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  • Cloning: If you want to make a copy of something, you need three things: the thing to be copied,

    克隆:如果你想做出一個東西的副本, 你需要三樣東西:要被複製的東西,

  • The raw materials that youre going to turn into the copy, and a procedure for transforming

    製作拷貝所需的原料,以及把原料變成

  • the raw materials into a semblance of the original thing.

    跟原本的東西一模一樣的方法。

  • To copy a famous painting , you need a blank canvas, a brush, and the right colored paints,

    要複製名畫,你需要一個空白 帆布,刷子,和彩色塗料,

  • and then you carefully put paint on the blank canvas to match the original as closely as

    然後小心翼翼地在帆布上作畫, 盡可能畫得與原來的畫一模一樣,

  • you can and hopefully sell it for a lot of money. But your painting isn’t exactly the

    並希望把它賣掉後會拿到很多 錢。但是,你的畫並不完全

  • same as the originalthe red is a little too bright, that stroke is a little too heavy,

    和原來的一樣-紅色有點 太亮,那一劃有點太重,

  • there are a few too many atoms of carbon 14 in the new canvas, and so onit’s a

    新的畫布還稍微多了點碳14,等等-這是一個

  • copy, but not a perfect one. Is a perfect copy, identical even at the subatomic

    拷貝,但不完美。 一個完美的副本,甚至連在次原子的水準上

  • level, even possible? Like, can you make a copy of my brain down to the neuron and beyond,

    也一樣,有可能嗎?就像, 你能複製我的大腦到神經元和更小的層次,

  • so that even the position, momentum, and spin of every single sodium ion moving between

    以至於就連每個在神經元之間 移動的鈉離子的位置、動量和自旋

  • neurons is exactly, indistinguishably, the same as in the original? Physicists call this

    都是完全、不可區別地 與原本完全一樣?物理學家把

  • kind of perfect copyingcloning”, even though it definitely isn’t the same thing

    這種完美複製叫做"克隆", 它與生物學中的克隆是完全不一樣的東西

  • as cloning in biology where two organisms share the same DNA but how they grow and develop

    生物學裡的克隆,指的是兩個生物 共享相同的DNA,但他們是如何發育成長的

  • can be very differentcloning in physics means a much perfecter copy, where the relative

    可以有很大的差異-物理學裡的"克隆" 指的是更完美得多的副本,其中每個粒子

  • positions and momenta and energy levels of every particle and all of their bonds and

    的相對位置、動量、能量和它們所有的鍵結,以及

  • interactions are exactly the same in the copy as the original, such that if you turned your

    交互作用在複製品中與原本一模一樣, 如果你轉過頭

  • back and randomly switched them, there literally would be no way of telling which was the original

    並隨機地把他們交換, 就沒有辦法告訴這是原來的

  • and which was the copy. Unfortunately, the universe is a party pooper,

    而這是副本。 不幸的是,宇宙是一個掃興的傢伙,

  • and perfect cloning is impossible. I don’t simply mean that we don’t know how, or that

    完善的克隆是不可能的。我不只是 指我們不知道怎麼做,或者

  • we haven’t succeeded yet because it’s really hard to do in practice; no, I mean

    我們還沒有成功,因為它 很難實踐;不,我的意思是

  • that it has been mathematically proven that perfect cloning can’t be achieved even in

    它已經在數學上被證明 完美克隆在根本上就是無法實現的。

  • principle. Here, now, is that proof, using as little

    現在,我會在這裡證明,並盡量使用越少

  • math as possible. Everything in the universe is made up of elementary

    數學越好。 宇宙中的一切是由基本的

  • quantum particles and the forces by which they interact , so for the no-cloning proof

    量子粒子以及它們的交互作用 所組成,因此對於不可克隆原理的證明

  • we need to know what it means to clone a quantum particle, so first were going to need to

    我們要知道什麼叫做複製量子 粒子,所以首先我們需要

  • know three important and fundamental properties shared by all quantum particles.

