物理學 1919

太陽重力場對光之偏折的測定

法蘭克·戴森、亞瑟·愛丁頓與查爾斯·戴維森

掠過太陽的星光偏折 1.75″——正如愛因斯坦所言，是牛頓所許的兩倍。

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In depth · the introduction

1919 年，天文學家等著月亮遮住太陽——結果捕捉到星光偏折，偏折量恰是愛因斯坦此前大膽預言的那個數。

核心想法

愛因斯坦的廣義相對論說：質量會彎曲其周圍空間與時間的形狀，而光走的是當下最直的路，便不得不順著這彎曲而行。於是，一束掠過太陽的星光應當被略微彎折，一顆正貼著太陽的星，看上去應當被往外推開一點。

愛因斯坦給出了具體數字：緊貼太陽邊緣的星，應向外移約 1.75 角秒——一個髮絲般細的角度，卻是用牛頓舊物理所能解釋的兩倍。整場檢驗，歸根結底就是測出這極小的位移，再看它合的是愛因斯坦的數，還是較小的那個牛頓數。

事情的由來

麻煩在於，你根本看不見太陽旁邊的星——它的強光把星都淹沒了。唯一的例外是日全食：月球遮住太陽的那幾分鐘，群星會在變暗的白晝天空中冒出來。1919 年 5 月 29 日的這場日食恰到好處：被食的太陽將落在一團明亮密集的星群——畢宿星團——之中。

為防雲遮，英國派出了兩支觀測隊——一支去巴西的索布拉爾，一支去西非外海的普林西比島，亞瑟·愛丁頓親自前往。他們拍下被食太陽周圍的群星，再與幾個月後夜裡拍的同一片星場比對。靠近太陽的星，果然向外移了。當年 11 月，法蘭克·戴森在倫敦公布這些數字，結果登上世界各地的頭條，幾乎在一夜之間把愛因斯坦變成在世最有名的科學家。誠實起見要加一句腳註：資料是帶雜訊的，一台成像模糊、給出相左結果的儀器被擱置一旁——這一取捨後來招致偏見之譏，不過其後的重新分析已確認了結論。

它為何重要

兩個世紀以來，牛頓的重力一直是宇宙不容置疑的法則。1919 年的日食，是第一份硬證據，表明它並非定論——在足夠重的天體附近，愛因斯坦那幅更奇異的彎曲時空圖景，更貼近真實。它把廣義相對論從優美的數學變成了受檢驗的物理，並開啟了黑洞、膨脹的宇宙、重力波與 GPS 的一個世紀——而這一切，都倚靠著那幾張日食底片所確認的理論。

一個日常畫面

把空間的織物想像成一張繃緊的橡皮膜。在中央放一個重球——太陽——膜便繞它凹陷成一個坑。現在讓一顆玻璃彈珠筆直地滾過膜面，離重球遠遠的：當它越過坑的斜坡時，會略微偏向，儘管沒有任何東西從側面推它。星光在太陽附近也是如此——不是被舊意義上的「力」拉扯，而是順著太陽質量在空間本身鑿出的山谷而行。彈珠越貼近重球，坡越陡、偏越急——這正是為什麼掠過太陽邊緣的光，偏折最大。

它的位置

這正是那場確認了本館「愛因斯坦廣義相對論（1916）」一篇所述理論的實驗。它是一道樞紐：一端連著牛頓的《自然哲學的數學原理》（1687）——其重力正是在邊緣處被它拉下王座——另一端連著隨之而來的現代重力科學：LIGO 於 2016 年捕獲的重力波、黑洞的物理，以及讓天文學家得以秤量暗物質的透鏡星系。這一切，都建在那彎曲的時空之上——而幾張照相底片，最先在那裡抓住了太陽使光偏折的一幕。

The original document

Original source text

F. W. Dyson, A. S. Eddington & C. Davidson · Phil. Trans. R. Soc. Lond. A 220 (1920): 291–333

The question

The purpose of the expeditions was to determine what effect, if any, is produced by a gravitational field on the path of a ray of light traversing it.

Three alternatives

The report frames the test as a choice between three outcomes for a star seen close to the Sun's edge:

(1) The path is uninfluenced by gravitation. (2) The energy or mass of light is subject to gravitation in the same way as ordinary matter. If the law of gravitation is strictly the Newtonian law, this leads to an apparent displacement of a star close to the sun's limb amounting to 0″·87 outwards. (3) The course of a ray of light is in accordance with Einstein's generalised relativity theory. This leads to an apparent displacement of a star at the limb amounting to 1″·75 outwards.

The method

During the few minutes of totality on 29 May 1919, when the Moon hid the Sun's disc, each expedition photographed the field of stars surrounding it — a particularly rich part of the Hyades. Months later the same star field was photographed at night, with the Sun far away. Superposing the plates and measuring how far each star had shifted outward gives the deflection directly. Two sites were used against the risk of cloud: Sobral in northern Brazil, and the island of Príncipe in the Gulf of Guinea, where Eddington himself observed.

[ … ]

The measurements

Corrected to the Sun's limb, the well-exposed Sobral 4-inch plates gave 1.98″ ± 0.12″, and Eddington's Príncipe plates gave 1.61″ ± 0.30″ — both near Einstein's 1.75″ and far from the Newtonian 0.87″. A third set, the Sobral astrographic plates, gave a much smaller figure but had been blurred by the Sun's heat distorting the mirror, and was set aside. (Probable errors as quoted in the report.)

Conclusion

Thus the results of the expeditions to Sobral and Principe can leave little doubt that a deflection of light takes place in the neighbourhood of the sun and that it is of the amount demanded by Einstein's generalised theory of relativity, as attributable to the sun's gravitational field.

Royal Observatory, Greenwich · read to the Royal Society, 6 November 1919