[Buzzing safety alarm]

今天我來到了華盛頓特區的國家標準技術研究所，

I'm at the National Institute of Standards & Technology in Washington D.C.

現在我要去地下二樓。

and I'm going to the sub-basement.

光線有點變暗了。

It's getting dark down here.

我們去看他們如何重新為"公斤(千克)"定義標準。

We're going to find out how they're going to redefine a kilogram.

公斤的單位標準出現了大麻煩。

The kilogram is in trouble.

自1799年以來，它一直是以一塊圓柱形金屬塊的重量為標準，

Since 1799, it's been defined as the mass of a metal cylinder,

這塊金屬位於巴黎地下一座上鎖的金庫內。

in a locked vault in a basement in Paris.

上個世紀，這個國際通用公斤原型品與來自其他世界各地

But over the last century, careful measurements of this international prototype kilogram

理論上相同的國家標準金屬塊的精確量測記錄，

and in-theory-identical national standards from around the world,

顯示了這些金屬塊之間的重量差異正在發散中。

have shown that their masses are diverging.

其變異散佈範圍增加到50微克，也就是50 ppb (億分之五)。

The spread has grown to around 50 micrograms, or 50 parts per billion.

作為一個重量標準來說，這樣的變異是不合格的。

And having a standard of mass that changes is unacceptable.

更進一步來看，"公斤"是目前國際單位制中最後一個還在使用實際物體來定義的一個單位。

Plus, the kilogram is the last of the base SI units to still be defined by a physical object.

舉例來說，"公尺"以往是使用在巴黎的一條白金棒的長度作為標準。

The metre, for example, used to be defined as the length of a platinum bar in Paris,

然而，它在1983年被重新以光在兩億九千萬分之一秒 (1/299,792,458 s) 中所行經的距離來定義。

but in 1983 it was redefined as the distance light travels

然而，它在1983年被重新以光在兩億九千萬分之一秒 (1/299,792,458 s) 中所行經的距離來定義。

in 1/299,792,458 of a second.

這同時也精準定義了光速為每秒299,792,458.00000公尺 (注：意謂為整數，沒有小數點之後的數字了。)

This definition means that the speed of light is set to exactly 299,792,458

這同時也精準定義了光速為每秒299,792,458.00000公尺 (注：意謂為整數，沒有小數點之後的數字了。)

point 00000...

這同時也精準定義了光速為每秒299,792,458.00000公尺 (注：意謂為整數，沒有小數點之後的數字了。)

et cetera, metres per second.

注意一下這裡為什麼說得通？ 首先，你利用一個既有的"公尺"定義，

Note how this works: first, you take the existing definition,

好比說，取這條標準品白金棒的長度，

say, the length of that metre bar,

你盡可能地精確量測出它與宇宙物理常數 -- 光速之間的關聯性。

and you measure as carefully as you can how it relates to a physical constant of the universe:

你盡可能地精確量測出它與宇宙物理常數 -- 光速之間的關聯性。

the speed of light.

然後你藉此設定了精確的光速值，

Then you set the exact value of that constant

再用這光速值回推過來重新定義"公尺"到底是多長。

and use *it* to redefine how long a metre is.

我知道這聽起來怪怪的，像是"先有雞還是先有蛋"的繆論，

I know this might seem circular, but, importantly, it moves the point of truth

但是重要的是，它讓真理點得以脫離了(不可靠的)實際物體，而連結上不會變動的宇宙常數。

off of the physical object, and onto the unchanging constant of the universe.

自然而然地，這套理念也將套用在"公斤(千克)"之上。

So, naturally, the thought is to do the same thing with the kilogram.

不過... 他們要利用哪個宇宙常數，又要怎麼辦到呢？

But... using which constant, and how?

他們已經嘗試過了一大串不同的策略，

[Heavy mechanical noises]

而其中取得了最大成功的兩個是：

Well, there are a number of different strategies that were attempted

一、使用一個純矽球體來決定及設定亞佛加厥數；

but the two that achieved the greatest success were:

二、使用瓦特天平來決定及設定普朗克常數。

1) using a silicon sphere to determine and set Avogadro's number

嗨，你好嗎？我是Derek，很高興見到你。 Jon: [我很好！]

and 2) to use a Watt balance to determine and set Planck's constant.

瓦特天平到底在哪裡？

>>DEREK: Hi, how ya' doin'? I'm Derek. >>JON: Pretty good. >>DEREK: Nice to meet you.

