Arthur Stanley Eddington, Kt., O.M., F.R.S., Hon.F.R.S.E.
by W M H GreavesArthur Stanley Eddington, who was born on December 28, 1882, at Kendal in Westmorland, was the second child and only son of Arthur H Eddington, headmaster of the Friends' School in Kendal, and Sarah Ann Eddington née Shout. In 1884 the father died of typhoid, and the family moved to Weston-super-Mare where Eddington received his early education at Bryn Melyn School. In 1898 he entered Owens College, Manchester, obtaining at the end of his course a first-class honours degree in physics, and moreover attending all the honours lectures in mathematics. From Manchester he proceeded to Trinity College, Cambridge, graduating as Senior Wrangler in the Mathematical Tripos Of 1904, and being placed in the following year in Class 1, Division I of Part II of the Tripos. He was Smith's Prizeman in 1907, and was elected a Fellow of Trinity in the same year. But previous to this he had left Cambridge, having accepted, in 1906, the post of Chief Assistant at the Royal Observatory, Greenwich.
It is probable that his original intention was to be primarily a physicist; at any rate prior to leaving Cambridge he worked in the Cavendish Laboratory on thermionic emission. But although he forsook this work and became officially an astronomer, his outlook remained essentially physical, and in addition to attaining the first rank as a theoretical astronomer, he was destined to take his place among the leading theoretical physicists of our time. He remained for seven years at Greenwich and, in taking his share in routine observations, he acquired an experience in observational astronomy which supplemented his earlier laboratory training and was to stand him in good stead. Unlike some theorists, Eddington was always able to appraise correctly the value of experimental and observational evidence, and he possessed a firm grip on the principles governing the interplay between theory and experiment which determine the development of any physical science. He never hesitated to set up hypotheses and to follow up their consequences, and his attitude to hypotheses may be gathered from two extracts from his first book, Stellar Movements and the Structure of the Universe. In the preface he wrote: "There can be no harm in building hypotheses, and weaving explanations which seem best fitted to our present partial knowledge. These are not idle speculations if they help us, even temporarily, to grasp the relations of scattered facts, and to organise our knowledge." And again on page 243 of the same book he wrote with regard to spiral nebulae (it must be remembered that this book was published in 1914 - twelve years before the determination of the distances of the nearer spirals established that they were systems similar to the Galactic System of stars): "If the spiral nebulae are within the stellar system, we have no notion what their nature may be. That hypothesis leads to a full stop. ... If, however, it is assumed that these nebulae are external to the stellar system, that they are in fact systems co-equal with our own, we have at least an hypothesis which can be followed up, and may throw some light on the problems that have been before us. For this reason the 'island universe' theory is much to be preferred as a working hypothesis; and its consequences are so helpful as to suggest a distinct probability of its truth."
At the same time Eddington never forgot the function of physical hypothesis, namely the deduction from it of consequences capable of experimental and observational test. To him experiment and observation were always the final court of appeal whenever a physical hypothesis had been introduced, as they must be to any Natural Philosopher. But this did not mean that he accepted experimental results blindly and uncritically. It was here that his early training came to his aid and, for example, he would never abandon a hypothesis without further examination simply because an experimenter had produced a measure and probable error which seemed to negative the hypothesis. He had played the experimental game himself, and he knew how to assess results, when to accept, and when to defer judgment. These critical faculties he of course shared with many others. But on the theoretical side of research he was, on his own ground, supreme; and he possessed a flair for choosing a profitable hypothesis and a perfectly extraordinary power of physical insight.
In 1913 Eddington left Greenwich for Cambridge, on his election to the Plumian Chair of Astronomy, a Chair which he retained till his death. He was elected a Fellow of the Royal Society in 1914 and was awarded its Royal Medal in 1928. In 1924 he was awarded the Gold Medal of the Royal Astronomical Society, and in the same year he was awarded the Bruce Gold Medal of the Astronomical Society of the Pacific. He was President of the Royal Astronomical Society during 1921-23, and President of the Physical Society during 1930-32. He was created a Knight Bachelor in 1930, and received the Order of Merit in 1938. He was honoured by many Universities and Academies, and at the time of his death was President of the International Astronomical Union.