    知道所有的量子粒子都有的 三個重要、基本的屬性。

  • Ok, quantum property number one: particles can be in several states at onceLike Schrödinger’s

    好吧,量子特性一:粒子 可以同時在好幾個狀態。就像掩體裡

  • cat, stuck in a bunker with unstable gunpowder that has a 42% chance of exploding in any

    薛丁格的貓和不穩定的 任何一分鐘都有42%的機會會爆炸的火藥

  • minute, but maybe it hasn’t yet, so that the gunpowder is in a superposition ofgunpowder

    ,但它也許還沒有爆炸,所以火藥是"火藥

  • has already explodedandgunpowder hasn’t exploded yet” . Or like a photon going through

    已經爆炸"和"火藥還沒有 爆炸"的疊加態。或像光子同時經過

  • two slits at once to interfere with itself and make a nice pattern on the wall . Or an

    兩個狹縫、與自身干涉 並在牆壁上留下一個很棒的圖案。或

  • electron in an atomic orbital, its wavefunction occupying many points in space all at once.

    在原子軌域上的電子,它的波函數 一次佔據了空間中的多個點。

  • In summary: in quantum mechanics, the whole is equal to the sum (that is, superposition)

    總而言之:在量子力學中,全部 等於他的所有不同可能狀態的

  • of its different possible parts . Alright, property number two: multiple particles,

    總和(即,疊加)。 好吧,特性二:把多個粒子,

  • when viewed together as one singleobject” (like an atom, or entangled pair of photons,

    作為一個單一的"對象"來考慮的時候 (如一個原子或糾纏的光子對,

  • or the gunpowder together with Schrödinger’s cat, or whatever), are the product of their

    或者火藥和薛丁格的貓, 或隨便甚麼東西),是它的組成的

  • components, or, since it’s quantum mechanics, a superposition of products of their components,

    乘積,或者,因為它是量子力學, 它的組成的乘積的疊加態,

  • so the situation inside Schrödinger’s box could be described as a superposition of the

    所以薛丁格的盒子裡面的情況,可以被描述為

  • product ofgunpowder has already explodedandthe cat is deadand the product

    "'火藥已經爆炸'和'貓死了'的乘積"和

  • ofgunpowder hasn’t explodedandthe cat is alive” . In summary: composite quantum

    "'火藥尚未爆炸'和'貓是活的'的乘積" 的疊加態。總之:放一起考慮的量子

  • objects are multiplied together . And finally, quantum property number three:

    物體被乘在一起。 最後,量子特性三:

  • any change to a particle that’s in a superposition of states affects all of the states independently

    任何對處在疊加態中的粒子的改變 會獨立地影響所有狀態。

  • . Kind of like how if you go two miles to the right and one mile up and then rotate

    有點像是,如果你往右兩英里 再往上一英里,然後把地圖

  • your map ninety degrees , that’s the same as first spinning each arrow individually

    旋轉九十度,跟各旋轉這些箭頭

  • 90° and then adding them together. Or if you have an electron in a superposition of

    九十度再加在一起一樣。或者如果 你有個在往右移的電子

  • hereandtherethat’s moving to the right, that means thatelectron

    在“這裡”和“那裡”的疊加態,這意味著“下一秒鐘

  • in one secondwill be in a superposition ofwhereverhereis in one second

    的電子“將在 “'這裡'下一秒鐘的位置”

  • andwhereverthereis in one second”. In summary: when you have a superposition,

    和“'那裡'下一秒鐘的位置”的疊加態。 總結:當你有一個疊加態,

  • aka, a sum of several parts , any change or transformation of the sum of the parts is

    也就是好幾部分的總和,任何對總和的改變或變換就

  • equal to the sum of the transformations of the parts , whether that transformation is

    等於對個別部分的變換的總和,不論轉換是

  • a rotation, a movement, or even an entire hypothetical cloning process.