Stephan: [瓦特天平就在這個門後面。]

>>DEREK: Where is the Watt balance?

就在這裡面？

>>STEPHAN: The Watt balance is behind these closed doors, and...

Stephan: [沒錯，但是現在的問題是我們正來到一個緊要關頭...將決定我們是否能在五月底以前得到一個數字。]

>>DEREK: It's in there?

Stephan: [沒錯，但是現在的問題是我們正來到一個緊要關頭...將決定我們是否能在五月底以前得到一個數字。]

>>STEPHAN: It's correct, and right now the problem is that...

要得到什麼數字？

We are in a crunch to get a number by the end of May.

Stephan: [普朗克常數。這就是我們正在用瓦特天平量測的東西。]

>>DEREK: What's the number?

2011年的國際度量衡大會中做出決議，

>>STEPHAN: The Planck's constant. This is what we measure with the Watt balance.

"公斤"應該以普朗克常數為基礎重新定義。

In 2011, the General Conference on Weights and Measures

但那並不代表採用亞佛加厥數的策略是徒勞的。

decided that the kilogram should be redefined based on Planck's constant,

我是指，你可以用亞佛加厥數去計算普朗克常數，反過來也是可以的。

but that doesn't mean that the Avogadro approach was futile.

所以，說到底兩種策略都將同時被用來重新定義普朗克常數和亞佛加厥數。

I mean, you can use Avogadro's number to calculate Planck's constant and vice-versa.

所以，說到底兩種策略都將同時被用來重新定義普朗克常數和亞佛加厥數。

So, ultimately, both approaches are going to be used to redefine

Stephan: [不放棄矽球法的一個好處是，]

Planck's constant and Avogadro's number simultaneously.

Stephan: [你只要去檢視這些不同數值之間的換算結果是否相符，對吧？]

>>STEPHAN: One good thing about having silicon spheres,

Stephan: [在我想到矽球法時，它的構想是來自於化學。]

is that you only want to redefine if you have agreement between different numbers, right?

Stephan: [所量測的亞佛加厥數就是化學常數之一。]

And the silicon sphere method is a method in my mind that comes out of chemistry.

Stephan: [我們量測普朗克常數，則是從物理學出發。]

You measure Avogadro's constant, which is a constant that comes out of chemistry.

Stephan: [如果這兩種結果相符，這就會是很強烈的跡象，對吧？因為你知道化學與物理學兩方面都同意了這個結果。]

This method comes out of physics, we measure Planck's constant.

因為在我的前個影片中已討論過亞佛加厥法了，

So if they both agree, it's a pretty strong sign, right? Because you know chemistry and physics agree.

所以我現在想聚焦在瓦特天平上。

Now, since I've already discussed the Avogadro approach in a previous video,

為了要紀念於2016年過逝的發明者Bryan Kibble，它現在被改稱為Kibble天平。

here I want to focus on the Watt balance.

為了要紀念於2016年過逝的發明者Bryan Kibble，它現在被改稱為Kibble天平。

It's actually now called a Kibble balance in honor of its inventor, Bryan Kibble,

傳統天平的原理，是讓天平臂兩端掛上的物體所受到的重力相互平衡。

who actually passed away in 2016.

Kibble天平看起來也很相似，但是平衡的動作主要發生在左手端，

You know, traditional balances work by equating the gravitational forces on objects in two pans.

這裡的稱盤連接上一個處於磁場中的線圈。

The Kibble balance looks kind of similar, but all of the balancing happens on the left-hand side,

在右手端則是一個馬達。

where a mass pan is attached to a coil of wire in a magnetic field.

這整個裝置是被密封的，且在真空下操作。

On the right-hand side is a motor.

這天平有兩種操作模式：稱重模式及速率模式，

The whole apparatus is sealed and operated in vacuum.

這天平有兩種操作模式：稱重模式及速率模式，

The balance operates in two modes:

兩者都是測定普朗克常數所必需的。

Weighing mode and velocity mode,

在稱重模式中，1公斤的標準質量被放在稱盤上，

and both are required to determine Planck's constant.

然後將電流導入磁場中的線圈，

In weighing mode, a kilogram mass standard is placed on the mass pan

調整電流直到線圈的電磁力與這1公斤的重量相當。

and then current is passed through the coil in the magnetic field

調整電流直到線圈的電磁力與這1公斤的重量相當。

and adjusted until the weight of the kilogram is equal and opposite

方程式是，質量 m 乘以當地的重力加速度 g 要等於磁場強度 B 乘上線圈長度 L 再乘上通過的電流值 I。

to the electromagnetic force on the coil.

