物理学 1865

电磁场的动力学理论

詹姆斯·克拉克·麦克斯韦

电与磁，是同一个场——而光，是穿行其中的一道涟漪。

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In depth · the introduction

麦克斯韦发现，电与磁是同一件事物的两副面孔——而光本身，就是一道在其中荡漾的波。

核心想法

到麦克斯韦的时代，实验已经表明电与磁纠缠在一起：移动的磁铁能把电沿着导线推动，而电流能让指南针的指针偏转。麦克斯韦的第一步，是不再把这些当作物体之间相互伸来的力，而把它们想象成看不见的「场」——弥漫在整个空间里的影响图样——并写下一组简洁的方程，描述电场与磁场如何彼此创生、彼此弯折。

接着，便是那惊人的部分。他的方程说，这些场里的一阵抖动不会停在原地：它会以波的形式向外行进，而它的速度，他能用早已在实验室里测得的数字算出来。答案，正是光速。这不可能是巧合。麦克斯韦由此断定：光，无非就是一种电磁波——而既然可见光是这样一种波，那就一定还有别的、波长更长或更短、我们眼睛看不见的波。

它是如何诞生的

麦克斯韦的工作，立在迈克尔·法拉第的肩上。法拉第几乎全靠自学，是位实验家，他在磁体与电荷周围的空间里布满了想象中的「力线」，却缺乏把它们说精确的数学。麦克斯韦欣赏法拉第那些物理图景，立志为它们配上方程。在更早的 1862 年一篇论文里，他甚至把场想象成一格格旋转的涡胞、夹着一个个「惰轮」——一个力学模型——并注意到，它的弹性意味着会有以光速行进的波动。

在 1865 年这篇论文里，他卸下了那套繁复的机械装置，以成熟的形态呈现这套理论：一个「电磁场的动力学理论」，立足于方程本身，而不再依赖任何特定的力学图像。这篇论文于 1864 年 12 月在皇家学会宣读。完全的印证来得稍晚——1887 年，在麦克斯韦 48 岁早逝八年之后，海因里希·赫兹在实验台上产生并捕获到了这些波。

它为何重要

麦克斯韦完成了物理学继牛顿之后的第二次伟大统一：他表明电、磁、光本是同一种现象，由同一组定律支配。这一洞见，是整个电气与无线时代的根基——每一段广播、电话、Wi-Fi 信号，都是他的一种波。而他的方程里还藏着一条线索——内蕴其中的、恒定的光速——它将在一代人之后，把爱因斯坦引向相对论。

一个可以想象的画面

想象两位舞者，电与磁，他们只能靠给对方递暗号来移动。当电场起落，它的变化在身旁唤出一个磁场；当那磁场起落，它的变化又在更前一步唤出一个电场——这一对就这样在空无之中接力蛙跳，每一方的变化都在催生着另一方。这场自我更新的接力，以光速向前飞奔，就是一道光波。改变舞者抖动的快慢——也就是频率——你就改变了它的颜色，从无线电、到可见光、到 X 射线；但这场接力，永远以同一个速度 c 推进。

后来发生了什么

麦克斯韦那个对谁都一样、恒定不变的光速，是经典物理回答不了的一道谜——直到 1905 年，爱因斯坦把它立为狭义相对论的基石，废除了绝对的空间与时间。麦克斯韦方程无需任何修订；它们一直都是相对论性的。

在另一条战线上，光的波动描述，在炽热发光的物体与光电效应面前撞上了极限，逼着物理学承认：光也是一份份离散的能量包——光子。把麦克斯韦的场与量子调和起来，便成了量子电动力学，这是科学中受检验最精密的理论。而麦克斯韦那四条方程，至今仍是它精确的经典极限——也仍是每一位电气工程师手中的工具。

The original document

Original source text

引言——一个关于场的理论

J. C. Maxwell · A Dynamical Theory of the Electromagnetic Field · Phil. Trans. R. Soc. 155 (1865): 459–512 · Part I

The theory I propose may therefore be called a theory of the Electromagnetic Field, because it has to do with the space in the neighbourhood of the electric or magnetic bodies, and it may be called a Dynamical Theory, because it assumes that in that space there is matter in motion, by which the observed electromagnetic phenomena are produced.

The electromagnetic field is that part of space which contains and surrounds bodies in electric or magnetic conditions. It may be filled with any kind of matter, or we may endeavour to render it empty of all gross matter, as in the case of Geissler's tubes and other so-called vacua.

There is always, however, enough of matter left to receive and transmit the undulations of light and heat; and it is because the transmission of these radiations is not greatly altered when transparent bodies of measurable density are substituted for the so-called vacuum, that we are obliged to admit that the undulations are those of an ethereal substance, and not of the gross matter, the presence of which merely modifies in some way the motion of the ether.

能量寓于媒介之中

Part I · on the seat of the energy

Now the energy communicated to the body in heating it must have formerly existed in the moving medium, for the undulations had left the source of heat some time before they reached the body, and during that time the energy must have been half in the form of motion of the medium and half in the form of elastic resilience.

We may therefore receive, as a datum derived from a branch of science independent of that with which we have to deal, the existence of a pervading medium of small but real density, capable of being set in motion, and of transmitting motion from one part to another with great, but not infinite, velocity.

横波，正如光

Part VI · Electromagnetic Theory of Light

The disturbance at any point is transverse to the direction of propagation, and such waves may have all the properties of polarized light.

By the electromagnetic experiments of MM. Weber and Kohlrausch, v = 310,740,000 metres per second is the number of electrostatic units in one electromagnetic unit of electricity, and this, according to our result, should be equal to the velocity of light in air or vacuum.

The velocity of light in air, by M. Fizeau's experiments, is V = 314,858,000; according to the more accurate experiments of M. Foucault, V = 298,000,000.

结果的吻合，与那个结论

Part VI · the inference

Hence the velocity of light deduced from experiment agrees sufficiently well with the value of v deduced from the only set of experiments we as yet possess.

The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws.

Read December 8, 1864 · King's College, London