Grant: Each of these pieces of glass is what's called a "polarizing filter", which means

格蘭特。這些玻璃中的每一塊都是所謂的 "偏振濾鏡"，這意味著

when a photon of light reaches the glass, it either passes through, or it doesn't.

當一個光子到達玻璃時，它要麼通過，要麼不通過。

And whether or not it passes through is effectively a measurement of whether that photon is polarized

而它是否通過，實際上是對該光子是否被偏振的一種測量

in a given direction.

在一個特定的方向上。

Henry:  Try this: Find yourself several sets of polarized sunglasses.

亨利：試試這個。給自己找幾套偏光太陽鏡。

Look through one set of sunglasses at some light source, like a lamp, then hold a second

通過一副太陽鏡看一些光源，如燈，然後拿著第二副太陽鏡看。

polarizing filter, between you and the light.

在你和光線之間有一個偏振鏡。

As you rotate that second filter, the lamp will look lighter and darker.

當你旋轉第二個過濾器時，燈看起來會變亮和變暗。

It should look darkest when the second filter is oriented 90 degrees off from the first.

當第二個濾鏡的方向與第一個濾鏡偏離90度時，它應該看起來最暗。

What you're observing is that the photons with polarization that allows them to pass

你所觀察到的是，具有偏振性的光子使它們能夠通過

through a filter along one axis have a much lower probability of passing through a second

濾光片沿一個軸線通過的概率要低得多，因為它可以通過第二個軸線。

filter along a perpendicular axis – in principle 0%.

沿著垂直軸線的過濾器 - 原則上是0%。

Grant: Here's where things get quantum-ly bizarre.

格蘭特。這裡是事情變得量子化的奇怪之處。

All these filters do is remove light – they “filter” it out.

這些過濾器所做的就是去除光線--它們 "過濾 "了光線。

But if you take a third filter, orient it 45 degrees off from the first filter, and

但是，如果你拿著第三個過濾器，把它的方向與第一個過濾器偏離45度，並且

put it between the two, the lamp will actually look brighter.

把它放在兩者之間，燈實際上會看起來更亮。

This is not the middle filter generating more light – somehow introducing another filter

這不是中間的過濾器產生更多的光--以某種方式引入另一個過濾器

actually lets more light through.

實際上是讓更多的光線通過。

With perfect filters, if you keep adding more and more in between at in-between angles,

有了完美的濾鏡，如果你在中間的角度不斷添加更多的東西。

this trend continues – more light!

這一趨勢仍在繼續--更多的光!

Henry:  This feels super weird.

亨利：這感覺超級奇怪。

But it's not just weird that more light comes through; when you dig in quantitatively

但是，更多的光亮出現並不只是奇怪；當你從數量上進行挖掘時

to exactly how much more comes through, the numbers don't just seem too high, they seem

確切地說，還有多少是通過的，這些數字不只是看起來太高，它們似乎是

impossibly high.

不可能的高。

And when we tug at this thread, it leads to an experiment a little more sophisticated

而當我們拽住這根線時，就會引出一個更復雜的實驗

than this sunglasses demo that forces us to question some very basic assumptions we have

比起這個太陽鏡演示，它迫使我們質疑一些非常基本的假設，我們有

about the way the universe works – like, that the results of experiments describe properties

關於宇宙的運作方式--比如，實驗的結果描述的屬性是什麼？

of the thing you're experimenting on, and that cause and effect don't travel faster

實驗的東西，而且因果關係的傳播速度並不快。

than the speed of light.

比光速更快。

Grant:  Where we're headed is Bell's theorem: one of the most thought-provoking discoveries

格蘭特。 我們的方向是貝爾定理：最發人深省的發現之一

in modern physics.

在現代物理學中。

To appreciate it, it's worth understanding a little of the math used to represent quantum

為了欣賞它，值得了解一點用來表示量子的數學。

states, like the polarization of a photon.

狀態，如光子的偏振。

We actually made a second video showing more of the details for how this works, which

實際上，我們製作了第二個視頻，展示了更多關於如何工作的細節，其中包括

you can find on 3blue1brown, but for now let's just hit the main points.

你可以在3blue1brown上找到，但現在我們只說說主要內容。

First, photons are waves in a thing called the electromagnetic field, and polarization

首先，光子是一種叫做電磁場的東西中的波，而偏振

just means the direction in which that wave is wiggling.

只是指該波擺動的方向。

Grant: Polarizing filters absorb this wiggling energy in one direction, so the wave coming

格蘭特。偏振濾光片在一個方向上吸收了這種擺動的能量，是以，波的到來

out the other side is wiggling purely in the direction perpendicular to the one where energy

在另一邊純粹是在垂直於能量的方向上搖擺。

absorption is happening.

