experiment where, according to the theory, an event at one point in the universe could

根據此實驗，一個事件發生於宇宙中的一點可以立即影響另一個任意遠的事件，

instantaneously affect another event arbitrarily far away. He called this "spooky action at

他稱之為「鬼魅般的超距作用」，認為這是荒誕無比的──

a distance" because he thought it was absurd. It seemed to imply faster than light communication,

因為這意味著打破相對論對於光速為訊息傳遞的限制。

something his theory of relativity ruled out. But nowadays, we can do this experiment, and

但如今，我們已經可以完成這實驗，也發現，的確，有如鬼魅般。

what we find is, indeed, spooky. But in order to understand it, we must first understand

但想要理解它，我們必須先理解何為「自旋」。

spin. All fundamental particles have a property called spin. No, they're not actually spinning,

所有基本立子都有一種特性叫自旋，他們並不真的在自己旋轉，

but the analogy is appropriate. They have angular momentum, and they have an orientation

但這個比喻是適當的──他們都有角動量，且在空間中有方向。

in space. Now, we can measure the spin of a particle, but we have to choose the direction

現在我們可以量測一個粒子的自旋，但我們必須決定量測哪個方向，

in which to measure it, and this measurement can have only one of two outcomes. Either

且量測的解果只會有兩種：不是與量測的方向對齊，稱為自旋向上；

the particle’s spin is aligned with the direction of measurement, which we'll call

就是與量測方向相反，稱為量測向下。

spin up, or, it is opposite the measurement, which we'll call spin down. Now, what happens

但如果粒子自旋的方向垂直，而我們水平量測的呢？

if the particle spin is vertical, but we measure it's spin horizontally? Well then, it has

那麼他就會有50%的機率自旋向上；50%的機率自旋向下，

a 50% chance of being spin up, and a 50% chance of being spin down, and after the measurement,

而且量測完後，這個粒子就會維持自旋的結果，所以量測的確改變粒子的自旋。

the particle maintains this spin, so measuring its spin actually changes the spin of the

那如果我們量測其自旋與垂直線成60度角？

particle. What if we measure spin at an angle 60 degrees from the vertical? Well now, since

那麼因為此粒子比較對齊量測的方向，它會有3/4的機率自旋向上；

the spin of the particle is more aligned to this measurement, it will be spin up 3/4 of

有1/4的機率自旋向下，其機率為半角餘弦的平方。

the time, and spin down 1/4 of the time. The probability depends on the square of the cosine

現在一個有如愛因斯坦發表的實驗可以用兩個粒子來表示，

of half the angle. Now, an experiment like the one Einstein proposed can be performed

但是這兩個粒子必須以一個特殊的方法來製造，

using two of these particles, but they must be prepared in a particular way. For example,

例如兩個由能量自發而產生的，但因為宇宙的總角動量必須守恆，

formed spontaneously out of energy. Now, since the total angular momentum of the universe

你知道如果一個粒子被量測後自旋向上，另一個量測方向一致的粒子自旋一定向下。

must stay constant, you know that if one particle is measured to have spin up, the other, measured

我必須指出只當兩粒子的測量方向相同時兩兩的自旋才一定相反。

in the same direction, must have spin down. I should point out, it's only if the two particles

現在事情變得有一點詭異了：你可能會認為每個粒子被創造時都被賦予確切指定的自旋，

are measured in the same direction that their spins must be opposite. Now here's where things

但這行不通──想像這兩個粒子的自旋相反且垂直，被以水平方向的測量後，

start to get a little weird. You might imagine that each particle is created with a definite

每一個都分別有50/50的機率自旋向上/下，所以其實會有50%的機率兩個量測會得到相同的結果，

well-defined spin, but that won't work, and here's why. Imagine their spins were vertical

但這卻違反了角動量守恆定律。根據量子力學，這兩個粒子根本就沒有被賦予確切指定的自旋，

and opposite. Now, if they're both measured in a horizontal direction, each one has a

他們其實是纏結在一起的，意味著他們的自旋其實都是相反的，

50/50 chance of being spin up. So, there's actually a 50% chance that both measurements

所以當其中一個粒子被量測且自旋被確認後，你可以馬上知道另一粒子的確切量測結果為何，

will yield the same spin outcome, and this would violate the law of conservation of angular

這已經被許多實驗嚴格的檢測了許多次：不管量測的角度及兩粒子相距多遠，

momentum. According to quantum mechanics, these particles don't have a well-defined

量測結果一定相反。現在停下來想想，這有多麼瘋狂：

spin at all. They are entangled, which means their spin is simply opposite that of the

