物理学 1923

X 射线被轻元素散射的量子理论

阿瑟·康普顿

X 射线撞上电子后波长变长，像台球被撞慢——光以粒子的方式携带动量。

Choose your version

In depth · the introduction

把 X 射线照向一块碳，射线弹回来时「颜色」却变了——而这个小小的变化，了结了一场关于「光是波还是粒子」、持续了二十年的争论。

核心想法

一个世纪以来，光一直被理解为波，而波在反弹时不会改变颜色。可当阿瑟·康普顿用 X 射线轰击物质时，散射回来的射线却更「软」了——被拉到稍长一点的波长；而且偏折得越急，拉得越长。

他的解释，是把 X 射线不当作波，而当作粒子：一颗携带动量的小小光弹。当它撞上一个电子，便把电子撞飞，恰如一颗台球撞上另一颗，自己则带着更少的能量弹开——对光而言，这意味着更长的波长。他甚至能把公式写下来：拉长的量，只取决于反弹的角度，别无其他。实验与公式相符。原来，光，是像个实物那样撞过来的。

它是如何诞生的

早在 1905 年，爱因斯坦就提出过光是一份一份的，可在此后二十年里，大多数物理学家都把它当作一个好用的技巧，而非字面的真理——波动理论实在太成功，让人不忍割舍。康普顿在圣路易斯的华盛顿大学工作，一直在为散射 X 射线里一个波动理论解释不了的怪象而困惑。

约在 1922 年，他迈出了那一步：给每一份 X 射线的能量包一个确定的动量，并把它与电子的相遇当作一次干脆的碰撞。数字干净利落地落了出来，而他在石墨上细致的谱仪测量证实了它们。荷兰物理学家彼得·德拜，几乎在同一时刻独立地得到了同一公式。当别人很快拍到反冲电子与散射射线步调一致地飞出，此案便告了结。康普顿于 1927 年获得诺贝尔奖。

它为何重要

这就是那个让光子成真的实验。光电效应曾暗示光以一块块的形式递送能量，而康普顿则表明，光还携带动量、并在碰撞中反冲——在一切力学意义上，都像个粒子。在康普顿之后，你再也不能把光量子当作一个算起来方便的说法挥手打发掉。光，竟同时既是波又是粒子；而接受这个悖论，正是通向现代量子力学的门——仅仅两年之后，它就来了。

一个可以想象的画面

想象一局台球。母球（X 射线）滚进来，撞上一颗静止的球（电子）。母球穿不过去——它擦着弹开，被撞的那颗球带着一些速度滚走。母球离开时，比来时慢。对光来说，「慢」不太对——光永远以光速行进——所以它用另一种方式卸掉能量：把自己拉到更长的波长。而正如台球里，擦边的一碰几乎什么都不改变，正面相撞却夺走最多的速度；X 射线的拉长，在轻微偏折时最小，在径直弹回时最大。用下面的工具，瞄准这一弹，看波长怎样变长。

它在知识谱系里的位置

康普顿的这次碰撞，是光的故事里的一处合页。在它身后，站着普朗克（1900）与爱因斯坦（1905），是他们最先提出光是一份一份的，以及玻尔（1913），是他把量子放进了原子；在它身旁，站着光电效应，那是光子的另一个证据。在它身前，站着德布罗意（1924），他把康普顿的逻辑反转过来，赋予物质一个波长，还有海森堡——他 1927 年的不确定性原理，用的正是康普顿发现的那个反冲：当你想看一个电子时，光子必然给它的那一脚。康普顿的测量，正是光的粒子从一个假说，变成一个你能称量的事实的那一刻。

The original document

Original source text

Arthur H. Compton · Physical Review, Series 2, vol. 21, no. 5, pp. 483–502 · May 1923 · Washington University, St. Louis

The problem — scattered X-rays come back “softer”

On the wave theory of light, an X-ray passing through matter should set the electrons oscillating at its own frequency, and they should re-radiate at exactly that frequency: the scattered ray ought to have the same wavelength as the incident ray, with an intensity falling off with angle as J. J. Thomson's classical formula prescribes. Yet measurements — Compton's own among them — showed that the scattered radiation was consistently “softer” (longer in wavelength, more easily absorbed) than the primary beam, and that this softening grew steadily as the scattering angle increased. Classical electrodynamics had no room for such a shift.

The hypothesis — one quantum strikes one electron

Compton breaks with the wave picture and treats the X-ray as a quantum carrying energy hν and momentum h/λ. He pictures it making a single relativistic elastic collision with one free electron, like one billiard ball striking another, and imposes conservation of energy and of momentum on the pair. The recoiling electron carries off energy and momentum; the scattered quantum, left with less of both, must emerge with a lower frequency — a longer wavelength.

The result

Working the conservation equations through, the increase in wavelength depends only on the scattering angle θ — not on the incident wavelength, and not on the scattering material: Δλ = (h/mₑc)(1 − cos θ). The constant h/mₑc, the Compton wavelength, equals 0.0243 Å (2.43 pm). The shift vanishes straight ahead (θ = 0) and reaches its maximum, twice the Compton wavelength, for back-scattering (θ = 180°).

The test — molybdenum X-rays on graphite

Compton scattered the molybdenum Kα line (about 0.71 Å) from a block of graphite — carbon being a “light element” whose electrons are loosely bound — and measured the wavelengths of the scattered rays with a Bragg crystal spectrometer at a series of angles. At each angle the spectrum showed a shifted (“modified”) line beside an unshifted one, and the displacement of the modified line grew with angle exactly as the formula required, reaching about 0.024 Å at 90°. His verdict was plain:

This remarkable agreement between our formulas and the experiments can leave but little doubt that the scattering of X-rays is a quantum phenomenon.

[ … ]

The paper closes by drawing the consequence its title only hints at: scattering is not a wave gently re-radiating, but a corpuscle of radiation, with definite energy and momentum, deflecting a single electron — direct evidence for the reality of the light quantum.

Arthur H. Compton · Washington University, St. Louis · 1923