Eddington, Sir Arthur Stanley

(1882-1944), theoretical physicist and astrophysicist

by C. W. Kilmister

© Oxford University Press 2004 All rights reserved

Eddington, Sir Arthur Stanley (1882-1944), theoretical physicist and astrophysicist, was born on 28 December 1882 in Kendal, Westmorland, the second child of Arthur Henry Eddington (d. 1884) and his wife, Sarah Ann Shout of Darlington, whose family was of Dutch origin. Both came from traditional Quaker families. His father, a Somerset man, was headmaster and proprietor of Stramongate, the Friends' school in Kendal, where John Dalton the chemist had taught a century earlier.

Education and early work in astronomy
Before Eddington was two his father died of typhoid and he, his mother, and his sister Winifred, who was six, moved to Weston-super-Mare. He early showed his unusual interest in numbers by learning the twenty-four times table. In Weston he attended Bryncelyn School and won a Somerset county scholarship so that at fifteen he entered Manchester University. His course consisted of a general year followed by three years of physics under Arthur Schuster and mathematics under Horace Lamb. Eddington consciously modelled his own elegant prose style upon that of Lamb. When he graduated from Manchester with first-class honours, an entrance scholarship (later changed to a major scholarship) enabled him to enter Trinity College, Cambridge, in 1902 to read mathematics. In 1904 he was senior wrangler in part one of the mathematical tripos and in the following year was placed in the first division of the first class in part two.

Eddington returned to Cambridge in the autumn of 1905 to earn his living as a mathematical coach, but early in 1906, aged twenty-four and a year before his first published paper, moved to Greenwich as chief assistant to the astronomer royal, in place of Frank Dyson who became the astronomer royal of Scotland. Some of the work was observational but he also had time to carry out a theoretical investigation of the motion of stars. When the apparent stellar motions caused by the earth's rotation have been allowed for, the much smaller proper motions remain. The Dutch astronomer Jacobus Kapteyn had found in 1904 that the proper motions evidenced two 'star streams'; Eddington greatly extended Kapteyn's work and used his results as successful bases for a Smith's prize essay and a Trinity fellowship dissertation. He was an obvious choice to fill the Plumian chair of astronomy in Cambridge when Sir George Darwin retired in 1913. When Sir Robert Ball died in the following year it was decided to join the directorship of the observatory to the Plumian chair, so Eddington, with his mother and his sister, took up residence at the observatory, where he was to stay for the rest of his life. In that year he published his first book Stellar Movements and the Structure of the Universe, and he was also elected to the Royal Society. The book marks an end to his contributions to that particular field for he realized that the Kapteyn-Eddington explanation was less elegant than an alternative put forward by Karl Schwarzschild.

Stellar research
Research underlying two of Eddington's three major claims to fame began in 1916. His interest in the stars had turned to their internal structure and their heat-producing mechanism. He had been stimulated by wanting to understand the energy process that would explain the specific property of one class of stars, the Cepheid variables, the discovery of which allowed astronomers to set up a scale of distance. Their distinctive property was that their intrinsic brightness was fixed by the period of variation. In 1914 Harlow Shapley at Harvard proposed that the variability might be due to periodic pulsations, a vague hypothesis because of lack of knowledge of the internal structure of stars. Eddington seized upon the challenge, and developed a theory which accounted for many Cepheid characteristics. It was generally accepted that in some way all stars produced their heat deep inside and it reached the surface by convection. Eddington realized that radiation, not convection, played the major role. It was the radiation pressure which prevented the star from collapsing under its own weight. With some further assumptions and a huge amount of laborious computation, Eddington was able to explain the empirical link between the period of a Cepheid and its absolute magnitude. He then derived, and in March 1924 announced, the 'mass-luminosity relation'. He then calculated the central temperature of stars, and so hypothesized that the source of the stars' energy was the burning of hydrogen into helium. This has since proved to be the case. These results, collected and published as The Internal Constitution of the Stars (1926), were a major contribution to the problem of stellar evolution, and elevated Eddington into the front rank of international astrophysicists.

The second of Eddington's major innovations of 1916 had a more lasting effect on his life. He was by then secretary to the Royal Astronomical Society and William de Sitter in the Netherlands sent him a copy of Einstein's new theory of gravitation, 'general relativity'. The special theory of relativity of 1905 had caused relatively little excitement in Cambridge, and Eddington had not thought about it. Now he became very interested in both of Einstein's theories, and expounded clearly for the first time in England what had seemed to be difficult mathematics. His report was later expanded into The Mathematical Theory of Relativity (1923).