方程式是，質量 m 乘以當地的重力加速度 g 要等於磁場強度 B 乘上線圈長度 L 再乘上通過的電流值 I。

The equation for this is Mass times the local gravitational acceleration

在這個方程式中比較難以精確量測的變數是磁場強度 B 和線圈長度 L。

is equal to the Magnetic field, times the length of wire in the coil, times the current flowing through it

但是很幸運地Kibble天平提供了速率模式以繞過這個問題。

In this equation the variables that are difficult to measure exactly are the magnetic field strength, and the length of wire in the coil

在速率模式中，1公斤的標準質量被抬離稱盤，

But luckily the Kibble balance allows us to get around this problem using velocity mode

另一端的馬達則開始讓線圈以固定速率在磁場中往復地移動。

In velocity mode the kilogram mass is lifted off the mass pan and now the motor on the other side of the balance is used to

這運動在線圈中誘發的電壓值 V 等於磁場強度 B 乘上線圈長度 L 再乘上移動速率 v 。

Move the coil back and forth at constant velocity through the magnetic field.

這運動在線圈中誘發的電壓值 V 等於磁場強度 B 乘上線圈長度 L 再乘上移動速率 v 。

This motion induces a voltage in the coil which is equal to the magnetic field,

這樣就可以用這兩個聯立方程式來消除 B 與 L 的乘積，

times the length of wire in the coil, times its velocity.

這樣就可以不必知道它們的精確數值。

Now we have two equations which we can solve for B times L and so we can set them equal to each other and

如果我們重排一下方程式，你可以得到電壓 V 乘上電流 I 等於質量 m 乘上重力加速度 g 再乘上速率 v。

eliminate these variables without having to know precisely what their values are

等式的左手邊是電力，右手邊是機械力，

and if we rearrange a little bit you get voltage times current equals mass times gravity times velocity.

這就是為什麼會被稱為 瓦特(電功率單位)天平 的緣故。

on the left hand side, there is electrical power and on the right hand side, mechanical power,

但你如何從這裡導出連結光子頻率與光子能量的普朗克常數？

and that's why this was called the Watt, the unit of power, balance

事實上確實有個利用了涉及約瑟夫森接面的巨觀量子效應來精確量測電壓值方法。

But how do you go from this to Planck's constant the number that relates a photon's frequency to its energy?

一個約瑟夫森接面是由兩個超導體之間夾著薄薄一層絕緣體所組成。

Well it turns out there's actually a way of measuring voltage accurately using a macroscopic quantum effect that involves Josephson junctions

如果你在這接面上施加一道微波輻射，你會在這接面兩端產生電壓，它的數值會等於 hf 除以 2e。

so a Josephson junction consists of two superconductors separated by a thin piece of insulator

這裡的 h 就是普朗克常數，f 是微波的頻率，e 是一個電子的電荷。

Now if you apply a microwave radiation to that junction, you create a voltage across the device and its value is precisely known to be

藉由調整頻率和堆疊你想要的約瑟夫森接面串接層數，

hf over 2 e. Where h is Planck's constant, f is the frequency of the radiation, and e is the charge on an electron

你可以實質上精準地產生任何你想要的電壓值。

Now by tuning that frequency and stacking as many of these Josephson junctions as you want in series

這方法應用在Kibble天平中就是將這高達數十萬層的約瑟夫森接面疊堆，

you can create virtually any voltage you like very very precisely.

將它放入線圈的電路中，當它在磁場中移動時，

The way this is used in the Kibble balance is a stack of hundreds of thousands of Josephson junctions

你就精確地利用這些約瑟夫森接面疊堆來平衡線圈所誘發的電壓。

are put into the circuit with the coil as it is moved through the field

這樣你就可以量測到非常非常準確的電壓值了。

and so you exactly balance the voltage which is induced in the coil using those Josephson junctions

那麼我們又該如何來量測電流呢？

So you can measure that voltage very very accurately.

事實上因為這個電壓量測的方法真的實在是好棒棒，所以我們根本不必直接量測電流值，

But how do we measure current?

