Time: it's when things happen.

時間則描述事情何時發生

We can measure where things are

我們能分別觀察事發地點

and when things take place,

和事發時間

but in modern physics,

但現代物理學發現

we realize when and where

事發的時間與地點

are actually part of the same question.

其實都屬於同一個問題

Because when it comes to understanding the universe,

因為如果要了解宇宙

we need to replace three-dimensional space plus time

就得捨棄傳統思維： 三維空間加上一維時間

with a single concept:

改用另一個觀念

four-dimensional space-time.

那就是四維時空

We'll explore and explain space-time

我們將在一系列的動畫中

in this series of animations.

解釋四維時空的概念

Animations?

動畫?

Yeah.

沒錯

Well, we're not very animated are we?

但我們不怎麼靈活吧?

Sure we are! Look, I can go from here to here.

怎麼會!我還能瞬間移動呢!

Whoa! How'd you get from here to there?

你怎麼辦到的?

How fast did you go?

移動速度多快?

Did you run? Walk?

用跑的還是走的?

Did you even go in a straight line?

難道還沿直線移動?

Ah! To answer that, you'll need to make our cartoon physics

要回答你, 得先把誇張的動畫物理學

look more like physics physics.

變得更符合實際物理學

You'll need more panels.

需要更多圖

More panels, please!

請秀更多圖

Okay, in each panel, Andrew's in a slightly different place.

每張圖安德魯都在不同位置

So I can see each one records

每張記錄不同時間

where Andrew is at a different time.

安德魯所在位置

That's great. But it would be easier to see

說得好,但要看得更清楚

what's going on if we could cut out

就得更細分圖片

all the hundreds of panels and stack them up

把細分的幾百張疊起來

like a flip book.

就像本手翻書

Right, now let's flip through the book

就是這樣,現在開始翻頁

so that we can see one panel after another

就能看到一張又一張圖

getting through 24 in every second.

每秒能翻24張

See! I told you it was an animation.

我就說吧!這就是動畫

Now you can see me walking along.

你現在能看到我走路的過程

Drawing all those panels and putting them into a flip book

畫出這些圖並做成手翻書

is just one way of recording the way I'm moving.

只是紀錄我動作的其中一種方式

It's how animation, or even movies, work.

這就是動畫和電影的原理

As it turns out, at my walking speed,

結果發現我走路的速度

it takes two seconds to get past each fence post,

經過一段圍籬得花兩秒

and they're spaced four meters apart.

每段圍籬長四公尺

So we can calculate my velocity --

這樣一算,我的速度...

how fast I'm moving through space - -

也就是我在空間中移動得多快

is two meters per second.

也就是每秒兩公尺

But I could've worked that out from the panels

但我連翻圖也不用翻

without flipping through them.

就能算出結果

From the edge of the flip book,

從手翻書邊緣

you can see all of the copies of the fence posts

就能看到每張圖的圍籬

and all of the copies of Andrew

和安德魯

and he's in a slightly different place in each one.

他在每張圖的位置都有些不同

Now we can predict everything that will happen to Andrew

這樣就能預測

when we flip through 24 pages every second,

每秒翻24張的狀況

including his speed of motion,

安德魯移動的速度

just by looking.

用看的就知道

No need to flip through at all.

The edge of this flip book

手翻書邊緣呈現的圖

is known as a space-time diagram

就叫做時空圖

of Andrew's journey through, you guessed it,

沒錯,就是呈現安德魯

space and time.

移動時的時空狀態

We call the line that represents Andrew's journey

這條代表安德魯移動軌跡的線

his world line.

就叫世界線

If i jog instead of walking,

如果我不用走的,而用跑的

I might be able to get past a fence post every second.

經過圍籬可能只花一秒

He's not very athletic.

他可沒什麼運動細胞

Anyway, when we look at this new flip book from the edge,

總之,從邊緣看手翻書時

we can do the same analysis as before.

能用同樣方式分析

The world line for Andrew jogging

安德魯慢跑的世界線

is more tilted over

比起走路的世界線

than the world line for Andrew walking.

更陡斜

We can tell he's going twice as fast as before

能看出他的速度變成兩倍快

without flipping the panels.

不用動手翻就一目了然

But here's the clever bit.

有趣的地方來了

In physics, it's always good to view things from other perspectives.

物理學鼓勵 從不同觀點分析同個問題

After all, the laws of physics

畢竟物理定律

should be the same for everyone

適用於所有人

or no one will obey them.

否則不能成為定律

So let's rethink our cartoon

所以重新看看我們的動畫

and have the camera follow Andrew jogging along

讓鏡頭跟著安德魯跑

as the fence posts approach and pass behind him.

看看圍籬如何在他身旁移動

Still viewing it as a flip book of panels,

形式還是手翻書

we don't need to redraw anything.

不需重畫

We simply move all of the cutout frames slightly

只要角度稍微轉一下

until Andrew's tilted world line

讓安德魯的世界線

becomes completely vertical.

變成垂直線

To see why, let's flip it.

翻翻看就知道怎麼一回事

Yes, now I'm stationery, just jogging on the spot,

好,現在我原地跑步

in the center of the panel.

一直處在畫面中心

On the edge of the flip book,

在手翻書邊緣

my world line was going straight upwards.

我的世界線垂直向上

The fence posts are coming past me.

使得一個個圍籬經過我

It's now their world lines that are tilted.

是圍籬的世界線變傾斜

This rearrangement of the panels is known as a

這種轉換畫面的方式

Galilean transformation,

就叫做伽利略變換

and it lets us analyze physics from someone else's perspective.

這讓我們從不同角度 分析物理現象

In this case, mine.

這就是從我的角度看

After all, it's always good to see things from other points of view,

總之換種角度看事情總是不錯

especially when the viewers are moving

尤其是觀眾

at different speeds.

以不同速度移動時

So long as the speeds aren't too high.

只要速度不要太快就好

If you're a cosmic ray moving at the speed of light,

如果是以光速前進的宇宙射線

our flip book of your point of view falls apart.

這本手翻書就不夠用了

To stop that from happening,

為了避免這種狀況

we'll have to glue panels together.

必須把每張圖都黏在一起

Instead of a stack of separate panels,

而不只是一張張疊起來

we'll need a solid block of space-time,

我們需要的是一個堅固的時空圖

which we'll come to in the next animation.

這會在下個動畫解釋