Verifying Einstein
Events in the outside world now impinged on Eddington's essentially intellectual existence. At thirty-four he was eligible to be conscripted, although as a Quaker he would have refused to serve. However after Gallipoli the scientific establishment felt the need to safeguard post-war science against the loss of its best workers: the solar eclipse of May 1919 would provide an exceptional opportunity to test one of the predictions of Einstein's bold new theory of gravitation which challenged Newton's laws (Einstein predicted that starlight grazing the sun during total eclipse would be deflected by an amount significantly larger than the Newtonian value) and it was natural to choose Eddington to prepare two expeditions, and lead one. Overcoming difficulties at the end of the war, his successful photographic observation from Principe in the Gulf of Guinea was 'dramatic verification of Einstein's esoteric theory' (Gingerich, 282), shot the latter to fame, and overnight made Eddington a public figure. Like his rival Sir James Jeans he became a personality mentioned in the pages of Punch, and, following Jeans, he wrote highly successful popular scientific books. The best of them is perhaps The Nature of the Physical World (1928), while Space, Time and Gravitation (1920) was immensely important as the authoritative popularization of Einstein's theory. Brilliant, confident, generous to his students but brutal in debate, during the 1920s Eddington clashed with Jeans and latterly Milne at the Royal Astronomical Society but never bore grudges. In 1935 at the society he ridiculed the young Cambridge graduate S. Chandrasekhar who used quantum mechanics to calculate stellar collapse; Chandrasekhar was later proved right.

In two other, more subtle ways, general relativity affected Eddington's intellectual development. He already saw clearly that Einstein's theory had two distinct parts: first, a general and scarcely improvable formulation of what any possible relativistic gravitational theory should be, based on the 'tensor calculus'; second, a specific set of field equations for which the arguments were much weaker. Eddington attached importance to his alternative way of seeing the Einstein field equations as a mere definition of the absence of matter. This pushed him into the ontological position of seeing matter, not as substance, but as a construction. He was led in turn to thinking deeply about the nature of physical theory and to concluding that its results were not intrinsic results about the external world but were about the measurements that were made of the world. This was the first stage of an intellectual programme which dominated most of the rest of his life, though he was not able to carry it through. He perceived the basis of natural philosophy as epistemology.

The second subtle influence of relativity was a little more technical. Eddington's exposition of relativity, even more than Einstein's, relied heavily on the ability of the tensor calculus to generate in a mechanical way relativistically legitimate forms of mathematical theory. In common with other physicists and most mathematicians he also believed that, conversely, all legitimate forms were produced in this way and he stated as much in his book. It had become for him part of the scarcely corrigible general part of the theory. Since the turn of the century, general relativity had been only one of the two basic but inconsistent advances in physics. The other, quantum mechanics, which dealt with the very small, had advanced rapidly but without much attention from Eddington. Then in 1928 Paul Dirac, a young theoretical physicist, constructed an equation describing the electron in order to put right some of the defects of quantum mechanics in spectroscopy. It was relativistically legitimate and yet was not producible by the tensor calculus mechanism. Eddington was amazed and concerned.

Unified field theory, 1928-1944
Eddington's work in reaction to this discovery was his third major claim to fame, and in the long run probably his most enduring. It occupied nearly all his working time until his death in 1944. He began by thinking that something had mysteriously slipped through the net. The solution to the mystery, in his view, was Dirac's use of an unusual algebraic structure and Eddington set about elaborating this structure. His initial view was that quantum mechanics was a sub-theory of some elaborate structure that would arise from general relativity by incorporating the Dirac algebra. The suggestion of a unified theory of which general relativity and quantum mechanics would be special cases was at first received with interest and approval by the international community, for the schism in physics was widely regarded with horror. The analogy would be the way in which James Clerk Maxwell had united the disparate theories of magnetism and electricity in the nineteenth century.

Maxwell's unification had led to the theoretical determination of a physical constant, the speed of light, in terms of the electric and magnetic properties of the medium. So here, for Eddington, the unification would be expected to yield theoretical values of some of the numerical physical constants which had by now been discovered. Principal among these were the 'fine-structure constant' whose inverse is now measured to be 137.0360 and the ratio of the masses of the proton and the electron (now 1836.1527). Eddington began to publish his first speculations in that direction in an inadequate form in 1928. He related the inverse fine-structure constant with the 136 terms in his elaboration of the Dirac algebra. A more satisfactory presentation and a suggestion giving the mass-ratio within one per cent followed in 1932 and 1933. His international reputation sank rapidly. Of the most eminent theoretical physicists, only Erwin Schrödinger made a serious attempt to come to terms with Eddington's arguments. The generally held but mistaken opinion was that Eddington held the absurd belief that these measured constants could be determined from no physics at all. In fact, he was happy to borrow all kinds of qualitative results from physics but he saw the numerical constants as being part of what he had believed since 1919 to be epistemically based. They were structural parameters and the whole determination was seen as an investigation of physics as structure. There was no inherent impossibility in such an argument, and it is Eddington's lasting claim to fame to have pointed out its possibility.