取而代之的是直接量測固定電阻上的電壓值，這樣可以得到一樣的結果。

Well it turns out this voltage measuring method is so good that instead of trying to measure current directly

當這電流通過一個電阻時，我們再次使用約瑟夫森接面疊堆來量測電壓值。

we instead measure V on R which is the same thing

接下來要量測電阻值時，我們採用了另一個被稱為量子霍爾效應的巨觀量子效應。

So this current is passed through a resistor, and we measure that voltage again using Josephson junctions

雖然這已經超出了本影片的範圍，

And then to measure resistance we use another macroscopic quantum effect called the quantum hall effect.

但我想應該這樣子說就夠了...

Which is Beyond the scope of this video but,

電阻值的量測會是個整數分數 1/p 乘以普朗克常數再除以電子電荷的平方。

suffice is to say that the resistance measurement will be an integer fraction, one over p

所以如果我們把這些全代入我們的方程式中求解 h，

times Planck's constant divided by the charge on the Electron squared

普朗克常數等於 4 除以 p n平方，那是我們所有已知的常數，再乘上當地重力加速度 g 以及速率 v，

So if we sub all of this into our equation and solve for h, we have that Planck's constant is equal to four

除以頻率的平方後最終乘上1公斤的質量。

over p n squared, those are all constant numbers that we know, times the local acceleration due to gravity times velocity

現在我們有了一個非常精準的方程式，可以從1公斤的質量來算出普朗克常數。

divided by frequency squared times the mass which is one kilogram.

現在要得到一個誤差10 ppb (億分之一) 才算夠好的答案的話，

So here we have a very precise equation for Planck's constant in terms of the mass of one kilogram

你需要非常精確地知道這些數值。

Now to get an answer that's good to say, ten parts per billion

舉例來說，在量測線圈於磁場中的移動速率 v 時，

You need to know all of these values very accurately

我們用上了雷射干涉儀。

So to measure V for example the velocity of the coil as it moves through the Magnetic field,

當與線圈之間的距離改變了穿過偵測器的雷射干涉條紋。

we use a laser interferometer

基本上只要計數在特定時間中通過了多少條紋，

as the distance to the coil changes the interference Fringes pass over a detector

你就可以很精確地測出線圈的速度。

And essentially by counting how many fringes go past in a certain period of time

在重力加速度的量測上，一個被稱為重力儀的設備

you can determine the speed of the coil very accurately

被用來映射出天平室被建造以前時的本地重力加速度。

To measure g, a device called a gravimeter was used

重力儀藉由使一個角反射器於真空管內落下，再以計數干涉條紋的方式來量測它的加速度。

to map out the local acceleration due to gravity in the balance room before it was built in there

重力儀藉由使一個角反射器於真空管內落下，再以計數干涉條紋的方式來量測它的加速度。

The gravimeter actually drops a corner reflector down a vacuum tube and measures its acceleration

這就是Kibble天平室裡重力加速度的3D列印地圖。

again through interferometry, counting the fringes as they pass

這塊隆起歸因於天平中一塊沉重的強力永久磁鐵的質量。

This is a 3D printed map of the acceleration due to gravity in the Kibble balance room

重力加速度的監測必須持續地進行，因為在這樣的精密度水準下，

The bump is due to the mass of the powerful and very heavy permanent magnet that's in the balance

它有可能會受到來自於太陽及月亮的位置，甚至於建築物下方地下水位的影響。

The acceleration due to gravity must continually be measured because it can be affected at this level of precision

到了2018年時，公斤將不再由巴黎的那塊東西來定義了。

By the positions of the sun and moon and even the water table underneath the building

它將會根據確定後的普朗克常數來定義，

In 2018 the kilogram will no longer be defined by an object in Paris

當Kibble天平與矽球體的所有量測結果出爐後就將被定案。

Instead it will be defined based on the fixed value of Planck's constant

Stephan: [所以現在我們的方法是把質量代進去，我們就可以得出普朗克常數。]

which is being finalized right now as a result of all these measurements from the Kibble balances and silicon spheres

Stephan: [在2018年的重新定義之後，普朗克常數將被確定，然後你可以用它來實現重量單位。]

So right now what we do is, we put the mass in, and we get h out

Stephan: [很容易吧！]

and in 2018, after redefinition, h will be fixed and you use that to realize the unit of mass

就那麼簡單。

>>STEPHAN: Easy >>DEREK: Yeah, just that-- just that easy. >>STEPHAN: Yeah -

>>DEREK: Just that simple. >>STEPHAN: Simple

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