Everything attracts everything else.

令萬物相互吸引

Ouch!

哎喲！

Including you.

包括你，

Ow!

啊！

In this final lesson,

在這個系列的最後一課，

we'll explore what gravity means for space-time,

我們將探索重力對時空的影響，

or rather what space-time means for gravity.

應該說：時空對重力的影響。

Until now, we've been dealing with things moving at constant speeds,

到目前，我們講的都是等速運動的物體

with straight world lines in space-time.

在時空中，世界線是直線的情況

But once you add gravity,

但是一旦加入了萬有引力

if you measure a speed at one moment,

如果你在某一刻測量物體的速度

then again a bit later,

稍等一下，再測量一次

the speed may have changed.

物體的速度可能就會不同了

In other words, as I discovered, gravity causes acceleration,

換句話說，我發現，重力會產生「加速」

so we need the world line to look different from one moment to the next.

所以不同的時刻，我們就需要不同的世界線

As we saw in the last lesson,

如同我們上一課所學的

the correct way to tilt an object's world line is using a Lorentz transformation:

要正確地扭曲一個物體的世界線，要用洛倫茲轉換理論：

Einstein's stretch and squash trick.

愛因斯坦的扭曲小把戲

So, to map out what gravity is doing to Tom's motion,

如果要來分析萬有引力是如何影響Tom的運動

we need to create a whole load of little patches of space-time,

我們要創造很多的時空碎片

each transformed by different amounts.

每一個碎片都經過了不同的程度的轉換

So that my world line is at a different angle in each one.

我的世界線在每個碎片中就都會是不同角度

And then, we're ready to stitch everything together.

然後，我們就可以把這些時空碎片全部拼接起來

We assemble a cozy quilt of space-time

我們如棉被般，把它拼成了一整個時空

where world lines look curved.

在這裡，世界線看起來是彎曲的

Where the world lines join, the objects collide.

當世界線相交時，代表物體相互碰撞了

By making these connections between the patches,

當我們把這些碎片連起來時

a curvature gets built into space-time itself.

這個曲率本身就形成了時空

But Einstein's true genius

但愛因斯坦的天才之處

was to describe precisely how each patch is stretched and squashed

在於他精確地算出每個碎片是如何地伸展、扭曲

according to nearby mass and energy.

根據物體四周的質量與能量

The mere presence of stuff curves the space-time,

物體的存在就會使時空扭曲

and curving space-time moves the stuff around.

而扭曲的時空可以讓物體移動

This is gravity, according to Einstein.

這就是愛因斯坦對重力的詮釋

Previously, Isaac Newton had explained gravity using the ideas of force and acceleration,

在此之前，牛頓以力與加速度來解釋力的概念

without any wibbly wobbly space-time,

沒有提到這些扭曲的時空

and that did pretty well.

而這理論已經相當不錯了

But Einstein's theory does just slightly better at predicting,

但是愛因斯坦的理論在預測上表現得更好

for example, the orbit of Mercury around the Sun,

例如預測水星繞太陽的軌道

or the way that light rays are deflected by massive objects.

或者巨大物體影響光的行進方向

More importantly, Einstein's theory predicts things that simply don't exist in older theories

更重要的是，愛因斯坦的理論推測出舊理論中不存在的概念

where space, time and gravity were separate.

舊理論中認為空間、時間、重力毫不相關

The stitching can leave wrinkles in the space-time material.

時空碎片的拼接會讓時空出現「皺褶」

These are called gravitational waves,

我們稱其為「重力波」

which should be detectable as tiny, repetitive, subtle squashes and stretches in space.

藉由偵測空間中細微、重複的起伏變化，可以探測重力波

So we're building experiments to check if they are there.

我們正在開發可以探測到重力波的實驗

In the meantime, indirect evidence,

同時，從間接的證據上看

most recently in the polarization patterns of light left over from the Big Bang,

例如宇宙大爆炸留下的光波極化現象

strongly suggest that they are.

即是重力波存在的有力證據

But despite Einstein's successes,

雖然愛因斯坦的理論相當成功

when too much stuff gets concentrated in too small a space,

當在極小的空間中有太多物質聚集

like in a black hole,

比如在黑洞中

the curvature of space-time becomes so large,

時空的曲率變得太大

that his equations collapse.

愛因斯坦的公式也因此崩塌 (不適用) 了！

We need a new picture of space-time that incorporates quantum mechanics

所以我們需要用新的概念，結合量子力學來解釋時空

to unlock the secret at the heart of black holes.

藉此來解開黑洞的秘密

Which means there's plenty more to be discovered about space, time, and space-time in the future.

也就是說關於時間、空間、時空，還有很多等著我們來發現！