MILNE, EDWARD ARTHUR

(b. Hull, England, 14 February 1896; d Dublin, Ireland, 21 September 1950)

astrophysics, cosmology.

Milne was one of the foremost pioneers of theoretical astrophysics and modern cosmology, and his name was often linked with those of Eddington and Jeans, although, unlike them, he wrote no books on astronomy for the general public. He was the eldest of three brothers who all entered on scientific careers. His father, Sydney Arthur Milne, was headmaster of a Church of England school at Hessle, near Hull, in Yorkshire. His mother, born Edith Coekcroft, lived to an advanced age and survived her famous son.

Milne went to school at Hymers College, Hull, and entered Trinity College, Cambridge, in 1914 with an open scholarship in mathematics and natural science, having gained a record number of marks in the examination. The first World War had already begun when Milne went to Cambridge, but his defective eyesight prevented him from undertaking active military duties. Early in 1916 he accepted the invitation of the biophysicist A. V. Hill to join the Anti-Aircraft Experimental Section (as it was later called) of the Munitions Inventions Department. The work was largely concerned with ballistics and sound ranging and involved many problems relating to the atmosphere of the earth. This was the beginning of Milne’s deep interest in atmospheric theory. For his war services he was awarded the M.B.E.

In 1919 Milne returned to Cambridge and soon afterward was elected a fellow of Trinity College. In 1920 H. F. New all appointed him assistant director of the solar physics observatory. In 1924 he succeeded Sydney Chapman as Beyer professor of applied mathematics at the University of Manchester, a post which he held until January 1929, when he became first Rouse Ball professor of mathematics at Oxford and fellow of Wadham College. He held both these posts for the rest of his life but was granted leave of absence during the Second World War, from 1939 to 1944, in order to work at the Ordnance Board, at Chislehurst in Kent. There he dealt with a wide variety of problems, including ballistics, rockets, sound ranging, and the optimum distribution of guns.

Important though his researches were to military science, it is by his original contributions to astrophysics and cosmology that Milne’s reputation must be judged. These fall into three clearly defined parts, which can be associated with three consecutive stages in his career. From 1920 to 1929 his researches centered on problems of radiative equilibrium and the theory of stellar atmospheres. From 1929 to 1932 he was mainly concerned with the theory of stellar structure, and from 1932 onward with relativity and cosmology.

Milne’s interest in stellar atmospheres was first aroused by H.F. Newall, who sensed his special fitness for the task of tackling theoretical problems associated with the outermost layers of stars, particularly those that concern the transfer of radiation through an atmosphere and those relating to the ionization of the material. These problems have to be combined, and this combination leads to subtle considerations of the detailed interaction of matter and radiation. It was in this field that Milne first made his name in astronomical circles, and it was primarily through his work that by the end of the 1920’s astrophysicists were provided with the theoretical techniques appropriate for the study of stellar atmospheres.

The idealized problem of radiative transfer through a scattering atmosphere without absorption was first studied by A. Schuster in a fundamental paper in 1905, and the theory of radiative equilibrium in an absorbing atmosphere was examined by K. Schwarzschild in 1906. Milne combined and extended these pioneer investigations. He soon realized that the concept of radiative equilibrium implies the constancy of the net flux of radiation through the atmosphere. He obtained an integral equation for this net flux and used it to derive a useful approximation for the dependence of temperature on optical depth. This work was not only of great scientific importance but also yielded a result of mathematical interest, an integral equation now known as Milne’s equation.

In his Smith’s Prize essay of 1922 (Philosophical Transactions of the Royal Society, 223A [1922], 201 255), Milne extended his theory to the law of darkening of a stellar disk toward the limb and its relation to the distribution of energy in the star’s continuous spectrum, assuming radiative equilibrium with a “gray” coefficient of absorption (that is, independent of wavelength). He demonstrated how closely this prediction was obeyed by the sun. Milne was the first to investigate the inverse problem of obtaining the temperature distribution from the observed darkening toward the limb. He also showed how both this and the observed continuous spectrum could be used to infer the dependence of opacity on frequeney. (Milne’s method was later used to show that the sun’s opacity is in fact due to the negative huirogen ion.) An admirable account of his theory and of related investimations was given by Milne in his “Thermodynamics of the Stars,” published as a part of the Handbuch der Astrophysik (1930), It was a milestone in the history of the subject and was the starting point for more elaborate investigations by E. Hopf, S. Chandrasekhar, and others.

In 1923 Milne began a fruitful collaboration with R. H. Fowler on the intensities and widths of absorption lines in stellar spectra. This work was based on M. N. Saha’s theory of high-temperature ionization. By modifying Saha’s technique, Milne and Fowler developed a theory of the maximum intensity, instead of the marginal appearance, of any given absorption line in the spectral sequence. They deduced that the pressures of the levels in stellar atmospheres at which absorption lines are formed are of the order of 10^-4 atmosphere, a value considerably lower than had previously been assumed. They were also able to determine a reliable temperature scale for the sequence of stellar spectra, one of the greatest advances in modern astrophysics. Although much of the work was Fowler’s, the original key idea was Milne’s.

Another problem to which Milne made a classic contribution was that of the escape of molecules from stellar and planetary atmospheres, In particular he investigated the equilibrium of the calcium chromosphere under the balance of gravitational forces and radiation pressure. He discovered that, for varying radiation from below, this equilibrium is unstable, so that in certain circumstances atoms can ultimately be ejected from the sun with velocities of the order of 1,000 kilometers a second.

Milne’s numerous papers on stellar atmospheres led to his election as a fellow of the Royal Society in 1926, at the age of thirty, and culminated in his Bakerian lecture of 1929, “The Structure and Opacity of a Stellar Atmosphere.” It was for his researches in this field that he was awarded the gold medal of the Royal Astronomical Society in 1935.