吸收正在發生。

But unlike a water or sound wave, photons are quantum objects, and as such they either

但與水或聲波不同，光子是量子物體，是以它們要麼是

pass through a polarizer completely, or not at all, and this is apparently probabilistic,

完全通過偏振片，或根本不通過，這顯然是概率問題。

like how we don't know whether or not Schrodinger's Cat will be alive or dead until we look in

就像我們不知道薛定諤的貓會不會活著或死了，直到我們看一看

the box.

盒子裡。

Henry: For anyone uncomfortable with the nondeterminism of quantum mechanics, it's tempting to imagine

亨利。對於任何對量子力學的非確定性感到不舒服的人來說，都很容易想象到

that a probabilistic event like this might have some deeper cause that we just don't

像這樣的概率事件可能有一些更深層次的原因，只是我們不知道。

know yet.

還不知道。

That there is some “hidden variable” describing the photon's state that would

有一些描述光子狀態的 "隱性變量"，它將

tell us with certainty whether it should pass through a given filter or not, and maybe that

確切地告訴我們，它是否應該通過一個特定的過濾器，也許這

variable is just too subtle for us to probe without deeper theories and better measuring

如果沒有更深入的理論和更好的測量，我們就無法探究這個變量。

devices.

設備。

Or maybe it's somehow fundamentally unknowable, but still there.

或者，也許它在某種程度上是根本不可知的，但仍然存在。

Henry:  The possibility of such a hidden variable seems beyond the scope of experiment.

亨利：這種隱藏變量的可能性似乎超出了實驗的範圍。

I mean, what measurements could possibly probe at a deeper explanation that might or

我的意思是，有什麼測量方法可以探測到更深層次的解釋，可能或

might not exist?

可能不存在？

And yet, we can do just that.

然而，我們可以做到這一點。

Grant:...With sunglasses and polarization of light.

格蘭特：......用太陽鏡和偏振光。

Grant: Let's lay down some numbers here.

格蘭特。讓我們在這裡列出一些數字。

When light passes through a polarizing filter oriented vertically, then comes to another

當光線通過一個垂直方向的偏振濾光片，然後來到另一個

polarizing filter oriented the same way, experiments show that it's essentially guaranteed to

偏振濾光片的方向相同，實驗表明，它基本上可以保證

make it through the second filter.

使其通過第二個過濾器。

If that second filter is tilted 90 degrees from the first, then each photon has a 0%

如果第二個過濾器與第一個過濾器傾斜90度，那麼每個光子有0%的

chance of passing through.

通過的機會。

And at 45 degrees, there's a 50/50 chance.

而在45度，有50/50的機會。

Henry: What's more, these probabilities seem to only depend on the angle between the

亨利：更重要的是，這些概率似乎只取決於與 "我 "之間的角度。

two filters in question, and nothing else that happened to the photon before, including

這兩個濾波器，而之前發生在光子身上的其他事情，包括

potentially having passed through a different filter.

可能是通過了不同的過濾器。

Grant: But the real numerical weirdness happens with filters oriented less than 45° apart.

格蘭特。但真正的數字怪異現象發生在濾光片的方向相距小於45°的情況下。

For example, at 22.5 degrees, any photon which passes through the first filter has an 85%

例如，在22.5度時，任何通過第一個過濾器的光子都有85%的

chance of passing through the second filter.

有機會通過第二個過濾器。

To see where all these numbers come from, by the way, check out the second video.

順便看看所有這些數字是怎麼來的，請看第二個視頻。

Henry: What's strange about that last number is that you might expect it to be more like

亨利：最後一個數字的奇怪之處在於，你可能期望它更像是

halfway between 50% and 100% since 22.5° is halfway between 0° and 45° – but it's

由於22.5°是0°和45°之間的一半，所以它是50%和100%之間的一半。

significantly higher.

顯著提高。

Henry: To see concretely how strange this is, let's look at a particular arrangement

亨利：為了具體瞭解這一點有多奇怪，讓我們看看一個特殊的安排

of our three filters:  A, oriented vertically, B, oriented 22.5 degrees from vertical, and

我們的三個過濾器。 A，垂直方向，B，與垂直方向成22.5度，和

C, oriented 45 degrees from vertical.

C，方向與垂直方向成45度。

We're going to compare just how many photons get blocked when B isn't there with how

我們要比較的是，當B不存在時，有多少光子被阻擋，有多少光子被阻擋。

many get blocked when B is there.