兩個粒子都沒有確切的自旋，但只要量測其中一個，你就可以立即知道另一個粒子的自旋，

other particle. So, when one particle is measured, and its spin determined, you immediately know

但兩者卻可能相距幾光年遠。有一些理論學家把此結果詮釋為：

what the same measurement of the other particle will be. This has been rigorously and repeatedly

第一次量測會以超光速的速度影響第二次的量測，但愛因斯坦可不這麼想，

tested experimentally. It doesn't matter at which angle the detectors are set, or how

他對此感到非常困擾，他寧可相信其代替解釋：粒子擁有隱藏資訊，

far apart they are, they always measure opposite spins. Now just stop for a minute, and think

使得任何量測方向都會有給定的自旋方向，只是量測之前我們不知道這資訊是什麼。

about how crazy this is. Both particles have undefined spins, and then you measure one,

現在因為兩個粒子在被創造時所擁有的隱藏資訊是在相同地點產生的，

and immediately you know the spin of the other particle, which could be light-years away.

所以兩個粒子間不需要任何比光速還快的訊息傳遞。

It's as though the choice of the first measurement has influenced the result of the second faster

有一段時間，科學家們接受了這個觀點認為粒子有些量測之前無從得知的資訊，

than the speed of light, which is, indeed, how some theorists interpret the result. But

但隨後約翰‧貝爾用一種方法來測試這個想法，

not Einstein. Einstein was really bothered by this. He preferred an alternate explanation,

這個實驗可以確認粒子是否一直都有隱藏資訊，以下是它如何運作：

that all along the particles contained hidden information about which spin they would have

有兩個自旋量測器，每個都可以以三種不同方向的其中一種去量測自旋，

if measured in any direction. It's just that we didn't know this information until we measured

而量測的方向會備隨選擇，且獨立於另一個量測器，

them. Now, since that information was within the particles from the moment they formed

現在一對纏結的粒子或被送入這兩台量測器中，

at the same point in space, no signal would ever have to travel between the two particles

且紀錄下量測結果為相同──都向上/下，或著相異，我們會持續重複此實驗，

faster than light. Now, for a time, scientists accepted this view that there were just some

且以多種隨機組合的量測方向去量測，希望找出兩個量測器給出相異結果的機率，

things about the particles we couldn't know before we measured them. But then along came

而這個機率就是判斷是否一直有隱藏資訊的關鍵，為了瞭解其中的原因，

John Bell with a way to test this idea. This experiment can determine whether the particles

讓我們算出有隱藏資訊的相異結果理論機率，現在你可以想像隱藏資訊為粒子相互認同的秘密計畫，

contain hidden information all along, or not, and this is how it works. There are two spin

現在你可以想像隱藏資訊為粒子相互認同的秘密計畫，

detectors, each capable of measuring spin in one of three directions. These measurement

且唯一標準是以相同方向量測兩個粒子時，結果必須相反，

directions will be selected randomly, and independent of each other. Now, pairs of entangled

舉例來說：第一種是其中一個粒子會在每種量測方向給出向上的自旋，

particles will be sent to the two detectors, and we record whether the measured spins are

而它的另一對都會給出向下的自旋；

the same, both up, or both down, or different. We'll repeat this procedure over and over,

另一種是其中一個粒子會在第一個方向給出向上的自旋、第二個方向給出向下的自旋、第三個方向給出向上的自旋，

randomly varying those measurement directions, to find the percentage of the time the two

而它的另一對會在第一個方向給出向下的自旋、第二個方向給出向上的自旋、第三個方向給出向下的自旋，

detectors give different results, and this is the key, because that percentage depends

任何其他種類的計畫在數學上都相等，所以我們可以靠這兩種計畫算出理論機率。

on whether the particles contain hidden information all along, or if they don't. Now, to see why

現在我以視覺表現出這些粒子的計畫，也就是它們的隱藏資訊。

this is the case, let's calculate the expected frequency of different readings if the particles

在計畫一當中，結果會很明顯地100%相異，量測的方向的並不重要；

do contain hidden information. Now, you can think of this hidden information like a secret

但計畫二中不同的方向卻會產生不結果，

plan the particles agree to, and the only criterion that plan must satisfy is that if

例如當兩個量測器都量測第一個方向，粒子A會給出自旋向上、粒子B會給出自旋向下，

the particles are ever measured in the same direction, they must give opposite spins.

