诺奖得主Wilczek：无知的科学价值_风闻

撰文 | Frank Wilczek

翻译 | 胡风、梁丁当

中文版

在量子物理中，只有对粒子的动量信息保持无知，才有可能获取它的位置信息。

在乔治·奥威尔（George Orwell）的小说《1984》中，有一句荒谬的标语“无知即力量”。这句标语是乔治 · 奥威尔笔下腐朽邪恶的政权的深刻缩影。如果把它巧妙地调整一下，改成“无知或为力量”，那这句新的标语就成了如今科技前沿的生动写照。如果我们能聪明地利用无知，它可以成为一种超能力，使我们的感官更敏锐（通过测量仪器），思维更开阔（通过计算机）。

这条标语看似自相矛盾，其根源却在于量子现实的本质，它从根本上对我们所了解的任意物体的特性施加了限制。如果我们掌握所有关于物体状态的理论知识，那么我们就能够准确地预测，在测量物体的位置与运动速度时，它出现在某个地点以及具有某个速度的概率。然而，根据量子理论，位置的模糊度与动量的模糊度的乘积必须大于一个极限值。这就是海森堡不确定性原理。

现在，假设我们要精确地测量某个物体的位置，以探测引力波引起的微小的时空扭曲。为了最大限度地减少位置测量的误差，同时不违反海森堡原理，我们需要尽可能地增加动量的模糊度。这种测量艺术被称为“量子压缩”，它是当前热门的前沿研究领域。

要想制造出性能优越的量子计算机，最主要的困难在于如何让它始终保持对自己的状态一无所知。经典计算机在运行过程中会经过一系列的“位置”，每个位置由一串0和1组成的字符所编码,其中的0和1代表晶体管的两种状态。与之相对的是，量子计算机的计算单元就像量子粒子一样，它可以同时处在所有这些位置上。

要想确保量子计算机能够可靠地运行，这种位置的模糊性是必要的。因为只有这样，计算机才能在动量模糊度较小的情况下准确地执行下一步程序。如果计算机无意泄露了位置分布的信息，就会降低位置的模糊度。根据不确定性原理，这必然会导致动量模糊度升高，从而破坏程序执行的可靠性。

在我刚开始思考如何利用量子世界的不确定性——某种程度上，也可以被称为“无知”——的时候，我曾经认为这是量子世界独有的奇特现象。但我逐渐认识到这是一个更为广泛的概念，它清楚地揭示了我们与周围世界沟通的许多方式其实并不简单。

比如，让我们想一想我们通常是怎样辨认出某个人的。当光子投射到视网膜上，而后经大脑处理产生的图像会受到诸多因素的影响，比如这个人的位置、朝向、她是否被其它物体遮挡、她的穿着等等。尽管如此，我们仍然能够判断出“这是贝茜”。显然，在这个过程中我们选择性地忽略了很多细节，而这样做是有益的。

还有一个问题也透露着无知的价值 ：为什么不是所有人都有完美的音准呢？在我们的内耳中，有一对小小的“反向钢琴”。它们通过拨动特定的键（实际上是特定的毛发）来对特定的音调产生响应。通过这种方式，耳朵可以收集到所有的信息，但只有极少一部分人能够完全利用它们。对于我们这些没有完美音准的人来说，或许大脑在运作时，无意识地“选择”了无知——忽视那些音调的信息，好让我们专注于更加有用的信息上。

在圣经故事中，亚当和夏娃因为吃了“分别善恶树”上的果实而受到惩罚。无论你怎样看待这个故事，它都生动地提醒我们 ：无知是一项值得留意的选择。

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.

Advertisement - Scroll to Continue

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

弗兰克·维尔切克是麻省理工学院物理学教授、量子色动力学的奠基人之一。因发现了量子色动力学的渐近自由现象，他在2004年获得了诺贝尔物理学奖。

本文经授权转载自微信公众号“蔻享学术”。

特 别 提 示

1. 进入『返朴』微信公众号底部菜单“精品专栏“，可查阅不同主题系列科普文章。

2. 『返朴』提供按月检索文章功能。关注公众号，回复四位数组成的年份+月份，如“1903”，可获取2019年3月的文章索引，以此类推。