當B在那裡時，許多人被阻擋。

When B is not there, half of those passing through A get blocked at C.  That is, filter

當B不存在時，一半通過A的人在C處被阻擋。

C makes the lamp look half as bright as it would with just filter A.

C使燈看起來比只用濾鏡A時的亮度低一半。

Henry: But once you insert B, like we said, 85% of those passing through A pass through

亨利：但是一旦你插入B，就像我們說的那樣，85%的通過A的人要通過

B, which means 15% are blocked at B.  And 15% of those that pass through B are blocked

B，這意味著15%的人在B處被阻擋，而通過B的人中有15%被阻擋了

at C. But how on earth does blocking 15% twice add up to the 50% blocked if B isn't there?

但是，如果B不在那裡，兩次封鎖的15%究竟是如何增加到封鎖的50%的？

Well, it doesn't, which is why the lamp looks brighter when you insert filter B, but

嗯，不是的，這就是為什麼當你插入過濾器B時，燈看起來更亮，但

it really makes you wonder how the universe is deciding which photons to let through and

這真的讓你想知道宇宙是如何決定讓哪些光子通過和

which ones to block.

哪些是要阻止的。

Grant: In fact, these numbers suggest that it's impossible for there to be some hidden

格蘭特。事實上，這些數字表明，不可能存在一些隱藏的

variable determining each photon's state with respect to each filter.

變量確定每個光子相對於每個過濾器的狀態。

That is, if each one has some definite answers to the three questions “Would it pass through

也就是說，如果每個人都對 "會不會通過 "這三個問題有一些明確的答案

A”, “Would it pass through B” and “Would it pass through C”, even before those measurements

A"、"會不會通過B "和 "會不會通過C"，即使在這些測量之前

are made.

做出。

Grant: We'll do a proof by contradiction, where we imagine 100 photons who do have some

格蘭特。我們將做一個矛盾證明，我們想象100個光子，他們確實有一些

hidden variable which, through whatever crazy underlying mechanism you might imagine, determines

隱性變量，通過你可能想象的任何瘋狂的基本機制，決定了

their answers to these questions.

他們對這些問題的回答。

And let's say all of these will definitely pass through A, which I'll show by putting

讓我們假設所有這些都將肯定通過A，我將通過把

all 100 inside this circle representing photons that pass through A.

這個圓圈內的所有100個代表通過A的光子。

Grant: To produce the results we see in experiments, about 85 of these photons would have to have

格蘭特。為了產生我們在實驗中看到的結果，這些光子中約有85個必須有

a hidden variable determining that they pass through B, so let's put 85 of these guys

一個決定他們通過B的隱藏變量，所以讓我們把這些人中的85人

in the intersection of A and B, leaving 15 in this crescent moon section representing

在A和B的交匯處，在這個新月部分留下15個代表

photons that pass A but not B. Similarly, among those 85 that would pass through B,

同樣地，在那些會通過B的85個光子中，有多少個會通過A，而不是B。

about 15% would get blocked by C, which is represented in this little section inside

大約15%會被C擋住，這在這個小部分中體現出來。

the A and B circles, but outside the C circle.

在A和B圈內，但在C圈外。

So the actual number whose hidden variable has them passing through both A and B but

是以，實際的數字，其隱藏變量有他們通過A和B，但

not C is certainly no more than 15.

不是C肯定不超過15。

Grant: But think of what Henry was just saying, what was weird was that when you remove filter

格蘭特。但想想亨利剛才說的，奇怪的是，當你去掉過濾器時

B, never asking the photons what they think about 22.5 degree angles, the number that

B，從不問光子對22.5度角的看法，這個數字是

get blocked at C seems much too high.

被擋在C位似乎太高了。

So look back at our Venn diagram, what does it mean if a photon has some hidden variable

所以回頭看看我們的維恩圖，如果一個光子有一些隱藏的變量，這意味著什麼？

determining that it passes A but is blocked at C?

確定它通過A但在C處被阻擋？

It means it's somewhere in this crescent moon region inside circle A and outside circle

這意味著它是在這個月牙區域的某處，在圓圈A內，在圓圈外

C.

C.

Grant: Now, experiments show that a full 50 of these 100 photons that pass through A should

格蘭特。現在，實驗表明，這100個通過A的光子中，有整整50個應該是

get blocked at C, but if we take into account how these photons would behave with B there,

在C處被阻擋，但如果我們考慮到這些光子在B處會有什麼表現。

that seems impossible.

