Eddington experiment

Arthur Stanley Eddington, Plumian Professor of Astronomy

One of the first considerations of gravitational deflection of light was published in 1801, when Johann Georg von Soldner pointed out that Newtonian gravity predicts that starlight will be deflected when it passes near a massive object. Initially, in a paper published in 1911, Einstein had incorrectly calculated that the amount of light deflection was the same as the Newtonian value, that is 0.83 seconds of arc.[3]

In October 1911, responding to Einstein's encouragement, German astronomer Erwin Freundlich contacted solar eclipse expert Charles D. Perrine in Berlin to inquire as to the suitability of existing solar eclipse photographs to prove Einstein's prediction of light deflection. Perrine, the director of the Argentine National Observatory at Cordoba, had participated in four solar eclipse expeditions while at the Lick Observatory in 1900, 1901, 1905, and 1908. He did not believe existing eclipse photos would be useful. In 1912 Freundlich asked if Perrine would include observation of light deflection as part of the Argentine Observatory's program for the solar eclipse of October 10, 1912, in Brazil. W. W. Campbell, director of the Lick Observatory, loaned Perrine its intramercurial camera lenses. Perrine and the Cordoba team were the only eclipse expedition to construct specialized equipment dedicated to observe light deflection. Unfortunately all the expeditions suffered from torrential rains which prevented any observations. Nevertheless Perrine was the first astronomer to make a dedicated attempt to observe light deflection to test Einstein's prediction.[4] Eddington had taken part in a British expedition to Brazil to observe the 1912 eclipse but was interested in different measurements.[4] Eddington and Perrine spent several days together in Brazil and may have discussed their observation programs including Einstein's prediction of light deflection.[5]

In 1914 three eclipse expeditions, from Argentina, Germany, and the US, were committed to testing Einstein's theory by observing for light deflection. The three directors were Erwin Finlay-Freundlich, from the Berlin Observatory, the US astronomer William Wallace Campbell, director of the Lick Observatory, and Charles D. Perrine, director of the Argentine National Observatory at Cordoba. The three expeditions travelled to the Crimea in the Russian Empire to observe the eclipse of 21 August. However, the First World War started in July of that year, and Germany declared war on Russia on 1 August. The German astronomers were either forced to return home or were taken prisoner by the Russians. Although the US and Argentine astronomers were not detained, clouds prevented clear observations being made during the eclipse. Perrine's photographs although not clear enough to prove Einstein's prediction were the first obtained in an attempt to test Einstein's prediction of light deflection.[6][7][8]

[9] A second attempt by American astronomers to measure the effect during the 1918 eclipse was foiled by clouds in one location[10] and by ambiguous results due to the lack of the correct equipment in another.[1][11]

Einstein's 1911 paper predicted deflection of star light near the Sun to be 0.83 seconds of arc and encouraged astronomers to test this prediction by observing stars near the Sun during a solar eclipse.[12] It is fortunate for Einstein that the weather precluded results by Perrine in 1912 and Perrine, Freundlich, and Campbell in 1914. If results had been obtained they may have disproved the 1911 prediction setting back Einstein's reputation. In any case, Einstein corrected his prediction in his 1915 paper on General Relativity to 1.7 seconds of arc. Einstein and subsequent astronomers both benefitted from this correction.[13]

Eddington's interest in general relativity began in 1916, during World War I, when he read papers by Einstein (presented in Berlin, Germany, in 1915), which had been sent by the neutral Dutch physicist Willem de Sitter to the Royal Astronomical Society in Britain. Eddington, later said to be one of the few people at the time to understand the theory, realised its significance and lectured on relativity at a meeting at the British Association in 1916. He emphasised the importance of testing the theory by methods such as eclipse observations of light deflection, and the Astronomer Royal, Frank Watson Dyson began to make plans for the eclipse of May 1919, which would be particularly suitable for such a test. Eddington also produced a major report on general relativity for the Physical Society, published as Report on the Relativity Theory of Gravitation (1918). Eddington also lectured on relativity at Cambridge University, where he had been professor of astronomy since 1913.[14]

Wartime conscription in Britain was introduced in 1917. At the age of 34, Eddington was eligible to be drafted into the military, but his exemption from this was obtained by his university on the grounds of national interest. This exemption was later appealed by the War Ministry, and at a series of hearings in June and July 1918, Eddington, who was a Quaker, stated that he was a conscientious objector, based on religious grounds.[15] At the final hearing, the Astronomer Royal, Frank Watson Dyson, supported the exemption by proposing that Eddington undertake an expedition to observe the total eclipse in May the following year to test Einstein's General Theory of Relativity. The appeal board granted a twelve month extension for Eddington to do so. Although this extension was rendered moot by the signing of the Armistice in November, ending the war, the expedition went ahead as planned.