    旋轉,移動,或甚至是整個假想中的克隆過程。

  • So let’s recap, for the no-cloning proof, well use three of the properties that all

    讓我們回顧一下,對於不可克隆的證明, 我們將使用宇宙裡所有基本粒子

  • fundamental particles in the universe obey: individual particles can be in superpositions,

    都遵從的三個特性: 個別粒子可以在疊加態,

  • which looks like adding; groups or combinations of particles are products of their components

    這看起來像加法;一群粒子是其組成的乘積

  • (or sums of products of their components), which looks like multiplying; and any transformation

    (或者其乘積的總和), 這看起來像乘法;任何對一個粒子

  • of a particle or group of particles is the same as the sum of the transformation applied

    或一群粒子的變換,跟對部分做變換後的總和

  • to the parts, which looks like distributing. Ok, now we can get into the meat of the proof!

    一樣,這看起來就像分配律。 好了,現在我們終於可以進入證明的核心部分!

  • So in terms of the properties we just outlined, let’s talk about what it would mean to have

    所以就我們剛才列出的性質, 讓我們來談談這對於量子克隆機而言

  • a quantum cloning machine. We’d need the thing to be cloned , the materials to make

    有甚麼意義。我們需要 被克隆的東西,用來做出克隆的

  • a clone out of, and a procedure to transform the materials into an exact copy of the original

    原料,和一個能把原料變成跟原本 模板完全一樣的副本的過程。

  • . Our machine shouldn’t have to know in advance what the thing to be cloned is, otherwise

    我們的機器不應該知道 要被克隆的東西是甚麼,否則

  • it’s not really a machine for cloning things as much as a machine for building a known

    這就不是真的克隆機器, 而只是一台用來製造已知的東西

  • thing . So, if a cloning procedure were to exist, we should be able toapply cloning

    的機器。所以,如果克隆過程能 存在,我們應該能“克隆”

  • to any specimen we want , and end up with two copies of the specimen.

    任何我們想要的目標,並在結束 的時候產生兩個副本。

  • The problem occurs, however, if the specimen were cloning is a superposition, like if

    但,問題出現在,我們想要克隆 的那目標是一個疊加態的時候,就像如果

  • it’s the gunpowder from inside Schrödinger’s cat’s box, in a superposition ofexploded

    它是薛丁格的貓的箱子裡的火藥,在“爆炸”與

  • andnot exploded”. If we apply our hypothetical cloning to the whole gunpowder-inside-the-box-superposition,

    “還沒爆炸”的疊加態。如果我們將我們的假想 克隆過程套用在整個疊加態的火藥上,

  • we getexplodedplusnot explodedtimesexplodedplusnot exploded”.

    我們得到“爆炸”加“還沒爆炸”,乘“爆炸”加“還沒爆炸”。

  • But since, in quantum mechanics, a procedure applied to the whole gets distributed through

    但是,因為在量子力學中,一個被施加在整體 的過程可以通過分配律

  • as the sum of the procedure applied to the parts, that means that we should get the same

    等同於被施加到過程的部分的總和, 這意味著我們這麼做也應該得到相同的結果:

  • result by applying cloning to each part of the superposition , separately cloningexploded

    施加克隆到的每個疊加態的部分, 分別是克隆“爆炸”

  • andnot explodedand then adding them together. But, we don’t get the same thing,

    和“還沒爆炸”,然後再把他們加在 一起。但是,我們沒有得到同樣的東西,

  • since exploded times exploded plus not exploded times not exploded is not the same as exploded

    爆炸乘爆炸加沒爆炸乘沒爆炸,不會等於爆炸

  • times exploded plus exploded times not exploded plus not exploded times exploded plus not

    乘爆炸加爆炸乘沒爆炸、再加上沒爆炸乘爆炸加

  • exploded times not exploded. There are these extra terms here that don’t match up.