His major work can be divided into four groups, viz.: Statistical Astronomy, General Relativity, the Theory of Stellar Structure, and the fusion of Relativity and Quantum Theory. As regards the first two of these Eddington merely took his place among other leading scientists, and in addition to his own contributions he performed the necessary and useful task of collecting and presenting various researches in a coherent and rational form. But in the Theory of Stellar Structure and in the fusion of Relativity and Quantum Theory he was engaged in the development of subjects which were essentially his own, and in which his physical insight had full scope. He was primarily, as I have said, a theoretical physicist, and his general attitude towards theoretical research in physics has been stated by himself in his book The Internal Constitution of the Stars. The following is quoted from pages 101-103 of that book. The extract is not as widely known as it should be:
"I conceive that the chief aim of the physicist in discussing a theoretical problem is to obtain 'insight' - to see which of the numerous factors are particularly concerned in any effect and how they work together to give it. For this purpose a legitimate approximation is not just an unavoidable evil; it is a discernment that certain factors-certain complications of the problem-do not contribute appreciably to the result. We satisfy ourselves that they may be left aside; and the mechanism stands out more clearly, freed from these irrelevancies. This discernment is only a continuation of a task begun by the physicist before the mathematical premises of the problem could be stated; for in any natural problem the actual conditions are of extreme complexity and the first step is to select those which have an essential influence on the result - in short, to get hold of the right end of the stick. The correct use of this insight, whether before or after the mathematical problem has been formulated, is a faculty to be cultivated, not a vicious propensity to be hidden from the public eye. Needless to say the physicist must if challenged be prepared to defend the use of his discernment; but unless the defence involves some subtle point of difficulty it may well be left until the challenge is made.
"I suppose that the same kind of insight is useful to the mathematician as a tool; but he is careful to efface the tool marks from his finished products-his proofs. He is content with a rigorous but unilluminating demonstration that certain results follow from his premises, and he does not generally realise that the physicist demands something more than this. For the physicist has always to bear in mind a thousand and one other factors in the natural problem not formulated in the mathematical problem, and it is only by a demonstration which keeps in view the relative importance of the contributing causes that he can see whether he has been justified in neglecting these. As regards rigour, the physicist may well take risks in a mathematical deduction if these are no greater than the risks incurred in the mathematical formulation. As regards accuracy, the retention of absurdly minute terms in a physical equation is as clumsy in his eyes as the use of an extravagant number of decimal places in arithmetical computation.
"Having said this much on the one side we may turn to appreciate the luxury of a rigorous mathematical proof. If the results obtained do not agree with observation the fault must assuredly lie with the premises assumed. The mathematician's power of narrowing down the possibilities supplements the physicist's power of picking out the probabilities. If space were unlimited we might try to duplicate investigations where necessary so as to satisfy both parties. But if one investigation must suffice I do not think we should usually give way to the mathematician. Cases could be cited where physicists have been led astray through inattention to mathematical rigour; but these are rare compared with the mathematicians' misadventures through lack of physical insight.
"The point to remember is that when we prove a result without understanding it-when it drops unforeseen out of a maze of mathematical formulae - we have no ground for hoping that it will apply except when the mathematical premises are rigorously fulfilled - that is to say, never, unless we happen to be dealing with something like aether to which 'perfection' can reasonably be attributed. But when we obtain by mathematical analysis an understanding of a result - when we discern which of the conditions are essentially contributing to it and which are relatively unimportant - we have obtained knowledge adapted to the fluid premises of a natural physical problem.
"I think the idea that the purpose of study is to arrive at a string of proofs of propositions is a little overdone even in pure mathematics. Our purpose in studying the physical world includes much that is not comprised in so narrow an ideal. We might indeed say that, whereas for the mathematician insight is one of the tools and proof the finished product, for the physicist proof is one of the tools and insight the finished product. The tool must not usurp the place of the product, even though we fully recognise that disastrous results may occur when the tool is badly handled."
