物理學 1865

電磁場的動力學理論

詹姆斯·克拉克·馬克士威

電與磁，是同一個場——而光，是穿行其中的一道漣漪。

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In depth · the introduction

馬克士威發現，電與磁是同一件事物的兩副面孔——而光本身，就是一道在其中盪漾的波。

核心想法

到馬克士威的時代，實驗已經表明電與磁糾纏在一起：移動的磁鐵能把電沿著導線推動，而電流能讓指南針的指針偏轉。馬克士威的第一步，是不再把這些當作物體之間相互伸來的力，而把它們想像成看不見的「場」——瀰漫在整個空間裡的影響圖樣——並寫下一組簡潔的方程，描述電場與磁場如何彼此創生、彼此彎折。

接著，便是那驚人的部分。他的方程說，這些場裡的一陣抖動不會停在原地：它會以波的形式向外行進，而它的速度，他能用早已在實驗室裡測得的數字算出來。答案，正是光速。這不可能是巧合。馬克士威由此斷定：光，無非就是一種電磁波——而既然可見光是這樣一種波，那就一定還有別的、波長更長或更短、我們眼睛看不見的波。

它是如何誕生的

馬克士威的工作，立在邁克爾·法拉第的肩上。法拉第幾乎全靠自學，是位實驗家，他在磁體與電荷周圍的空間裡布滿了想像中的「力線」，卻缺乏把它們說精確的數學。馬克士威欣賞法拉第那些物理圖景，立志為它們配上方程。在更早的 1862 年一篇論文裡，他甚至把場想像成一格格旋轉的渦胞、夾著一個個「惰輪」——一個力學模型——並注意到，它的彈性意味著會有以光速行進的波動。

在 1865 年這篇論文裡，他卸下了那套繁複的機械裝置，以成熟的形態呈現這套理論：一個「電磁場的動力學理論」，立足於方程本身，而不再依賴任何特定的力學圖像。這篇論文於 1864 年 12 月在皇家學會宣讀。完全的印證來得稍晚——1887 年，在馬克士威 48 歲早逝八年之後，海因里希·赫茲在實驗台上產生並捕獲到了這些波。

它為何重要

馬克士威完成了物理學繼牛頓之後的第二次偉大統一：他表明電、磁、光本是同一種現象，由同一組定律支配。這一洞見，是整個電氣與無線時代的根基——每一段廣播、電話、Wi-Fi 訊號，都是他的一種波。而他的方程裡還藏著一條線索——內蘊其中的、恆定的光速——它將在一代人之後，把愛因斯坦引向相對論。

一個可以想像的畫面

想像兩位舞者，電與磁，他們只能靠給對方遞暗號來移動。當電場起落，它的變化在身旁喚出一個磁場；當那磁場起落，它的變化又在更前一步喚出一個電場——這一對就這樣在空無之中接力蛙跳，每一方的變化都在催生著另一方。這場自我更新的接力，以光速向前飛奔，就是一道光波。改變舞者抖動的快慢——也就是頻率——你就改變了它的顏色，從無線電、到可見光、到 X 射線；但這場接力，永遠以同一個速度 c 推進。

後來發生了什麼

馬克士威那個對誰都一樣、恆定不變的光速，是經典物理回答不了的一道謎——直到 1905 年，愛因斯坦把它立為狹義相對論的基石，廢除了絕對的空間與時間。馬克士威方程無需任何修訂；它們一直都是相對論性的。

在另一條戰線上，光的波動描述，在熾熱發光的物體與光電效應面前撞上了極限，逼著物理學承認：光也是一份份離散的能量包——光子。把馬克士威的場與量子調和起來，便成了量子電動力學，這是科學中受檢驗最精密的理論。而馬克士威那四條方程，至今仍是它精確的經典極限——也仍是每一位電氣工程師手中的工具。

The original document

Original source text

引言——一個關於場的理論

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.

能量寓於媒介之中

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.

橫波，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.

結果的吻合，與那個結論

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