這似乎是不可能的。

Either those photons would have passed through B, meaning they're somewhere in this region

要麼這些光子已經通過了B，意味著它們在這個區域的某個地方

we talked about of passing both A and B but getting blocked at C, which includes fewer

我們談到的A和B都通過了，但在C處受阻，其中包括較少的

than 15 photons.

超過15個光子。

Or they would have been blocked by B, which puts them in a subset of this other crescent

或者他們會被B所阻擋，這使他們處於這個其他新月形的子集之中

moon region representing those passing A and getting blocked at B, which has 15 photons.

月亮區域代表那些通過A並在B處被阻擋的光子，它有15個光子。

So the number passing A and getting blocked at C should be strictly smaller than 15 +

是以，通過A並在C處受阻的數量應該嚴格小於15+。

15...but at the same time it's supposed to be 50?

15...但同時又應該是50？

How does that work?

這怎麼能行呢？

Grant: Remember, that number 50 is coming from the case where the photon is never measured

格蘭特。記住，這個數字50來自於光子從未被測量的情況。

at B, and all we're doing is asking what would have happened if it was measured at

而我們所做的是問，如果在B處測量，會發生什麼？

B, assuming that it has some definite state even when we don't make the measurement,

B，假設即使我們不進行測量，它也有一些確定的狀態。

and that gives this numerical contradiction.

而這就給出了這個數字上的矛盾。

Grant: For comparison, think of any other, non-quantum questions you might ask.

格蘭特。作為比較，想想你可能會問的任何其他非量子問題。

Like, take a hundred people, and ask them if they like minutephysics, if they have a

比如，找一百個人，問他們是否喜歡微小的物理學，是否有

beard, and if they wear glasses.

鬍子，以及他們是否戴眼鏡。

Well, obviously everyone likes minutephysics.

嗯，顯然每個人都喜歡分鐘物理學。

Then among those, take the number that don't have beards, plus the number who do have a

然後在這些人中，取沒有鬍子的人數，加上有鬍子的人數。

beard but not glasses.

有鬍子但不戴眼鏡。

That should greater than or equal to the number who don't have glasses.

這應該大於或等於不戴眼鏡的人數。

I mean, one is a superset of the other.

我的意思是，一個是另一個的超集。

But as absurdly reasonable as that is, some questions about quantum states seem to violate

但是，儘管這很荒謬地合理，但一些關於量子態的問題似乎違反了

this inequality, which contradicts the premise that these questions could have definite answers,

這種不平等，這與這些問題可能有明確答案的前提相矛盾。

right?

對嗎？

Henry:  Well...Unfortunately, there's a hole in that argument.

亨利：嗯......不幸的是，這種說法有一個漏洞。

Drawing those Venn diagrams assumes that the answer to each question is static and

繪製這些維恩圖時，假定每個問題的答案都是靜態的，並且

unchanging.

不變的。

But what if the act of passing through one filter changes how the photon will later interact

但是，如果通過一個過濾器的行為改變了光子以後的互動方式呢？

with other filters?

與其他過濾器？

Then you could easily explain the results of the experiment, so we haven't proved

那麼你可以很容易地解釋實驗的結果，所以我們還沒有證明

hidden variable theories are impossible; just that any hidden variable theory would have

隱性變量理論是不可能的；只是任何隱性變量理論都會有

to have the interaction of the particle with one filter affect the interaction of the particle

讓粒子與一個過濾器的相互作用影響粒子的相互作用

with other filters.

與其他過濾器。

Henry:  We can, however, rig up an experiment where the interactions cannot affect each

然而，我們可以建立一個實驗，在這個實驗中，相互作用不能影響彼此。

other without faster than light communication, but where the same impossible numerical weirdness

在沒有比光速更快的通信的情況下，另一個人也可以在這裡進行通信，但同樣不可能的數字怪異現象

persists.

持續存在。

The key is to make photons pass not through filters at different points in time, but at

關鍵是要使光子不是在不同的時間點通過過濾器，而是在

different points in space at the same time.

在同一時間，空間的不同點。

And for this, you need entanglement.

而為此，你需要糾纏。

Henry: For this video, what we'll mean when we say two photons are "entangled" is that

亨利。在這段視頻中，當我們說兩個光子被 "糾纏 "時，我們的意思是

if you were to pass each one of them through filters oriented the same way, either both

如果你以同樣的方式將它們每個都通過過濾器，那麼，要麼都是

pass through, or both get blocked.

通過，或者兩者都被擋住了。

That is, they behave the same way when measured along the same axis.