結果相異；但如果量測器B以第二個方向量測，會給出自旋向上，結果相同。

So, for example, one plan could be that one particle will give spin up for every measurement

我們可以持續下去試出所有可能的組合，而我們會發現，

direction, and its pair would give spin down for every measurement direction. Or another

結果相異在九次當中有五次，

plan, plan two, could be that one particle could give spin up for the first direction,

所以計畫二相異的機率為5/9，而計畫一相異的機率為100%，

spin down for the second direction, and spin up for the third direction, whereas its partner

所以總而言之，如果真的有隱藏資訊，相異的機率應大於5/9，

would give spin down for the first direction, spin up for the second direction, and spin

那實驗作出來的結果呢？其實只有50%的機率會是相異的，

down for the third direction. All other plans are mathematically equivalent, so we can work

這並不合理

out the expected frequency of different results using these two plans. Here, I'm visually

所以實驗排除了隱藏資訊使不同方向有不同結果的想法。

representing the particles by their plans, their hidden information. With plan one, the

那量子力學如何解釋這個結果呢？

results will obviously be different 100% of the time. It doesn't matter which measurement

假設量測器A是以第一個方向量測且結果為自旋向上，

directions are selected, but it does for particles using the second plan. For example, if both

那你可以立即知道另一粒子在第一個方向量測結果為自旋向下，

detectors measure in the first direction, particle A gives spin up, while particle B

但每一次只有1/3的機率以第一個方向量測，然而粒子B以其他兩種方向量測的話，

gives spin down. The results are different. But if instead, detector B measured in the

它會跟量測方向有60度的夾角，

second direction, the result would be spin up, so the spins are the same. We can continue

如同影片開頭所說的會有3/4的機率自旋向上，

doing this for all the possible measurement combinations, and what we find, is the results

因為會被這兩種方向量測的機率只有2/3，所以粒子B給出自旋向上的機率為2/3乘上3/4為1/2，

are different five out of nine times. So, using the second plan, the results should

所以兩個量測器給出相同結果的機率為1/2；相異結果為1/2，正如同實驗結果，

be different 5/9 of the time, and using the first plan, the results should be different

所以量子力學是對的，但是如何解釋這些結果還有爭議：

100% of the time, so overall, if the particles contain hidden information, you should see

有些物理學家把這個看做是證明量子粒子中沒有隱藏資訊的證據，

different results more than 5/9 of the time. So what do we actually see in experiment?

且自旋只有在當粒子被量測後才有意義；

Well, the results are different only 50% of the time. It doesn't work, so the experiment

而其他物理學家相信纏結的粒子會在被量測時以超光速更新彼此的隱藏訊息。

rules out the idea that all along, these particles contain hidden information about which spin

所以這是否意味著我們可以使用纏結粒子達成超光速通訊？

they will give in the different directions. So, how does quantum mechanics account for

嗯...每個人都認定不行，這是因為你在兩個量測器發現的結果都是隨機的，

this result? Well, let's imagine detector A measures spin in the first direction, and

不會因不同的量測方向而產生差異。

the result is spin up. Now, immediately you know that the other particle is spin down

而在另一個量測器只會獲得50/50的機率為自旋向上/下，

if measured in the first direction, which would happen randomly 1/3 of the time. However,

只有當兩個量測器的操作員比對量測紀錄時會發現當他們選到相同方向時，

if particle B is measured in one of the other two directions, it makes an angle of 60 degrees

他們都會獲得相反的自旋，兩邊的量測資料都是隨機的，只是與另一個的隨機相反而已，

with these measurement directions, and recall, from the beginning of this video, the resulting

這的確有如鬼魅般，但卻不會讓兩點之間訊息的傳遞比光速還快，

measurement should be spin up 3/4 of the time. Since these measurement directions will be

也不會違反了相對論，

randomly selected 2/3 of the time, particle B will give spin up 2/3 times 3/4 equals half

至少，會讓愛因斯坦開心。

of the time. So both detectors should give the same results half of the time, and different

results half of the time, which is exactly what we see in the experiment. So quantum

mechanics works. But there is debate over how to interpret these results. Some physicists

see them as evidence that there is no hidden information in quantum particles, and it only

makes sense to talk about spins once they've been measured, whereas other physicists believe

that entangled particles can signal each other faster than light to update their hidden information

when one is measured. So, does this mean that we can use entangled particles to communicate

faster than light? Well, everyone agrees that we can't. And that is because the results

that you find at either detector are random. It doesn't matter which measurement direction

you select, or what's happening at the other detector, there's a 50/50 probability of obtaining

spin up or spin down. Only if these observers later met up and compared notebooks, would

they realize that when they selected the same direction, they always got opposite spins.

Both sets of data would be random, just the opposite random from the other observer. That

is, indeed, spooky, but it doesn't allow for the communication, the sending of information

from one point to another, faster than light, so it doesn't violate the theory of relativity.

And that, at the very least, would make Einstein happy.