It should be remarked at this point that Eddington was himself a master in the art of using mathematical analysis for obtaining an understanding of a physical result. A mathematician in the narrow sense he certainly was not, and we may well surmise that he would not have been particularly pleased by any suggestion that he was. His ability in mathematical manipulation was of a very high order, but the tool was always subordinated to the physical aim. The inductive nature of physical research occupied a prominent place in his mind. On page 105 of The Mathematical Theory of Relativity we find him writing: "We may put to the experiments three questions in crescendo. Do they verify? Do they suggest? Do they (within certain limitations) compel the laws we adopt? It is when the last question is put that the difficulty arises for there are always limitations which will embarrass the mathematician who wishes to keep strictly to rigorous inference." At the same time Eddington was not the man to bind himself slavishly to any system of Natural Philosophy, and the attitude he adopted in his work on the unification of Relativity and Quantum Theory must have scandalised those whose minds could not escape from the literal conceptions of inductive physics which they had inherited from their predecessors. For he perceived that a stage had been reached in which it was possible, not only to avoid the formulation of new physical hypotheses, but to deduce a number of quantitative physical results solely from principles based on established qualitative physics, and he advanced the view that, in this field, experiment need only be used to establish the qualitative framework. In his own words (pages 3 and 4 of Relativity Theory of Protons and Electrons): "All that we require from observation is evidence of identification - that the entities denoted by certain symbols in the mathematics are those which the experimental physicist recognises under the names 'proton' and 'electron'. Being satisfied on this point, it should be possible to judge whether the mathematical treatment and solutions are correct, without turning up the answer in the book of nature. My task is to show that our theoretical resources are sufficient and our methods powerful enough to calculate the constants exactly - so that the observational test will be the same kind of perfunctory verification that we apply sometimes to theorems in geometry." To this remark the writer of this notice (a former pupil of Eddington) adds the comment that the verification has been, in fact, anything but perfunctory, and that the agreement of the values of physical constants deduced from epistemological principles with those obtained by measurement using the most elaborate laboratory methods available is complete within the limits of experimental error. Further reference to this will be made presently.
The remark about geometry made in the extract just quoted is very apt. There has been some considerable misunderstanding about the character of this part of Eddington's work, in which he succeeded in deriving correctly the values of all those constants of nature which are pure numbers (such as the ratio of the mass of the proton to the mass of the electron). It has sometimes been supposed (erroneously) that Eddington claimed to have derived the whole of physics, or a large part of it, by pure cogitation, without depending in any way on the results of observation and experiment. Such an idea is refuted at once by an examination of the papers themselves. The position may be illustrated by reference to the history of an older problem. The ancient Egyptians were acquainted with the fact that the ratio of the area of a circle to the square on its radius was independent of the size of the circle; and for this number, which we denote by π, they found, by actual measurement, the value 256/81 (= 3.16...). In the third century before Christ, Archimedes showed that the number can be found to any desired degree of accuracy by pure theory, without the necessity for making measurements. For this purpose he assumed the axioms and propositions of geometry as they had been set forth in the preceding generation by Euclid; so that what Archimedes did was to assume the qualitative part of geometry and to deduce a quantitative aspect of it, namely the number π.
Now, as Sir Edmund Whittaker has remarked, Eddington is simply the modern Archimedes. He regarded himself as at liberty to borrow anything in qualitative physics - he did in fact assume the identity of mass and energy, the theory of the energy-tensor and the interpretation of its elements, the exclusion principle, and other propositions of the most advanced physical theory - but he did not assume any number determined empirically; and he deduced the quantitative propositions of physics, i.e. the exact values of the pure numbers that are constants of science - the numbers that are analogous to the number π in geometry.
It was Eddington's outstanding genius which led him to see that a stage had been reached in physics at which a rationalisation of the kind indicated was possible. In other researches, notably in his researches on stellar structure, his attitude was more nearly that of the orthodox inductivist (as, in fact, the nature of the subject demanded), and having set up specific physical hypotheses he would naturally appeal to observation on every possible occasion to check the deductions from them. In this field his genius took the form of a remarkable power of backing the winner, i.e. of selecting the most profitable hypotheses. His attitude here was essentially the attitude of the majority of contemporaneous theoretical physicists, but his physical insight was greater than that of the majority. It is distinctly startling to find that his later work on fundamental physics has produced a criticism to the effect that he was a mathematician who did not understand physics. To anyone conversant with his work such an idea is simply ridiculous, and it probably arises from the circumstance that in Eddington's later writings he does not exactly make things easy for a reader whose mental calibre is less than that of his own. His brain was no ordinary brain, and matters which were obvious to him, and which he treated as obvious, are by no means obvious to others. But it is usually the case that the requisite mental effort leads to agreement with his statements. At any rate it is certain that theoretical physics can never again be the same subject as it was before Eddington began the series of investigations which occupied a considerable part of the last sixteen years of his life. No theoretical physicist can afford not to study Eddington's work if he wishes to be fundamental, and the younger generation of physicists should not find the necessary adaptation of their ideas an impossible task. A situation has arisen somewhat analogous to that which resulted from the appearance of Maxwell's electro-magnetic theory, a theory which was altogether too much for some of Maxwell's contemporaries.