    沒爆炸乘沒爆炸。這裡有些多出來的項不相配。

  • Basically, if both quantum mechanics and cloning are true, then A plus B, squared must be the

    基本上,如果量子力學和克隆 都是真的,那麼A加B的平方必須跟

  • same as A squared plus B squared. But A plus B, squared, is not the same as A squared plus

    A的平方加B的平方一樣。但A加B, 再平方,不等於A平方加

  • B squared. And this contradiction means that either quantum mechanics is wrong (which would

    B平方。而這一矛盾意味著,量子力學是錯誤的(這將

  • fly in the face of the most precise and accurate experimental tests in all of science ), or

    與科學史上最精確和準確 的所有實驗站在對立面),或者

  • that a cloning procedure can’t exist. Spoiler alert: it ain’t looking so good for cloning.

    克隆過程不可能存在。劇透 提醒:這看來對克隆並不怎麼好。

  • This, by the way, is an example of what’s calledproof by contradiction”, a logically

    順便說,這就是一個所謂“反證法”的例子,在邏輯上

  • sound (but not always pretty) kind of proof where you suppose that the opposite of what

    穩固(但並不總是漂亮)的一種證明 在這裡你假設跟你想證明的目標

  • youre trying to prove is true, is true, and show that such an assumption leads to

    的相反是真的,並且證明,這樣的假設會導致

  • a contradiction or other logical problems, so it can’t be true, and thus what you actually

    矛盾或其他邏輯問題, 所以這不可能是真的,這樣你真的

  • are trying to prove must be true instead. Like, to prove there’s no biggest even number,

    想要證明的就一定是真的。 像是要證明沒有最大的偶數,

  • we’d first suppose there IS a biggest even number, call it E, which since it’s even

    我們會先假設有一個最大的偶數, 稱之\為E,因為它是偶數

  • it’s equal to two times some other number. But then if we add 1 to that other number

    它等於某個數字的兩倍。 不過,如果我們加1到那個數字上

  • and multiply by 2, we get an even number (since it has 2 as a factor), but this new number

    再乘以2,我們得到一個偶數(因為 它有個2作為因數),但這個新的數

  • is bigger than E, which was supposed to be the biggest even number. This is a contradiction,

    比E(最大的偶數)還要更大。這是個矛盾,

  • so our supposition that there is a biggest even number can’t be rightso there is

    因此我們有一個最大的偶數 的假設不可能是正確的......所以

  • no biggest even number. Ok, but back to cloning.

    沒有最大的偶數。好了,回到克隆。 我還想指出我們對不可克隆

  • So to summarize the proof of no cloning theorem, we first suppose the cloning IS possible,

    的證明並沒有檢驗任何特定的設備 或任何克隆要怎麼做的設計-它

  • then show that such cloning would logically results in the contradiction that

    只是使用我們知道任何形式的克隆 設備都一定有的性質。像是,它會

  • a cloned whole would not be the same as the sum of its parts, and hence perfect cloning

    存在於我們的物理世界,並且要能夠複製東西。

  • is not possible. I also want to point out that the proof of

    這個證明證明了任何同時擁有 這兩個性質的東西不能存在。

  • no cloning didn’t examine any specific apparatus or design for how cloning might be done – it

    要總結不可克隆定理的證明 ,我們先假設克隆是可能的,

  • just uses properties that we know any cloning apparatus would have to have. Like, it would

    然後再說明克隆邏輯上會導致矛盾。

  • have to exist in our physical universe, and it would have to be able to clone things.

    整體的克隆並不會和部分的克隆的總和 一樣,因此完美克隆

  • The proof proves that anything with both of these properties can’t exist.

    是不可能的。抱歉!

