but we can still measure its speed

但我們依然有辦法測量它的速度。

if we slow down the animation,

如果我們把畫面放慢，

we can analyze light's motion using

我們可以使用時空圖來分析光的運動，

a space-time diagram,

就像從側面來看一頁頁的手翻書。

which takes a flipbook of animation panels,

在這堂課裡，我們先補充一個實驗結果：

and turns them on their side.

當任何人所測量的光速，

In this lesson, we'll add the single experimental fact

都會得到相同的結果。

that whenever anyone measures just how fast light moves,

每秒299 792 458公尺。

they get the same answer:

這意味著

299,792,458 meters every second,

當我們把光畫在時空圖上時，

which means that when we draw light

光的世界線必須總是呈現相同的角度。

on our space-time diagram,

但是，我們之前看到

it's world line always has to appear at the same angle.

速度即是由世界線的角度來表示

But we saw previously that speed,

會隨著不同觀察者的視角而改變。

or equivalently world line angles,

為了弄清這個矛盾

change when we look at things from

讓我們來看看如下情況：

other people's perspective.

如果我開始移動，

To explore this contradiction,

而我站在這裡朝著湯姆發射雷射光。

let's see what happens if I start moving

首先，我們需要建構出時空圖

while I stand still and shine the laser at Tom.

這意味著

First, we'll need to construct the space-time diagram.

取出對應每一個時刻的每一幅圖片，

Yes, that means taking all of

然後把它們疊在一起。

the different panels showing the different moments in time

從側面我們看到雷射光的世界線

and stacking them up.

有著固定的、正確的角度，

From the side, we see the world line

就和早先的一樣。

of the laser light at its correct fixed angle,

目前為止一切順利。

just as before.

但是這個時空圖展示的是安德魯的視角。

So far, so good.

從我的視角來看是什麽樣的呢？

But that space-time diagram represents Andrew's perspective.

在上一課裡

What does it look like to me?

我們展示了如何得到湯姆的視角。

In the last lesson, we showed

只需把所有的圖片平移一點，

how to get Tom's perspective moving all the panels

直到湯姆的世界線完全垂直。

along a bit until his world line is completely vertical.

但是仔細看看光的世界線。

But look carefully at the light world line.

平移所有圖片的話，

The rearrangement of the panels

會使得光的世界線傾斜過度。

means it's now tilted over too far.

我所測得的光速將會比安德魯所測得的快。

I'd measure light traveling faster than Andrew would.

但是我們所做過的實驗，

But every experiment we've ever done,

我們所有的努力，

and we've tried very hard,

都證明光速是恒定的。

says that everyone measures light to have a fixed speed.

讓我們重新開始。

So let's start again.

在19世紀初，有個聰明的傢伙叫愛因斯坦。

In the 1900s, a clever chap named Albert Einstein

他想出了如何從湯姆的視角

worked out how to see things properly,

來正確地看待問題，

from Tom's point of view,

而同時依然能得到正確的光速。

while still getting the speed of light right.

首先我們需要把分離的畫面都粘合起來，

First, we need to glue together the separate panels

粘成完整的一塊，

into one solid block.

於是我們有了時空。

This gives us our space-time,

將時間和空間

turning space and time into

變成一整塊平順連續的材料。

one smooth, continuous material.

現在，變戲法的時候到了。

And now, here is the trick.

你要做的是

What you do is stretch your block of space-time

沿著光的世界線拉伸你的整塊時空，

along the light world line,

然後在垂直世界線的方向上

then squash it by the same amount,

等量地壓縮時空。

but at right angles to the light world line,

唵嘛呢叭咪吽！

and abracadabra!

湯姆的世界線變得垂直了，

Tom's world line has gone vertical,

所以這代表了他眼中的世界。

so this does represent the world from his point of view,

但是最重要的是，

but most importantly,

光的世界線從未改變角度。

the light world line has never changed its angle,

所以湯姆所測量的光速

and so light will be measured by Tom

也是正確的光速。

going at the correct speed.

這個傑出的戲法叫做

This superb trick is known as

勞侖茲轉換。

a Lorentz transformation.

這可不是騙人的把戲，

Yeah, more than a trick.

重新將時空分割為一幅幅畫面

Slice up the space-time into

你將得到物理上正確的動畫。

new panels and you have

我靜止坐在車裡，

the physically correct animation.

所有東西都朝我移來並經過我身邊，

I'm stationary in the car,

而光速依然

everything else is coming past me

是那個恒定的速度，

and the speed of light

和所有人測量的光速一樣。

works out to be that same fixed value

而另一方面，

that we know everyone measures.

有些奇怪的事情發生了，

On the other hand,

圍欄柱子的間隔不再是一米了。

something strange has happened.

而我媽媽會擔心

The fence posts aren't spaced a meter apart anymore,

我看起來變瘦了。

and my mom will be worried

這不公平！為什麼我看起來沒變瘦？

that I look a bit thin.

我以為物理學對每個人都是一樣的。

But that's not fair. Why don't I get to look thin?

的確是一樣的，你也看起來瘦了。

I thought physics was supposed to be the same

所有這些，時空的拉伸和壓縮，

for everyone.

把我們之前認為的

Yes, no, it is, and you do.

獨立的時間和空間

All that stretching and squashing

都混合到了一起。

of space-time has just muddled together

這個特別的壓縮效應，

what we used to think of separately

被稱為勞侖茲收縮。

as space and time.

好吧，可是我依然看起來不瘦。

This particular squashing effect

不，你的確看起來瘦了。

is known as Lorentz contraction.

現在我們對時空有了更多的了解，

Okay, but I still don't look thin.

我們應該重新畫出

No, yes, you do.

我眼中的情形是怎麽樣的。

Now that we know better about space-time,

對你來說，我表現出勞侖茲收縮。

we should redraw

而對你來說，我表現出了勞侖茲收縮。

what the scene looked like to me.

對。

To you, I appear Lorentz contracted.

好吧，至少這是公平的。

Oh but to you, I appear Lorentz contracted.

說到公平，

Yes.

不僅空間被時間攪渾，

Uh, well, at least it's fair.

時間也被空間攪渾。

And speaking of fairness,

有個效應叫做時間膨脹。

just as space gets muddled with time,

雖然在日常的速度下，

time also gets muddled with space,

比如湯姆的車速，

in an effect known as time dilation.

實際的效應非常非常地小，

No, at everyday speeds,

比我們剛才展示的要小得多。

such as Tom's car reaches,

然而精密的實驗，

actually all the effects are much, much smaller

比如觀察微小的粒子

than we've illustrated them.

在大型強子對撞機裡的運動，

Oh, yet, careful experiments,

確認了這些效應是真實存在的。

for instance watching the behavior of tiny particles

既然現在時空已是被實驗驗證的事實，

whizzing around the Large Hadron Collider

我們的野心可以更大一些。

confirmed that the effects are real.

我們是否可以開始

And now that space-time is

考慮時空本身的性質？

an experimentally confirmed part of reality,

我們會在下一堂課裡找到答案。

we can get a bit more ambitious.

What if we were to start playing

with the material of space-time itself?

We'll find out all about that in the next animation.