物理学 1924

量子理论研究（量子论研究）

路易·德布罗意

若光可以是粒子，那么物质便可以是波。

Choose your version

In depth · the introduction

一位年轻的贵族提出了一个简单而大胆的问题：如果光——一种波——能表现得像粒子，那粒子为什么不能表现得像波呢？

核心想法

到了 1924 年，物理学家们已经勉强接受：光是两面的——它既是一列会扩散、会干涉的波，又是一阵被称作光子的微小能量包。路易·德布罗意却注意到，这笔交易是单方面的。光，本是波，却被赋予了粒子般的行为；而物质，本由粒子构成，却从未被赋予波动般的行为。他提议把这本账平一平。

他的主张是：每一个运动的物体，都有一个波长，由一个简洁得惊人的公式给出——波长，等于普朗克常数除以动量。一样东西动得越快、越重，它的波就越短。对于一个棒球，这波小到无法想象，你永远察觉不到。可对于电子——又轻又快——这波大约只有一个原子那么大，大到足以举足轻重，也大到足以被测量。

它是如何诞生的

路易·德布罗意出身于法国一个显赫的大家族，起初学的是历史。他被新生的量子理论中的种种谜题吸引而转向物理，又受到哥哥莫里斯——一位研究 X 射线的实验物理学家——的影响，把光的双重身份这个问题，在脑中反复琢磨了许多年。

他的答案，成了他 1924 年在索邦答辩的博士论文。这想法太不寻常，以至于答辩委员们都拿不准它是否可能为真。他们征询了阿尔伯特·爱因斯坦的意见；爱因斯坦读后回信说，德布罗意「掀起了那道巨大帷幕的一角」。这一句话，改变了一切——不出三年，实验便把电子射向晶体，看见它们如波一般泛起涟漪、彼此干涉，分毫不差。

它为何重要

德布罗意波长，是现代物理转身时所凭的那道枢轴。它告诉了埃尔温·薛定谔该去寻找一个什么样的方程，而他在 1926 年找到的那个波动方程，成了整个化学与量子力学的引擎——让我们得以解释：原子为何成键、材料为何导电或绝缘、元素周期表为何长成那个样子。物质有波长这一想法，也正是电子显微镜得以存在的缘由，让我们看见了病毒，乃至一个个单独的原子。

一个可以想象的画面

想象一根长长的跳绳。握住两端，猛地一抖：波会沿着绳子传过去，可绳子本身只是上下摆动——那道能量的凸起，跑得比绳上任何一个点都快。德布罗意的物质波，正是这样运作的。电子，就是那道移动得较慢的凸起——「波包」——它把电子从这里带到那里；而内部那些细小、飞快的波纹（相位波），则一路抢先飞奔。他证明了，这两者永远步调一致，就像一只滚动的车轮，辐条与轮辋一同转动。

它的位置

这一想法是一座桥。它的身后，站着马克斯·普朗克与阿尔伯特·爱因斯坦——是他们最先发现，光以量子化的能量包出现；它的身前，站着薛定谔与维尔纳·海森堡——他们 1926 年的波动力学与矩阵力学，把德布罗意的一个暗示，变成了一套完整的理论。德布罗意凭这篇论文，获得了 1929 年的诺贝尔奖。他晚年一直在为一种「导波」图景辩护，那图景为多数物理学家所搁置——然而数十年后，它又被戴维·玻姆重新拾起；而关于这列波究竟是什么的争论，也从未真正合上。

The original document

Original source text

导言——一种有待恢复的对称

Louis de Broglie · Recherches sur la théorie des quanta · Thesis, Paris, 1924 · Annales de Physique (10) 3 (1925): 22–128

[Light, since Einstein's 1905 light-quanta, had been granted a particle aspect alongside its wave aspect. De Broglie's thesis asks whether the converse holds for matter.]

After long reflection in solitude and meditation, I suddenly had the idea, during the year 1923, that the discovery made by Einstein in 1905 should be generalised by extending it to all material particles and notably to electrons.

第一章——相位波

An internal periodic phenomenon

We shall assume the existence of a certain periodic phenomenon of a yet to be determined character, which is to be attributed to each and every isolated parcel of energy, and which depends on its proper mass through the Planck–Einstein equation.

[For a particle of rest mass m₀, de Broglie sets the rest-frame frequency by hν₀ = m₀c². Seen from the laboratory, the moving particle's internal clock runs slow (time dilation) at ν₁ = ν₀√(1−β²), yet an accompanying wave runs at the higher frequency ν = ν₀ ⁄ √(1−β²) and at phase velocity V = c²/v.]

We are then inclined to admit that any moving body may be accompanied by a wave and that it is impossible to disjoin motion of body and propagation of wave.

The theorem of the harmony of phases

[De Broglie proves that the slow internal clock of the particle and the fast external wave, though they have different frequencies, stay perpetually in step: at the particle's position the phase of the wave always agrees with the phase of the internal vibration. This is the harmony of phases that the wave's velocity V = c²/v was chosen precisely to secure.]

[ … ]

The phase wave guides the displacement of energy; its group velocity is equal to the velocity of the particle, while its phase velocity exceeds the velocity of light without, since it carries no energy, contradicting relativity.

物质的波长

[Combining the relations gives the result the thesis is remembered for: a moving body of momentum p has an associated wavelength.]

λ = h / p

[For an electron this wavelength is comparable to the spacing of atoms in a crystal — which is why de Broglie foresaw that a stream of electrons ought to be diffracted by a crystal lattice, just as X-rays are.]

重新解读玻尔的轨道

[De Broglie shows that Bohr's mysterious quantum condition for the allowed electron orbits is simply the requirement that the phase wave close on itself — that a whole number of wavelengths fit around the orbit, a standing wave rather than a wave that interferes with itself and dies away.]

The stability conditions of the trajectories in Bohr's theory are interpretable as the resonance condition of the phase wave along the closed path.