[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,we need to replace three dimensional space plus time
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,with a single concept: four dimensional spacetime.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,We'll explore and explain spacetime in this series of animations.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Animations?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Yeah.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Well, we're not very animated, are we?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Sure we are!
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Look! I can go from here to here.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Whoah! How'd you get from here to there?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,How fast did you go? Did you run? Walk?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Did you even go in a straight line?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Ah! To answer that, you'll need to make our cartoon physics
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,look more like physics physics.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,You'll need more panels.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,More panels please!
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Okay. In each panel, Andrew's in a slightly different place.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So I can see each one records where Andrew is
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,at a different time.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,That's great, but it would be easier to see
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,what's going on if we could cut out
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,all the hundreds of panels
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,and stack them up like a flip book.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Right. Now let's flip through the book
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,so that we can see one panel after another,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,getting through 24 in every second.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,See! I told you it was an animation.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Now you can see me walking along.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Drawing all those panels and putting them into a flip book
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,is just one way of recording the way I'm moving.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,It's how animation, or even movies, work.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,As it turns out, at my walking speed
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,it takes two seconds to get past each fence post,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,and they're spaced four meters apart.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So we can calculate my velocity,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,how fast I'm moving through space,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,is two meters per second.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,But, I could've worked that out from the panels
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,without flipping through them.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,From the edge of the flipbook,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,you can see all of the copies of the fencepost,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,and all of the copies of Andrew,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,and he's in a slightly different place in each one.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Now, we can predict everything that will happen to Andrew
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,when we flip through 24 pages every second
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,including his speed of motion just by looking.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,No need to flip through at all!
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,The edge of this flip book
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,is known as a space time diagram
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,of Andrew's journey through - you guessed it -
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,space and time.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,We call the line that represents
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Andrew's journey his world line.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,If I jog instead of walking,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,I might be able to get past a fencepost
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,every second.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,(He's not very athletic.)
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Anyway, when we look at this new flipbook from the edge,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,we can do the same analysis as before.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,The world line for Andrew jogging
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,is more tilted over than the world line for Andrew walking.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,We can tell he's going twice as fast as before
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,without flipping the panels.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,But here's the clever bit!
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,In physics, it's always good to view things from other perspectives.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,After all, the laws of physics
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,should be the same for everyone
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,or no one will obey them.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So, let's rethink our cartoon
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,and have the camera follow Andrew jogging along
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,as the fencepost approach and pass behind him.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Still viewing it as a flipbook of panels,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,we don't need to redraw anything.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,We simply move all of the cutout frames slightly
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,until Andrew's tilted world line bcomes
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,completely vertical.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,To see why, let's flip it.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Yes! Now I'm stationery,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,just jogging on the spot
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,in the center of the panel.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,On the edge of the flipbook,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,my world line was going straight upwards.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,The fenceposts are coming past me.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,It's not their world lines that are tilted.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This rearrangement of the panels
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,is known as a Gallileon transformation.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And it lets us analyize physics
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,from someone else's perspective,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,in this case mine.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,After all, it's always good to see things
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,from other points of view.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Especially when the viewers are moving
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,at different speeds.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So long as the speeds aren't too high.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,If you're a cosmic ray moving at the speed of light,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,our flipbook of your point of view falls apart.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,To stop that from happening,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,we'll have to glue panels together.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Instead of a stack of separate panels,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,we'll need a solid block of space time.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Which we'll come to in the next animation.