  • However, for those wanting to live in a sci-fi future, all is not lost. Even if perfect cloning

    然而,對於那些希望生活在一個科幻 未來的人們,並沒有失去一切。即使完美克隆

  • isn’t possible, “pretty decent copiescloning is. Like, it’s possible to clone

    是不可能的,“相當不錯的克隆” 是可能的。就像,要克隆一個量子位元

  • a qubit with an average of 83% fidelity . And even more exciting: the no-cloning theorem

    並達到平均83%的保真度是有可能的。 更令人振奮的是:不可克隆原理

  • is only about cloning; teleportation is still possible.

    只針對克隆;瞬間移動仍然有可能。

  • That’s because teleportation consists of a subject, materials to make the teleported

    這是因為瞬間移動包含 被傳送者,以及用來製作被傳送者

  • version out of, and a procedure to turn the teleported materials into the subject, leaving

    的原料,還有一個用來把原料做成被傳送者,留下

  • behind an empty machine. And a quick calculation shows that teleporting a superposition, or

    一台空機器的過程。簡單計算 就可以發現傳送疊加態,或

  • sum, is indeed equal to the superposition, or sum, of the individually teleported parts!

    總和,確實等於個別被傳送的部份的總和!

  • What’s more, “no cloningdoesn’t mean you can’t have two or more copies of

    更重要的是,“不可克隆” 不代表你不能在這個宇宙裡有兩個

  • the same thing in the universe, it just means it’s not possible to take an existing thing

    或更多一樣的東西,它只代表 不可能把現有的、你還不知道

  • that you don’t already know all the details about and make a perfect copy of it while

    關於它的所有細節的東西,做出完美的副本

  • leaving the original intact. You can build a machine to make multiple versions of things

    並保持原版不變。你可以製造 一台能夠生產許多複製品的機器-

  • as long as you know in advance exactly what it is youre making. So, is it possible

    只要你事先知道所有細節。那麼,有沒有可能

  • to learn every single detail about something? Well, the Heisenberg uncertainty principle

    了解一樣東西的每一個細節? 嗯,海森堡測不準原理

  • means that you can’t simultaneously measure all the relevant details of any one object,

    告訴我們你不能同時測量 任一個樣本的所有細節,

  • but if you have a number of objects that you know are the same, you can measure each of

    但如果你有許多你知道 都是一樣的樣本,你可以分別用不同的方法

  • them in a different way to get the full picture. So the irony is that in quantum mechanics,

    測量他們來獲取全貌。 所以,在量子力學中諷刺的是,

  • you can’t perfectly clone a thing you have only one of, but if you already have a lot

    你不能完美複製你只有一個的東西, 但如果你已經有很多個,

  • of copies of something , you can make more copies.

    那麼你可以製造更多的副本。

  • However, as far as we know, there’s only one of each of us in the universe, sono

    然而,據我們所知,在宇宙中, 我們每個人都是獨一無二的,所以量子力學中的

  • 100% perfect cloningin quantum mechanics meansno 100% perfect cloningin humans,

    "不可100%完美複製"也就代表 著“不可100%完美複製”人類。

  • either . While we may eventually be able to grow a child that’s genetically identical

    雖然我們最終可能可以 養育一個和你基因完全一樣的

  • to you, we likely won’t ever be able to make a perfect clone of you that has all of

    孩子,我們卻永遠不能夠製造一個 你的完美的克隆人,具有所有的

  • your memories, thoughts, and loves. How close we can get, of course, depends on whether

    你的記憶,想法和愛。我們能多麼 接近這個目標,理所當然取決於

  • or not consciousness relies on quantum processes in the brain. But that’s a question for

    意識是否仰賴於大腦中的 量子過程。但這個問題必須留給

  • another day.

    另一天了。

Cloning: If you want to make a copy of something, you need three things: the thing to be copied,

克隆:如果你想做出一個東西的副本, 你需要三樣東西:要被複製的東西,

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B2 中高級 中文 爆炸 量子 粒子 火藥 證明 複製

不可克隆定理 (The No Cloning Theorem)

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    林宜悉 發佈於 2021 年 01 月 14 日
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