也就是說，沿同一軸線測量時，它們的行為是相同的。

And this correlated behavior persists no matter how far away the photons and filters are from

而且這種相關的行為持續存在，無論光子和過濾器離我們有多遠

each other, even if there's no way for one photon to influence the other.

互相影響，即使一個光子沒有辦法影響另一個光子。

Unless, somehow, it did so faster than the speed of light.

除非，以某種方式，它的速度超過了光速。

But that would be crazy.

但那會很瘋狂。

Grant:  So now here's what you do for the entangled version of our photon-filter experiment.

格蘭特。 所以現在你要做的是我們的光子過濾器實驗的糾纏版本。

Instead of sending one photon through multiple polarizing filters, you'll send entangled

與其將一個光子送過多個偏振濾鏡，不如將糾纏的

pairs of photons to two far away locations, and simultaneously at each location, randomly

將成對的光子送到兩個遙遠的地方，並同時在每個地方隨機地

choose one filter to put in the path of that photon.

選擇一個過濾器放在該光子的路徑上。

Doing this many times, you'll collect a lot of data about how often both photons in

這樣做了很多次，你會收集到很多數據，比如說，這兩個光子的頻率是多少？

an entangled pair pass through the different combinations of filters.

糾纏的一對通過不同組合的過濾器。

Henry:  But the thing is, you still see all the same numbers as before.

亨利：但問題是，你仍然看到所有和以前一樣的數字。

When you use filter A at one site and filter B at the other, among all those that pass

當你在一個站點使用過濾器A，在另一個站點使用過濾器B時，在所有通過的

through filter A, about 15% have an entangled partner that gets blocked at B.  Likewise,

同樣，在通過過濾器A時，大約15%的人有一個糾纏的夥伴，在B處被阻斷。

if they're set to B and C, about 15% of those that do pass through B have an entangled

如果它們被設置為B和C，那麼，在通過B的人中，大約有15%的人有一個糾纏的

partner that gets blocked by C.  And with settings A and C, half of those that through

而在設置A和C的情況下，有一半的人通過了A和C。

A get blocked at C.

A在C處受阻。

Grant: Again, if you think carefully about these numbers, they seem to contradict the

格蘭特。同樣，如果你仔細思考這些數字，它們似乎與之相矛盾。

idea that there can be some hidden variable determining the photon's states.

認為可以有一些隱藏的變量決定光子的狀態。

Here, draw the same Venn Diagram as before, which assumes that each photon actually does

在此，請畫出與之前相同的維恩圖，其中假設每個光子實際上是

have some definite answers to the questions “Would it pass through A”, “Would it

對 "它是否會通過A"、"它是否會通過B"、"它是否會通過C "等問題有一些明確的答案。

pass through B” and “Would it pass through C”.

通過B "和 "會不會通過C"。

Grant: If, as Henry said, 15% of those that pass through A get blocked at B, we should

格蘭特。如果像亨利說的那樣，通過A的人中有15%在B處被阻擋，那麼我們應該

nudge these circles a bit so that only 15% of the area of circle A is outside circle

把這些圓推一下，使圓A的面積只有15%在圓外。

B.  Likewise, based on the data from entangled pairs measured at B and C, only 15% of the

B. 同樣地，根據在B和C測得的糾纏對的數據，只有15%的

photons which pass through B would get blocked at C, so this region here inside B and outside

通過B的光子會在C處被阻擋，所以B內和B外的這個區域

C needs to be sufficiently small.

C需要足夠的小。

Grant: But that really limits the number of photons that would pass through A and get

格蘭特。但這確實限制了通過A並得到的光子的數量。

blocked by C.  Why?

被C擋住了，為什麼？

Well the region representing photons passing A and blocked at C is entirely contained inside

那麼代表光子通過A並在C處受阻的區域完全包含在

the previous two.

前兩個。

And yet, what quantum mechanics predicts, and what these entanglement experiments verify,

然而，量子力學的預測，以及這些糾纏實驗所驗證的。

is that a full 50% of those measured to pass through A should have an entangled partner

是指那些被測量通過A的整整50%應該有一個糾纏的夥伴

getting blocked at C.

在C處被阻擋。

Grant: If you assume that all these circles have the same size, which means any previously

格蘭特。如果你假設所有這些圓都有相同的大小，這意味著任何以前的

unmeasured photon has no preference for one of these filters over the others, there is

未測量的光子對這些過濾器中的一個沒有偏好，有

literally no way to accurately represent all three of these proportions in a diagram like

從字面上看，沒有辦法在這樣的圖表中準確地表示所有這三種比例。