Einstein, recipient of the Nobel Prize in Physics in 1921, though not for his development of general relativity

The theory behind the experiment concerns the predicted deflection of light by the Sun. The first observation of light deflection was performed by noting the change in position of stars as they passed near the Sun on the celestial sphere. The approximate angular deflection δφ for a massless particle coming in from infinity and going back out to infinity is given by the following formula:[16]

${\displaystyle \delta \varphi \approx {\frac {2r_{s}}{b}}={\frac {4GM}{c^{2}b}}.}$

Here, b can be interpreted as the distance of closest approach. Although this formula is approximate, it is accurate for most measurements of gravitational lensing, due to the smallness of the ratio r_s/b. For light grazing the surface of the sun, the approximate angular deflection is roughly 1.75 arcseconds. This is twice the value predicted by calculations using the Newtonian theory of gravity. It was this difference in the deflection between the two theories that Eddington's expedition and other later eclipse observers would attempt to observe.

Sir Frank Watson Dyson, Astronomer Royal

The aim of the expeditions was to take advantage of the shielding effect of the Moon during a total solar eclipse, and to use astrometry to measure the positions of the stars in the sky around the Sun during the eclipse. These stars, not normally visible in the daytime due to the brightness of the Sun, would become visible during the moment of totality when the Moon covered the solar disc. A difference in the observed position of the stars during the eclipse, compared to their normal position at night, would indicate that the light from these stars had bent as it passed close to the Sun. Dyson, when planning the expedition in 1916, had chosen the 1919 eclipse because it would take place with the Sun in front of a bright group of stars called the Hyades. The brightness of these stars would make it easier to measure any changes in position.

Two teams of two people were to be sent to make observations of the eclipse at two locations: the West African island of Príncipe and the Brazilian town of Sobral.

The Príncipe expedition members were Eddington and Edwin Turner Cottingham, from the Cambridge Observatory, while the Sobral expedition members were Andrew Crommelin and Charles Rundle Davidson, from the Greenwich Observatory in London. Eddington was Director of the Cambridge Observatory, and Cottingham was a clockmaker who worked on the observatory's instruments. Similarly, Crommelin was an assistant at the Greenwich Observatory, while Davidson was one of the observatory's computers.

The expeditions were organised by the Joint Permanent Eclipse Committee, a joint committee between the Royal Society and the Royal Astronomical Society, chaired by Dyson, the Astronomer Royal. The funding application for the expedition was made to the Government Grant Committee, asking for £100 for instruments and £1000 for travel and other costs.

Sobral

Eclipse instruments at Sobral

Map of the path of totality for the eclipse

The Sobral equipment included one astrographic lens from the Greenwich Observatory, and another from the Royal Irish Academy.

J. J. Thomson, President of the Royal Society, supported Eddington's conclusions

The results were announced at a meeting of the Royal Society in November 1919,[18] and published in the Philosophical Transactions of the Royal Society in 1920.[2] Following the return of the expedition, Eddington was addressing a dinner held by the Royal Astronomical Society, and, showing his more light-hearted side, composed the following verse that parodied the style of the Rubaiyat of Omar Khayyam:[19]

Oh leave the Wise our measures to collate
One thing at least is certain, light has weight
One thing is certain and the rest debate
Light rays, when near the Sun, do not go straight.

— Arthur Stanley Eddington, RAS dinner[20]

The New York Times of November 10, 1919, reported on Einstein's confirmed prediction

The result was considered spectacular news and made the front page of most major newspapers. It made Einstein and his theory of general relativity world-famous. Einstein has been quoted as describing what his reaction would have been if general relativity had not been confirmed by Eddington and Dyson in 1919: "Then I would feel sorry for the dear Lord. The theory is correct anyway."[21]

Although the Eddington experiment and the publication of its results had an immediate impact in the popular press, the acceptance by the worldwide scientific community was less swift. Understanding of general relativity among other scientists was still poor, and during the 1920s scepticism about the theory and the results continued until new eclipse observations and other tests of relativity settled the matter.

