諾獎得主Wilczek：無知的科學價值_風聞

撰文 | Frank Wilczek

翻譯 | 胡風、梁丁當

中文版

在量子物理中，只有對粒子的動量信息保持無知，才有可能獲取它的位置信息。

在喬治·奧威爾（George Orwell）的小説《1984》中，有一句荒謬的標語“無知即力量”。這句標語是喬治 · 奧威爾筆下腐朽邪惡的政權的深刻縮影。如果把它巧妙地調整一下，改成“無知或為力量”，那這句新的標語就成了如今科技前沿的生動寫照。如果我們能聰明地利用無知，它可以成為一種超能力，使我們的感官更敏鋭（通過測量儀器），思維更開闊（通過計算機）。

這條標語看似自相矛盾，其根源卻在於量子現實的本質，它從根本上對我們所瞭解的任意物體的特性施加了限制。如果我們掌握所有關於物體狀態的理論知識，那麼我們就能夠準確地預測，在測量物體的位置與運動速度時，它出現在某個地點以及具有某個速度的概率。然而，根據量子理論，位置的模糊度與動量的模糊度的乘積必須大於一個極限值。這就是海森堡不確定性原理。

現在，假設我們要精確地測量某個物體的位置，以探測引力波引起的微小的時空扭曲。為了最大限度地減少位置測量的誤差，同時不違反海森堡原理，我們需要儘可能地增加動量的模糊度。這種測量藝術被稱為“量子壓縮”，它是當前熱門的前沿研究領域。

要想製造出性能優越的量子計算機，最主要的困難在於如何讓它始終保持對自己的狀態一無所知。經典計算機在運行過程中會經過一系列的“位置”，每個位置由一串0和1組成的字符所編碼,其中的0和1代表晶體管的兩種狀態。與之相對的是，量子計算機的計算單元就像量子粒子一樣，它可以同時處在所有這些位置上。

要想確保量子計算機能夠可靠地運行，這種位置的模糊性是必要的。因為只有這樣，計算機才能在動量模糊度較小的情況下準確地執行下一步程序。如果計算機無意泄露了位置分佈的信息，就會降低位置的模糊度。根據不確定性原理，這必然會導致動量模糊度升高，從而破壞程序執行的可靠性。

在我剛開始思考如何利用量子世界的不確定性——某種程度上，也可以被稱為“無知”——的時候，我曾經認為這是量子世界獨有的奇特現象。但我逐漸認識到這是一個更為廣泛的概念，它清楚地揭示了我們與周圍世界溝通的許多方式其實並不簡單。

比如，讓我們想一想我們通常是怎樣辨認出某個人的。當光子投射到視網膜上，而後經大腦處理產生的圖像會受到諸多因素的影響，比如這個人的位置、朝向、她是否被其它物體遮擋、她的穿着等等。儘管如此，我們仍然能夠判斷出“這是貝茜”。顯然，在這個過程中我們選擇性地忽略了很多細節，而這樣做是有益的。

還有一個問題也透露着無知的價值 ：為什麼不是所有人都有完美的音準呢？在我們的內耳中，有一對小小的“反向鋼琴”。它們通過撥動特定的鍵（實際上是特定的毛髮）來對特定的音調產生響應。通過這種方式，耳朵可以收集到所有的信息，但只有極少一部分人能夠完全利用它們。對於我們這些沒有完美音準的人來説，或許大腦在運作時，無意識地“選擇”了無知——忽視那些音調的信息，好讓我們專注於更加有用的信息上。

在聖經故事中，亞當和夏娃因為吃了“分別善惡樹”上的果實而受到懲罰。無論你怎樣看待這個故事，它都生動地提醒我們 ：無知是一項值得留意的選擇。

英文版

The Scientific Value of Ignorance

In quantum physics, maximizing knowledge of a particle’s location requires fuzziness about its momentum, and vice versa.

In George Orwell’s novel “1984,” “Ignorance is Strength” is a shocking slogan that epitomizes a corrupt and sinister regime. But in a more nuanced form, “Ignorance can be Strength,” it is an apt slogan for some cutting-edge science. Used wisely, ignorance can be a superpower that makes our senses more acute and our minds more capacious (through measuring devices and computers, respectively).

This seeming paradox is rooted in the nature of quantum reality, which imposes a fundamental limitation on our knowledge of the properties of any object. Given perfect theoretical knowledge of an object’s state, we can predict probabilities for where it will be found and how fast it will be seen to move, if we measure those things. But according to quantum theory, when we multiply the fuzziness in predicted position by the fuzziness in predicted momentum, the product cannot get below a definite limit. That is Heisenberg’s uncertainty principle.

Now suppose that we’d like to measure the position of a test body very precisely, so that we can detect the tiny distortions of space caused by gravitational waves. To minimize the fuzziness in its position, while remaining in Heisenberg’s good graces, we need to crank up the fuzziness in its momentum. The art of doing this is called “squeezing,” and it is a hot frontier of research.

The main difficulty in making good quantum computers is keeping nature ignorant about what they’re doing. A classical computer runs through a sequence of definite “positions,” each consisting of a series of 0s and 1s that represent the states of its transistors. A quantum computer, like a quantum particle, allows all these positions to coexist.

Fuzziness in position is necessary so that the computer can move reliably, with small fuzziness in “momentum,” to execute the next step in its program. If the computer inadvertently betrays information about its distribution of positions, it will reduce that distribution’s fuzziness and necessarily inject fuzziness into the corresponding momentum, thus making the program’s execution unreliable.

When I first began to think about leveraging ignorance in the quantum world, I considered it to be one of that world’s weird special features. But I’ve come to see it as a much broader idea that illuminates many things about how we deal with the everyday world.

Consider, for example, what it means to recognize someone. The underlying pattern of photons that arrives at our retina will be quite different depending on where that person is, how they’re oriented, whether they’re partially hidden behind other objects, what they’re wearing and many other factors. But in concluding “It’s Betsy,” we choose to ignore all that, and that’s obviously a useful thing to do.

Why don’t we all have perfect pitch? Within our inner ears we have little inverse pianos that move specific keys (actually, specialized hairs) in response to specific tones. The information is there, but few of us can access it. Those of us who don’t have perfect pitch may have “chosen” ignorance—unconsciously, as our brains got wired up—in order to focus on more generally useful relationships.

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Adam and Eve were punished for eating from “the tree of the knowledge of good and evil.” However you take that story, it is a vivid reminder that ignorance is an option worth keeping in mind.

Frank Wilczek

弗蘭克·維爾切克是麻省理工學院物理學教授、量子色動力學的奠基人之一。因發現了量子色動力學的漸近自由現象，他在2004年獲得了諾貝爾物理學獎。

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