【诺奖得主Wilczek科普专栏】量子物理中的时钟悖论
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。
1935年，物理学家埃尔温 · 薛定谔 (Erwin Schrödinger) 提出了一个思想实验，用于测试量子理论是否完全描述了现实。这个实验被后人称为“薛定谔的猫”，它假想了一个密封的盒子，里面有一只猫、一个装有毒气的瓶子和一个可以打碎这个瓶子的开关：当一个不稳定的原子核衰变，就会触动机关，打破瓶子、将猫毒死。
然而根据量子理论，原子核可以同时处于未衰变和衰变这两种不同的状态。只有当它被测量时，原子核的状态才会塌缩到其中一个确定状态，我们才能知道原子核有没有衰变。所以，这只可怜的猫同时处在活着和死了的状态中。它到底是死还是活，只有等到某人或某件事导致原子核的量子态塌缩之后方能确定。从这个奇怪的悖论中，薛定谔认识到量子理论有所缺失。可是恕我直言，我认为这个思想实验中奇怪的部分不在于猫，而在于不稳定原子核的行为。
为了说明这一点，让我们来看看放射性定年法。这是一种测定物体年代的神奇技术，可以为考古中的文物或地质学中的地层定年。在天体物理学中，它能够帮助确定遥远的恒星和星云的年龄。放射性定年毫无疑问是非常准确的，但其背后的原理却透着深刻的怪异之处。
很多物体都具有不稳定的原子核，它们最终会衰变成另一种同位素，并在此过程中放出能量。在相同的时间间隔内，样品中发生衰变的原子核的比例是固定的。有一半原子核发生衰变所需要的时间被称为同位素的半衰期。
放射性原子核之所以能成为理想的时钟，是因为它们具有可靠的不稳定性。我们可以通过观测大量的核衰变来精确测定一个同位素的半衰期。比如，用于测定有机物年代的放射性碳14的半衰期大约是5700年。但是我们不可能预测某一个特定的原子核何时发生衰变。事实上，单个原子核根本不能记录时间的流逝：老的核和年轻的核没有明显的差别，可以说，在原子核突然发生衰变之前，它们都是一样的年轻。然而通过监测一群这样的原子核衰变的概率，我们却可以精准测量时间。
像原子核这样简单的物体，或者中子、μ子这样更加基本的粒子，是如何“知道”它们的半衰期的？为它们记录时间的弹簧、钟摆或电池在哪里？这是个奇怪的问题！但是现代物理学给出的答案更加奇怪：这些物体就像是风暴中一触即发的炸弹，它们感受到的阵风来自充满量子涨落的空间，时不时阵风会足够强劲从而引发爆炸。在这个物理图景中，原子核基本上是简单且被动的，而充满量子场的空间却是复杂且活跃的。
在量子理论对自然的描述中，偶然性的引入并不是源于理论上的奇思妙想。正如放射性的基本事实所揭示的那样，无论我们喜欢与否，现实本身就是怪异而不确定的。通过把这些怪异纳入理性思维的范畴，量子力学便至少能够将其驯化。
In 1935, the physicist Erwin Schrödinger invented a thought-experiment to test whether quantum theory fully describes reality. Known as “Schrödinger’s Cat,” the experiment asks us to imagine a cat in a sealed box, together with a vial containing poisonous gas and a mechanism that can shatter the vial. The mechanism is triggered when an unstable atomic nucleus decays, breaking the glass and killing the cat.
According to quantum theory, however, the nucleus can be in different states, unchanged or decayed, at the same time. Only when it is observed do the possible states “collapse,” making it definite whether the nucleus has decayed or not. Thus the poor cat somehow hovers between life and death, waiting for somebody or something to collapse the nucleus’s state (and thus its own). This weird situation suggested to Schrödinger that quantum theory is missing something. With all respect to him, however, I think that the weird part of the setup isn’t the cat; it’s the behavior of the unstable nucleus.
To see why, consider radioactive dating, a marvelous technique for determining the age of objects. It is used in archaeology, to date human artifacts; in geology, to date stones and strata; and in astrophysics, to date distant stars and gas clouds. The accuracy of radioactive dating is undisputed, yet the principle behind it is deeply strange.
Many objects contain some nuclei that are unstable, meaning that they will eventually decay, changing into a different isotope and emitting energy in the process. In every equal interval of time, a fixed proportion of the unstable nuclei in a sample will decay. The amount of time it takes for half of them to decay is known as the isotope’s half-life.
What makes radioactive nuclei such ideal clocks is that they are reliably unreliable. An isotope’s half-life can be determined accurately by observing lots of decays. For instance, radioactive carbon, which is used to date organic material, has a half-life of about 5,700 years. But it’s impossible to predict when any individual nucleus will decay. In fact, an individual nucleus is a kind of anti-clock: It does not register the passage of time at all. There is no observable difference between old and young nuclei. They remain ideally young, we might say, until they suddenly and explosively die. By monitoring decays within this homogeneous population we measure time statistically, with confidence.
How do such simple things as atomic nuclei, or even more elementary particles like neutrons or muons, “know” their half-life? Where are the springs or pendulums or batteries that keep track of time for them? Strange questions! But the answer supplied by modern physics is stranger. These objects are like hair-trigger bombs in a stormy environment. Space itself, seething with quantum fluctuations, supplies passing gusts, and every so often one is strong enough to trigger an explosion. In this picture, nuclei are basically simple and passive. It is space, saturated with quantum fields, that is complex and active.
Quantum theory does not introduce chance into the description of nature as a theoretical whimsy. Reality, as revealed in the basic facts of radioactivity, simply is weird and chancy, whether we like it or not. By bringing that weirdness within the scope of rational thought, quantum theory can at least domesticate it.
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