The light deflection measurements were repeated by expeditions that observed the total solar eclipse of 21 September 1922 in Australia. An important role in this was played by the Lick Observatory[9] and the Mount Wilson Observatory, both in California, USA.[11] On April 12, 1923, William Wallace Campbell announced that the preliminary new results confirmed Einstein’s theory of relativity and prediction of the amount of light deflection with measurements from over 200 stars.[22] Final results published in 1928 used measurements of over 3,000 star images.[23]

In the post-Newtonian tests of gravity, the parameterized post-Newtonian formalism parameterizes, in terms of ten adjustable parameters, all the possible departures from Newton's law of universal gravitation. The earliest parameterizations of the post-Newtonian approximation were performed by Eddington (1922). The parameter concerned with the amount of deflection of light by a gravitational source is the so-called Eddington parameter (γ). It is the best constrained of the ten post-Newtonian parameters.

The early accuracy of eclipse measurements, however, was poor. Dyson et al. quoted an optimistically low uncertainty in their measurement, which is argued by some[24] to have been plagued by systematic error and possibly confirmation bias, although modern reanalysis of the dataset suggests that Eddington's analysis was accurate.[25][26]

A significant limitation in 1919 was the limited data set of only a handful of stars.[27] At the total solar eclipse of Sept. 21, 1922, the Lick Observatory expedition to Wallal, Australia, led by Director William W. Campbell photographed and measured over 3,000 star images.[28] The quantity and quality of the images achieved a level of accuracy which engendered a high degree of scientific confidence in the results which were consistent with Einstein's predicted amount of light deflection. While Eddington and Dyson deserve credit for the earliest proof that light deflection is real, Campbell's results in 1922 proved to the satisfaction of many still-skeptical scientists that Einstein's predicted value of light deflection was correct.[29]

In 1801 Johann Georg von Soldner had pointed out that Newtonian gravity predicts that starlight will bend around a massive object, but the predicted effect is only half the value predicted by general relativity as calculated by Einstein in his 1911 paper. The results of Soldner were revived by the Nobel laureate Philipp Lenard in an attempt to discredit Einstein.[30] Eddington had been aware in 1919 of the alternative predictions. Considerable uncertainty remained in these measurements for almost fifty years, until observations started being made at radio frequencies. It was not until the late 1960s that it was definitively shown that the amount of deflection was the full value predicted by general relativity, and not half that number.[31]

The experiment was central to the plot of the 2008 BBC television film Einstein and Eddington, with David Tennant in the role of Eddington.

• Tests of general relativity
• Einstein and Eddington

• The Golem: What You Should Know About Science (1993) - Harry M. Collins and Trevor Pinch
• Einstein's Jury: The Race to Test Relativity (2016) - Jeffrey Crelinsten
• Einstein's War: How Relativity Triumphed Amid the Vicious Nationalism of World War I (2019) - Matthew Stanley
• No Shadow of a Doubt: The 1919 Eclipse That Confirmed Einstein's Theory of Relativity (2019) - Daniel Kennefick. Princeton University Press.
• Gravity’s Century: From Einstein’s Eclipse to Images of Black Holes (2019) - Ron Cowen

• Eclipse 1919, website about the eclipse, the expeditions and centenary events
• Eddington's Eclipse and Einstein's Celebrity (BBC World Service)
• The man who made Einstein world-famous (BBC News, 24 May 2019)
• Matthew Stanley and Einstein's War (Center for Human Imagination)
• 100 years on: the pictures that changed our view of the universe (The Observer, 12 May 2019)
• How the 1919 Solar Eclipse Made Einstein the World's Most Famous Scientist (Discover magazine, May 2019)
• A Total Solar Eclipse 100 Years Ago Proved Einstein’s General Relativity (Smithsonian Magazine, 24 May 2019)
• Einstein, Eddington and the 1919 eclipse (Nature, April 2019)
• Arthur S. Eddington: From Physics to Philosophy and Back Again (Eddington Conference, 27–29 May 2019, Paris)