possesses a huge amount of energy, in principle – like, a 5kg cat has enough energy in its

假設擁有一個很大的能量，例如一隻5公斤的貓有足夠的

mass to power the entire country of Norway for a year – if only the energy could somehow

質量轉換成能量來供應整個挪威一年----只要能量能用某種方法

be fully extracted from the cat.

完全從貓轉換出來

But it turns out that efficiently extracting energy from mass is a very hard thing to do.

但要將質量有效率地轉換成能量是件難事

Anti-matter is, of course, the most efficient way of extracting energy from mass since,

當然，反物質，最有效率的方式將質量轉換成能量，

if you collide a cat with a cat made of anti-matter, 100% of the mass of the cat and anti-cat will

當你將貓與其反物質相撞，100%的貓與其反物質

be converted into energy (powering Norway for 2 years).

將轉換成能量(提供挪威2年的能量)

But the universe has almost no naturally-occurring anti-matter, so it’s not a practical choice

但是宇宙幾乎沒有自然生成的反物質，因此這並非是個實際的方法

for generating energy, since you’d first have to use a lot of energy to make a large

要產生能量，你首先要有很大的能量製造大量的反物質

mass of antimatter.

當我們不能使用反物質時，基本上我們剩下三種選項:化學反應

Since we can't use antimatter, there are basically three options left to us: chemical reactions,

核反應和引力反應----物質因重力拉近

nuclear reactions, and gravitational reactions - aka stuff getting pulled together by gravity,

如物質掉進黑洞中。

like matter falling into black holes.

以化學反應為例，它是個很難質能轉換的方法

Chemical reactions, for example, are so bad at extracting energy from mass that we don’t

甚至我們從不考慮及探討它如何運作(縱使它是個方法)。

even think about what they’re doing as converting mass to energy (even though it is).

以此為例，將以個充滿氫氣及氧氣的氣球反應產生一個不錯的大爆炸，

As an illustration, reacting a balloon of hydrogen and oxygen gases creates a nice big

但反應的生成能量僅跟半納克的反應物以先前說的方法生成之能量一樣

explosion, but the end-products of the reaction only weigh half a nanogram less than the initial

其質能轉換的效率極低----只有百億分之一。

reactants , which amounts to a measly 0.00000001% efficiency of converting mass into energy.

以這個比例

At that rate, you’d need ten billion cats to power Norway for a year.

核反應較更有效率，但仍難以達到理想的比例

Nuclear reactions are a lot more efficient, but still pretty bad on an absolute scale:

將鈾235撞擊成氪和鋇只將0.08%的鈾轉換成能量，

splitting uranium-235 into krypton and barium converts only about 0.08% of the uranium’s

且將氫和融合成氦，如太陽則能轉換其大約0.7%

mass into energy, and fusing hydrogen into helium like in the sun converts about 0.7%

的質量轉換成能量。

of the hydrogen’s mass into energy.

以這個程度你需要150隻的貓提供挪威一年的能量。

At that rate you’d need 150 cats to power Norway for a year.

這就是為何需要用黑洞----它就像我們從宇宙將質量轉成能量。

This where black holes come in – they’re about as good as it gets in our universe for

這聽起來很瞎，因為你應該聽過，沒有東西能逃出黑洞

extracting energy from mass.

只要它跑進黑洞裡面。

Which may sound weird, because, as you’ve probably heard, nothing can escape black holes

但黑洞的功效來自任何東西在通過事件視界之前往它靠近，

– once inside.

在通過事件視界的不回頭點(跑不出來了)之前。

But the efficiency of black holes comes from what stuff does while falling towards them,

任何東西掉進其重力場皆加速，獲得動能

before passing the no-turning-back point of the event horizon.

如果它撞到的東西能將動能轉成熱能。

Anything that falls in a gravitational field speeds up, gaining kinetic energy, and if

這樣熱能便能以紅外線的形式輻射出去，輕微的減少物體的質量

it then crashes into something it can convert that kinetic energy into heat.

對行星和恆星而言，這些質能轉換比是少得可憐的:

That heat can then radiate away as infrared radiation, slightly decreasing the mass of

一個東西掉到地面僅轉換成十億分之一的質量能量。

the object.

這基本上就跟化學反應一樣爛!

For planets and stars, this conversion of mass into energy is pretty pathetic: an object

但是黑洞對他們來說有特別的意義:他們超級無敵霹靂小且密度極大。

falling to the surface of the earth releases only about one billionth of its mass as energy.

一個地球重的黑洞大約直徑僅2公分，

That’s basically as bad as a chemical reaction!

提供更長的距離掉落----且重力會隨著距離靠近而增大，

But black holes have something special going for them: they are stupendouslysmall.

當物體掉落至黑洞時會被加速到難以置信的快速。

A black hole with the mass of the earth would be about 2 cm across, providing way farther

實際上，一個物體一路從事件視界掉進黑洞

for an object to fall – and since gravity gets stronger and stronger the closer you

大致上會將其動能轉成相當於其1/2的質量能量

are to an object, objects falling into black holes get accelerated to ridiculous speeds.

然而，如果該物體依然往黑洞裡墜落時，

Specifically, an object falling all the way to the event horizon of a black hole will

全部的能量皆卡在黑洞中

have kinetic energy equivalent to converting roughly half of its half of its E=mc2 mass

較實際的方法將質量轉成能量是

energy mass.