There remains the question of the extent to which Eddington carried out the construction of the theory satisfactorily. The answer is rather complicated. By 1933 Eddington believed that he had satisfactorily determined four fundamental constants. His publications of these results had not produced much adverse criticism--he had become too eminent a figure for that--but the silence of his colleagues was even more significant. For the second time the pressures of the outside world intruded into his intellectual isolation. He saw clearly that the advent of Hitler made war very likely. He felt the need to get the theory into finished form before disaster struck, even if his usual polished style was beyond achievement. The result was The Relativity Theory of Protons and Electrons (1936), a book which none the less provides the best description of his later ideas.

Eddington had by now seen that his earlier search for a unified theory in which general relativity and quantum mechanics were special cases was doomed to failure because the two theories started from wholly different concepts. His new point of view was to allow general relativity and quantum mechanics their independent approaches and to search for physical problems, of which there might be very few, to which both approaches were applicable. It would now be the agreement between predicted numerical values in the two theories which would yield the numerical values of physical constants. Eddington's chosen problem was a very simplified cosmological model--the 'Einstein universe'--the discussion of which was well known in general relativity. It cannot be said that his corresponding discussion in quantum mechanics is clear or satisfactory.

The adverse criticism engendered by Protons and Electrons drove Eddington further into isolation. His critics held that he had not succeeded in his approach, probably because it was impossible. He could have taken on the second point successfully but instead he ignored it and concentrated on the first. For eight years he laboured on his Fundamental Theory, posthumously published in 1946, in which many more physical constants were determined. It is difficult not to see the hand of the successful popular science writer in its beautifully written failures to provide cast-iron proofs. Eddington's speculative imagination may be reminiscent of science fiction but must be seen in the light of his overriding and correct conviction that quantum mechanics was failing to provide any imaginative picture of the origin of discreteness which it introduced. Any inadequately formulated ideas pointing in the right direction were hugely exciting and more valuable to him and his readers than mathematically consistent theories going the wrong way. In Fundamental Theory the 'rigid field convention' was central to these attempts. It enabled quantum conditions to be isolated from the classical background. This and his earlier 1936 book, as well as his realization of the possibility of a structural theory in physics, remain his most important contributions.

Eddington was elected to the Royal Society in 1914, was awarded a royal medal in 1928, knighted in 1930, and appointed to the Order of Merit in 1938. He was president of the Royal Astronomical Society in 1921-3, of both the Physical Society and the Mathematical Association in 1930-32 and of the International Astronomical Union from 1938 until he died. He never married; he died from cancer in the Evelyn Nursing Home, Cambridge, on 22 November 1944. Eddington was a member of the Society of Friends throughout his life, and his religious beliefs shaped what he regarded as his most important scientific work. While it may seem that in searching for unified fields, and asserting the primacy of mind or consciousness over quantum uncertainty 'his religion led him into scientific dead-ends' (Batten, 268), those cross-disciplinary problems continue to occupy the best minds decades later.


A. V. Douglas, Arthur Stanley Eddington (1956)
The Times (23 Nov 1944)
H. C. Plummer, Obits. FRS, 5 (1945-8), 113-25
N. B. Slater, The development and meaning of Eddington's fundamental theory (1957)
private information (2004) [T. Bastin]
S. Chandrasekhar, Eddington, the most distinguished astrophysicist of his time (1983)
A. H. Batten, 'A most rare vision: Eddington's thinking on the relation between science and religion', Quarterly Journal of the Royal Astronomical Society, 35 (1994), 249-70
History of the Royal Astronomical Society, 2: 1920-1980, ed. R. J. Tayler (1987), 54-5
O. Gingerich, The great Copernicus chase and other adventures in astronomical history (1992), 282
H. S. Hogg, 'Variable stars', Astrophysics and twentieth-century astronomy to 1950, ed. O. Gingerich (1984), 73-89, esp. 84-6
CGPLA Eng. & Wales (1945)

ETH Bibliothek, Zürich, corresp. with H. Weyl
Hebrew University, Jerusalem, corresp. with Albert Einstein
ICL, corresp. with Herbert Dingle
Nuffield Oxf., corresp. with Lord Cherwell
Queen's University, Kingston, Ontario, corresp. and papers
RS, letters to Sir Joseph Larmor
Trinity Cam., papers
U. Cam., Institute of Astronomy, papers

W. Stoneman, two photographs, 1925-38, NPG
W. Rothenstein, chalk drawing, 1928-1929, NPG
A. John, chalk drawing, 1933, Trinity Cam.
H. Coster, photographs, 1936, NPG
photograph, 1939, Hult. Arch.
Elliott & Fry, photograph, 1942, NPG [see illus.]
H. Carter, photograph, Central Office of Information, London
photograph, RAS

Wealth at death  
£47,237 1s. 10d.: probate, 8 March 1945, CGPLA Eng. & Wales

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