --> 99:59:59.999 look more like physics physics. 99:59:59.999 --> 99:59:59.999 You'll need more panels. 99:59:59.999 --> 99:59:59.999 More panels please! 99:59:59.999 --> 99:59:59.999 Okay. In each panel, Andrew's in a slightly different place. 99:59:59.999 --> 99:59:59.999 So I can see each one records where Andrew is 99:59:59.999 --> 99:59:59.999 at a different time. 99:59:59.999 --> 99:59:59.999 That's great, but it would be easier to see 99:59:59.999 --> 99:59:59.999 what's going on if we could cut out 99:59:59.999 --> 99:59:59.999 all the hundreds of panels 99:59:59.999 --> 99:59:59.999 and stack them up like a flip book. 99:59:59.999 --> 99:59:59.999 Right. Now let's flip through the book 99:59:59.999 --> 99:59:59.999 so that we can see one panel after another, 99:59:59.999 --> 99:59:59.999 getting through 24 in every second. 99:59:59.999 --> 99:59:59.999 See! I told you it was an animation. 99:59:59.999 --> 99:59:59.999 Now you can see me walking along. 99:59:59.999 --> 99:59:59.999 Drawing all those panels and putting them into a flip book 99:59:59.999 --> 99:59:59.999 is just one way of recording the way I'm moving. 99:59:59.999 --> 99:59:59.999 It's how animation, or even movies, work. 99:59:59.999 --> 99:59:59.999 As it turns out, at my walking speed 99:59:59.999 --> 99:59:59.999 it takes two seconds to get past each fence post, 99:59:59.999 --> 99:59:59.999 and they're spaced four meters apart. 99:59:59.999 --> 99:59:59.999 So we can calculate my velocity, 99:59:59.999 --> 99:59:59.999 how fast I'm moving through space, 99:59:59.999 --> 99:59:59.999 is two meters per second. 99:59:59.999 --> 99:59:59.999 But, I could've worked that out from the panels 99:59:59.999 --> 99:59:59.999 without flipping through them. 99:59:59.999 --> 99:59:59.999 From the edge of the flipbook, 99:59:59.999 --> 99:59:59.999 you can see all of the copies of the fencepost, 99:59:59.999 --> 99:59:59.999 and all of the copies of Andrew, 99:59:59.999 --> 99:59:59.999 and he's in a slightly different place in each one. 99:59:59.999 --> 99:59:59.999 Now, we can predict everything that will happen to Andrew 99:59:59.999 --> 99:59:59.999 when we flip through 24 pages every second 99:59:59.999 --> 99:59:59.999 including his speed of motion just by looking. 99:59:59.999 --> 99:59:59.999 No need to flip through at all! 99:59:59.999 --> 99:59:59.999 The edge of this flip book 99:59:59.999 --> 99:59:59.999 is known as a space time diagram 99:59:59.999 --> 99:59:59.999 of Andrew's journey through - you guessed it - 99:59:59.999 --> 99:59:59.999 space and time. 99:59:59.999 --> 99:59:59.999 We call the line that represents 99:59:59.999 --> 99:59:59.999 Andrew's journey his world line. 99:59:59.999 --> 99:59:59.999 If I jog instead of walking, 99:59:59.999 --> 99:59:59.999 I might be able to get past a fencepost 99:59:59.999 --> 99:59:59.999 every second. 99:59:59.999 --> 99:59:59.999 (He's not very athletic.) 99:59:59.999 --> 99:59:59.999 Anyway, when we look at this new flipbook from the edge, 99:59:59.999 --> 99:59:59.999 we can do the same analysis as before. 99:59:59.999 --> 99:59:59.999 The world line for Andrew jogging 99:59:59.999 --> 99:59:59.999 is more tilted over than the world line for Andrew walking. 99:59:59.999 --> 99:59:59.999 We can tell he's going twice as fast as before 99:59:59.999 --> 99:59:59.999 without flipping the panels. 99:59:59.999 --> 99:59:59.999 But here's the clever bit! 99:59:59.999 --> 99:59:59.999 In physics, it's always good to view things from other perspectives. 99:59:59.999 --> 99:59:59.999 After all, the laws of physics 99:59:59.999 --> 99:59:59.999 should be the same for everyone 99:59:59.999 --> 99:59:59.999 or no one will obey them. 99:59:59.999 --> 99:59:59.999 So, let's rethink our cartoon 99:59:59.999 --> 99:59:59.999 and have the camera follow Andrew jogging along 99:59:59.999 --> 99:59:59.999 as the fencepost approach and pass behind him. 99:59:59.999 --> 99:59:59.999 Still viewing it as a flipbook of panels, 99:59:59.999 --> 99:59:59.999 we don't need to redraw anything. 99:59:59.999 --> 99:59:59.999 We simply move all of the cutout frames slightly 99:59:59.999 --> 99:59:59.999 until Andrew's tilted world line bcomes 99:59:59.999 --> 99:59:59.999 completely vertical. 99:59:59.999 --> 99:59:59.999 To see why, let's flip it. 99:59:59.999 --> 99:59:59.999 Yes! Now I'm stationery, 99:59:59.999 --> 99:59:59.999 just jogging on the spot 99:59:59.999 --> 99:59:59.999 in the center of the panel. 99:59:59.999 --> 99:59:59.999 On the edge of the flipbook, 99:59:59.999 --> 99:59:59.999 my world line was going straight upwards. 99:59:59.999 --> 99:59:59.999 The fenceposts are coming past me. 99:59:59.999 --> 99:59:59.999 It's not their world lines that are tilted. 99:59:59.999 --> 99:59:59.999 This rearrangement of the panels 99:59:59.999 --> 99:59:59.999 is known as a Gallileon transformation. 99:59:59.999 --> 99:59:59.999 And it lets us analyize physics 99:59:59.999 --> 99:59:59.999 from someone else's perspective, 99:59:59.999 --> 99:59:59.999 in this case mine. 99:59:59.999 --> 99:59:59.999 After all, it's always good to see things 99:59:59.999 --> 99:59:59.999 from other points of view. 99:59:59.999 --> 99:59:59.999 Especially when the viewers are moving 99:59:59.999 --> 99:59:59.999 at different speeds. 99:59:59.999 --> 99:59:59.999 So long as the speeds aren't too high. 99:59:59.999 --> 99:59:59.999 If you're a cosmic ray moving at the speed of light, 99:59:59.999 --> 99:59:59.999 our flipbook of your point of view falls apart. 99:59:59.999 --> 99:59:59.999 To stop that from happening, 99:59:59.999 --> 99:59:59.999 we'll have to glue panels together. 99:59:59.999 --> 99:59:59.999 Instead of a stack of separate panels, 99:59:59.999 --> 99:59:59.999 we'll need a solid block of space time. 99:59:59.999 --> 99:59:59.999 Which we'll come to in the next animation.