諾獎得主Wilczek：量子物理中的時鐘悖論_風聞

撰文 | Frank Wilczek

翻譯 | 胡風、梁丁當

來源：蔻享學術

中文版

一個不穩定的原子核如何“知道”它何時會衰變？答案可能隱藏在空間結構中。

1935年，物理學家埃爾温 · 薛定諤 (Erwin Schrödinger) 提出了一個思想實驗，用於測試量子理論是否完全描述了現實。這個實驗被後人稱為“薛定諤的貓”，它假想了一個密封的盒子，裏面有一隻貓、一個裝有毒氣的瓶子和一個可以打碎這個瓶子的開關：當一個不穩定的原子核衰變，就會觸動機關，打破瓶子、將貓毒死。

然而根據量子理論，原子核可以同時處於未衰變和衰變這兩種不同的狀態。只有當它被測量時，原子核的狀態才會塌縮到其中一個確定狀態，我們才能知道原子核有沒有衰變。所以，這隻可憐的貓同時處在活着和死了的狀態中。它到底是死還是活，只有等到某人或某件事導致原子核的量子態塌縮之後方能確定。從這個奇怪的悖論中，薛定諤認識到量子理論有所缺失。可是恕我直言，我認為這個思想實驗中奇怪的部分不在於貓，而在於不穩定原子核的行為。

為了説明這一點，讓我們來看看放射性定年法。這是一種測定物體年代的神奇技術，可以為考古中的文物或地質學中的地層定年。在天體物理學中，它能夠幫助確定遙遠的恆星和星雲的年齡。放射性定年毫無疑問是非常準確的，但其背後的原理卻透着深刻的怪異之處。

很多物體都具有不穩定的原子核，它們最終會衰變成另一種同位素，並在此過程中放出能量。在相同的時間間隔內，樣品中發生衰變的原子核的比例是固定的。有一半原子核發生衰變所需要的時間被稱為同位素的半衰期。

放射性原子核之所以能成為理想的時鐘，是因為它們具有可靠的不穩定性。我們可以通過觀測大量的核衰變來精確測定一個同位素的半衰期。比如，用於測定有機物年代的放射性碳14的半衰期大約是5700年。但是我們不可能預測某一個特定的原子核何時發生衰變。事實上，單個原子核根本不能記錄時間的流逝：老的核和年輕的核沒有明顯的差別，可以説，在原子核突然發生衰變之前，它們都是一樣的年輕。然而通過監測一羣這樣的原子核衰變的概率，我們卻可以精準測量時間。

像原子核這樣簡單的物體，或者中子、μ子這樣更加基本的粒子，是如何“知道”它們的半衰期的？為它們記錄時間的彈簧、鐘擺或電池在哪裏？這是個奇怪的問題！但是現代物理學給出的答案更加奇怪：這些物體就像是風暴中一觸即發的炸彈，它們感受到的陣風來自充滿量子漲落的空間，時不時陣風會足夠強勁從而引發爆炸。在這個物理圖景中，原子核基本上是簡單且被動的，而充滿量子場的空間卻是複雜且活躍的。

在量子理論對自然的描述中，偶然性的引入並不是源於理論上的奇思妙想。正如放射性的基本事實所揭示的那樣，無論我們喜歡與否，現實本身就是怪異而不確定的。通過把這些怪異納入理性思維的範疇，量子力學便至少能夠將其馴化。

英文版

ILLUSTRATION: TOMASZ WALENTA

How does an unstable nucleus ‘know’ when it’s time to decay? The answer may lie in the fabric of space itself.

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.

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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