Turning to a brief résumé of some details of Eddington's work, his earlier activities on the subject of stellar statistics culminated in the publication, in 1914, of Stellar Movements and the Structure of the Universe. In addition to containing an account of his own contributions in this field, notably his investigations on the phenomenon of star streaming, the book aimed at giving a connected account of researches in sidereal astronomy and at co-ordinating them as far as was possible at the time. The final chapter dealt with the dynamics of the stellar system, a subject to which Eddington himself subsequently contributed. Much progress in the fields covered by the book has been made since, and some of this progress must be attributed to the stimulus provided by Eddington's first book.
But Eddington sought other fields to conquer. To astrophysicists he is known as the man who produced a systematised and coherent theory of the structure of stars. In a long series of papers he worked out (on a simple hypothesis as to the liberation of subatomic energy which he showed to be capable of giving a good approximation) his theory of the radiative equilibrium of the interior of a star; and the observable properties of real stars show a striking resemblance to those of what is known as Eddington's model. Assuming the perfect gas law he deduced a theoretical relationship between the mass of a star and its total output of radiation. He himself expected this relation to apply only to "giant stars" for which the average density is low and the material could be expected to be in the gaseous state throughout. But the observational data confirmed the theoretical relationship not only for giant stars but also for stars of the main sequence, such as the Sun, whose mean densities are of the order of that of water and for which the inferred densities at the centre can be as much as several hundred times that of water. Since the theoretical relation was based on the assumption that the gas law was obeyed approximately throughout the interior of a star, the agreement with observation indicated that the gas law is still valid for high densities, a result which at first sight seemed to be contradictory to ordinary experience. Eddington at once suggested an explanation. He pointed out that the atoms in a star are very much smaller than ordinary atoms. Owing to the high thermal ionization in the interior several layers of electrons have been stripped away, and the gas laws ought therefore to hold up to far greater densities. Eddington estimated that the atoms of moderate atomic weight would be stripped down to the K level and would have radii of the order of 10-10cm.; lighter elements such as carbon and oxygen would be reduced to the bare nucleus. The maximum density, corresponding to contact of these reduced atomic spheres, would be at least 100,000 and any star with mean density below 1000 ought to behave as a perfect gas.
The next step in Eddington's argument was sensational. An immediate corollary of his ideas is that in the stars it should be physically possible for matter to exist up to densities of the order of 100,000 times that of water, and that stars composed of matter of these transcendently high densities should not conform to his theoretical mass-luminosity relationship since the gas law would then no longer hold. Now the companion to Sirius, a star of the kind known as a "white dwarf", did not obey the mass-luminosity relationship, and the ordinary methods of calculating the average density of a component of a binary star led to a density of 53,000, i.e. of the order of a ton per cubic inch. This result had been previously dismissed as absurd, and it had been surmised that the spectroscopic estimate of surface temperature (which enters into the determination of radius) was at fault, the star being, according to this view, a star of very low surface temperature which was in some unspecified way able to imitate the spectral characteristics of a star of surface temperature 1000. But Eddington calmly remarked that according to the views that he had developed the high density was not absurd, and he reminded spectroscopists that an observational test was available; if the high density were correct, the Einstein shift of the spectrum should amount to about 20 km./sec. The existence of stellar matter at very high densities is now taken for granted, and to appreciate Eddington's scientific fearlessness and his power of emancipating himself from the influences of contemporaneous thought one must recapture the atmosphere of 1924. The idea then seemed simply fantastic, and probably caused inevitably derogatory comment on the part of some people. But the possibility of comment of this kind never prevented Eddington from pursuing his ideas to their logical conclusion.
It is of interest to recall the train of events which was fired by his physical insight. Stimulated by Eddington's paper, Adams of Mount Wilson measured the red-ward shift of the spectral lines of the companion to Sirius and established that the shift was, in fact, about 20 km./sec. In 1926 R H Fowler (afterwards Sir Ralph Fowler) published a paper "On Dense Matter" wherein he showed that the material in stars like the companion to Sirius must consist of a gas in what is called the degenerate state, i.e. a gas obeying the quantum statistics discovered independently by Dirac and Fermi. The highly ionised atoms were pressed close together, as Eddington had maintained, and the free electrons formed a degenerate gas - as Fowler put it "like a gigantic molecule in its lowest quantum state". The properties of degenerate matter now constitute an important department of physics, and it was shown by Sommerfeld that the electrons in a solid metal conductor are not attached to particular atoms but, constitute a degenerate gas at an apparent very low temperature (a gas becomes degenerate for sufficiently high densities or for sufficiently low temperatures). Eddington's name occupies an honoured place in the literature of the subject (to which he made further contributions in later years); it was Eddington who first realised the actual physical existence (in white dwarf stars) of degenerate matter.
