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