In May 1932 Milne turned his attention to the problem of the expansion of the universe. It occurred to him that this phenomenon might not be essentially different from the inevitable dispersion of a gas cloud liberated in empty space. Whatever its ultimate value, this simple idea fired his imagination and led him io develop an entirely new approach to theoretical cosmology. He abandoned the mathematically recondite method of general relativity and worked as far as possible in terms of special relativity and Euclidean space. He regarded Hubble’s empirical law of simple proportionality of the distances and recessional speeds of the galaxies as immediately explicable in terms of uniform motion. This meant that the common ratio of the respective distances and speeds of the galaxies provided a direct measure of the age of the universe, that is, of the time that has elapsed since the initial pointlike singularity when the universe was “created.” According to the scale of extragalactic distances determined by Hubble, this age was only some 2,000 million years, which is less than the ages now assigned to the sun and earth. According to the latest data bearing on Hubble’s law, based on revised estimates of extragalactic distances, the age of the universe, if it is of Milne’s type, would be nearer 10,000 million years, which is about twice the age now assigned to the sun and comparable with that currently assigned to the galaxy.

The second phase of Milne’s research career in astrophysics began with his move to Oxford in 1929. During the following three years he devoted his main energies to elaborating a theory of stellar structure based on a constructive mathematical criticism of the pioneer researches of Sir Arthur Eddington. Although much of Milne’s criticism of Eddington’s work has not been generally accepted, his methods led to important developments, notably T. G. Cowling’s fundamental study of the stability of gaseous stars and Chandrasekhar’s standard theory of white dwarf stars. In particular Milne seems to have been the first to suggest an association between the nova phenomenon and the collapse of a star from one configuration to another as a result of decreasing luminosity.

Milne’s world model is not in accord with general relativity, according to which a homogeneous isotropic world model that expands uniformly must be devoid of matter. Milne was not dismayed at this discrepancy, but instead made his kinematic approach to cosmology the basis of a new deductive system of theoretical physics, which came to be called kinematic relativity. He introduced the useful term “cosmological principle” to signify that observers associated with galaxies in his model and in many others, including those based on general relativity, would see similar “world pictures’s.

Milne went on to derive from his model many properties analogous to the laws of dynamics, gravitation, and electromagnetic theory. These developments of his theory were not generally accepted, and it is now thought that the most important effect of his work was that it led to fresh attempts to analyze the concepts of time and space-time. In particular A. G. Walker proved, as a generalization of Milne’s work, that the general metric of “orthodox” relativistic cosmology could be derived without appeal to general relativity, and G. J. Whitrow showed that special relativity can be based on determinations of distance in terms of time measurement by what is now called the radar technique. Milne himself was led to the conclusion that there may be different uniform scales of time operating in nature and that some of the fundamental constants of physics may vary with the cosmic epoch. He also showed, partly in collaboration with W. H. McCrea, that there exist useful Newtonian analogues of the expanding world models of relativistic cosmology and so was the founder of modern “Newtonian” cosmology.

Milne’s philosophical outlook was best expressed in his inaugural lecture at Oxford in 1929, in which he claimed that the primary aim of mathematical physics is to build up a system of theory rather than to seek the solution of particular problems.

Small in stature, Milne had outstanding qualities of mind and was a continual fount of inspiration to others as well as to himself. Although as a young man he was stricken with epidemic encephalitis (“sleepy sickness”), he made a remarkable recovery. For about twenty years after he recovered from the initial attack in 1923 he remained a man who radiated energy and vitality. Nevertheless, he did not escape the usual long-delayed aftereffects of encephalitis; and in the last five years of his life he suffered from rigidity of muscles and tremor of the left arm. Milne had the humility and simplicity of character that often goes with scientific genius, and he bore personal misfortunes with courage, dignity, and religious conviction. Both his wives predeceased him in tragic circumstances, and he was left to bring up three young daughters and a son. In his later years his heart became affected, and he died suddenly in Dublin, where he had gone to attend a scientific meeting.

BIBLIOGRAPHY

I. Original Works. “Thermodynamics of the Stars” and “Theory of Pulsating Stars” are in Handbuch der Astrophysik, III (Berlin, 1930), pt. 1, 65–255, and pt. 2, 804–821, respectively. Two of his books are Relativity, Gravitation and World-Structure (Oxford, 1935); and Kinematic Relativity (Oxford, 1948).

Milne contributed many original papers to scientific journals, notably Monthly Notices of the Royal Astronomical Society, Philosophical Transactions of the Royal Society, Proceedings of the Royal Society (sec. A), Philosophical Magazine, and Zeitschrift für Astrophysik. A complete list will be found at the end of the obituary notice by McCrea (see below).

Milne also wrote a valuable and highly individual textbook, Vectorial Mechanics (London, 1948), and left two other books in MS which were published posthumously: Modern Cosmology and the Christian Idea of God the Creator (Oxford, 1952) and Life of James Hopwood Jeans (Cambridge, l952).

II. Secondary Literature. Biographical notices are W. H. McCrea, in Obituary Notices of Fellows of the Royal Society of London, 7 (1951), 421–443; and in Monthly Notices of the Royal Aslnmoniical Society, 111 (1951), III, 160–170. The latter is followed by a short notice, pp. 170–172, by H. H. Plaskett. There is a short biographical notice by G. J. Whthrow in Nature, 166 (1950), 715–716. McCrea also wrote the article on Milne in the Dictionary of National Biography, 1941–1950, pp. 594–595.

G. J. Whitrow