將物體以慢速螺旋的方式掉進黑洞，撞擊到其他物質，加熱並將從損失的質量及動能產生的能量輻射出去，

However, if the object continues to fall into the black hole, all of that energy will be

當速度降更多時，物體便至更接近黑洞的軌道，等等，

stuck inside the black hole.

一路到最內層的軌道。

The way to actually convert mass into energy that goes out into the universe is to have

這正是黑洞積吸盤的功用!

the object slowly spiral into the black hole, crashing into other stuff, heating up, radiating

所以它有多麼能將質量轉成能量呢?

that energy away thereby losing mass and speed, slowing down more, spiraling to a yet lower

其實，一個不會旋轉的黑洞最裡面的軌道

orbit, and so on, all the way down to the innermost possible orbit.

大概是事件視界半徑的3倍，為了旋轉至那個點，物質必須

And this is exactly what accretion disks around black holes do!

將大約6%的質量轉成能量輻射到外太空。

So how good are they at converting mass to energy?

在那之後，如果它失去了更多的能量，它會陷入黑洞，

Well, for a non-rotating black hole, the innermost possible circular orbit is actually 3 times

並且沒有任何能量可以被轉換出來了。

farther out than the event horizon, and in order to spiral in to that point an object

但是只要能轉出6%的話，你只需把17隻貓丟進黑洞就可提供挪威一年的能量。

has to convert around 6% of its mass into energy radiated away to the outside universe.

跟化學反應0.00000001%的效率以及0.7%的核反應效率比起來，

After that point if it loses any more energy it’ll plunge down into the black hole, after

不會旋轉的黑動能轉換6%已經算不錯的了。

which no more energy can be extracted.

但會旋轉的黑洞更好，因為它會扭曲時空。

But at this 6% rate, you’d only need to throw 17 cats into a black hole to power Norway

他們從字面上“拖動”沿旋轉方向旋轉的時空，

for a year.

這代表說軌道能更靠近黑洞(你只要跟著黑洞一起轉)。

Compared to the 0.00000001% efficiency of chemical reactions and the 0.7% efficiency

細節取決於黑洞旋轉的速度，但轉速快的

of nuclear reactions, 6% for a non-rotating black hole may seem pretty good.

黑洞其能靠近的最內軌道幾乎和事件視界的範圍一致，而不是其直徑的3倍!

But rotating black holes are even better, because of how they bend spacetime.

這種黑洞的事件視界直徑是不旋轉的一半。

They literally “drag” things orbiting them in the direction of their rotation, which

統整以上敘述，這代表物質掉進轉動中的黑洞可以將大約42%的質量

means the innermost possible orbit can be much closer to the black hole (as long as

轉成能量。

you’re rotating along with the black hole).

或者以此比喻，你只需2隻半的貓就能提供挪威一年的能量。

The details depend on how fast the black hole is rotating, but for a very quickly rotating

所以，如果你想將一個物質的質量轉成能量時，

black hole the innermost possible orbit coincides with the event horizon!

不要被化學反應，或核裂變，或核融合:把它丟進快速旋轉的黑洞就對了。

And the event horizon itself is half as big as for a non-rotating black hole.

如果你正在想我如何計算質能轉換的效率，

Combined together, this means that matter falling into rotating black holes can convert

你只要將反應所釋出的能量除以參與反應的物質的質量乘上光速的平方

as much as 42% of its mass into energy.

----舉一個例子，當鐳核分裂成氡和氦時

Or equivalently, you’d only need 2 and a half inspiralling cats to power Norway for

釋出6.6電子伏特的能量，一個中子或質子的質量能量約為940電子伏特，

a year.

所以我在這讓你自己找出α衰變在將質量轉化為能量方面的效率！

So, if you really want to convert the mass of an object into energy, don’t bother with

或者您可以透過在Brilliant.org上完成這個測驗來了解更多關於核裂變和聚變的知識，

chemical reactions, or nuclear fission, or nuclear fusion: throw it into a rapidly rotating

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black hole.

如果你真的想深入理解物理學，你必須自己完成計算並解決問題，

If you’re wondering how I calculated the efficiencies of converting mass to energy,

而Brilliant提供了一種互動的在線方式來做到這一點。

you can just divide the energy any reaction releases by the mass energy of the things

您可以使用它的連結免費查看他們的黑洞課程，

involved – for example, when radium radioactively decays into radon and helium it releases 6.6

如果您決定以高級通道報名參加所有課程，您可以享受20％的折扣

MeV of energy, and the mass energy of a single neutron or proton is about 940MeV, so I’ll

如果你是從Brilliant.org/minutephysics進入的話.

leave it to you to figure out how efficient alpha decay is at converting mass to energy!

再說一次，這是Brilliant.org/minutephysics ，讓 Brilliant 知道你來自這裡。

Or you can learn more about nuclear fission and fusion by finishing this quiz on Brilliant.org,

which is this video’s sponsor and is full of interactive quizzes and mini courses on

physics and math.

If you really want to understand physics deeply, you have to work through calculations and

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You can check out their course on black holes for free using the link in the description,

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by going to Brilliant.org/minutephysics.

Again, that’s Brilliant.org/minutephysics which lets Brilliant know you came from here.