The derivation of the relation between the mass and luminosity of a star and the contributions to physical knowledge immediately associated with it forms a very important part, but nevertheless only a small part, of Eddington's work in theoretical astrophysics. It is impossible in this notice adequately to survey his astrophysical researches, and only a brief mention can be made of some of his more outstanding achievements in this field. He initiated and developed the pulsation theory of Cepheid variable stars, the idea being that such stars are in a state of oscillation about the equilibrium position considered in the main radiative equilibrium theory. Eddington showed that his pulsation hypothesis would account for the major characteristic of Cepheids, the relation between period and luminosity. But some difficulties still have to be resolved and the theory cannot be said to be completely established. After a false start represented by his "nuclear capture" hypothesis, which he soon discarded, he applied Kramers' theory of electron capture to the calculation of the opacity of stellar matter, and he thereby opened up a road which led him to the determination of the hydrogen content of a star; the realisation that the hydrogen content was high (about one-third of the total matter) emphasised the view that the liberation of subatomic energy necessary to maintain the outflow of radiation was due to the transmutation of hydrogen into helium, and eventually led to the study of the astrophysical applications of thermo-nuclear, reactions, in particular to the suggestion by Bethe and Weizsacker independently that the carbon-nitrogen cycle was effective for stars like the Sun. Other notable researches are Eddington's study of matter in interstellar space and his theory of the formation of absorption lines in stellar atmospheres which in more recent years has been referred to as a "classical paper". His astrophysical contributions up to 1926 are collected in a systematised treatment in his Internal Constitution of the Stars, but some important researches appeared in papers subsequent to the publication of this book. Incidentally Eddington may be said finally to have overthrown the boundary, never very well defined, between astrophysics and "pure physics" and to have emphasised the importance of the stars as laboratories in which matter can be studied under conditions of temperature and pressure not otherwise available. Astronomy was very fortunate to have secured the services of a very great physicist, and in doing so it eventually lost some of its isolationism and independence - to its great advantage.
With regard to Eddington's activities in the field of General Relativity only a brief outline is possible here. He has been described as the "apostle of relativity in this country". He was the first British scientist to appreciate the importance of Einstein's original papers, and he was largely responsible for the decision to send two British expeditions to test the predicted deflection of light on the occasion of the solar eclipse of May 29, 1919. The results obtained by these expeditions confirmed Einstein's prediction within the limits of observational error. In the subsequent development of the theory Eddington himself took part, and an account of his own contributions to generalised non-Riemannian geometry was included in his book The Mathematical Theory of Relativity published in 1923. This had been preceded in 1920 by Space, Time and Gravitation which gave a non-mathematical account of the theory, and which is especially valuable since it was written by a physicist from an essentially physical point of view.
From 1917 to 1928 Eddington had appeared in the alternate roIes of a relativist and a worker in the field of atomic physics with special reference to the properties of cosmical matter. From 1928 onwards his activities were largely (but by no means exclusively) devoted to a new and original theory in which he aimed at a fusion of Quantum Theory and Relativity. Coming events cast their shadows before, and on pages 78-179 of Space, Time and Gravitation (1920) appears the following (in connection with Weyl's theory):
"Finally the theory suggests a mode of attacking the problem of how the electric charge of an electron is held together; at least it gives an explanation of why the gravitational force is so extremely weak compared with the electric force. It will be remembered that associated with the mass of the sun is a certain length, called the gravitational mass, which is equal to 1.5 kilometres. In the same way the gravitational mass or radius of an electron is 7.10-56cm. Its electrical properties are similarly associated with a length 210-13cm., which is called the electrical radius. The latter is generally supposed to correspond to the electron's actual dimensions. The theory suggests that the ratio of the gravitational to the electrical radius, 3.1042,ought to be of the same order as the ratio of the latter to the radius of curvature of the world."
And again on page 167 of The Mathematical Theory of Relativity (1923) we find (in connection with Einstein's Cylindrical World):
"In favour of Einstein's hypothesis is the fact that among the constants of nature there is one which is a very large pure number; this is typified by the ratio of the radius of an electron to its gravitational mass = 3.1042.It is difficult to account for the occurrence of a pure number (of order greatly different from unity) in the scheme of things; but this difficulty would be removed if we could connect it with the number of particles in the world - a number presumably decided by pure accident. There is an attractiveness in the idea that the total number of the particles may play a part in determining the constants of the laws of nature; we can more readily admit that the laws of the actual world are specialised by the accidental circumstances of a particular number of particles occurring in it, than that they are specialised by the same number occurring as a mysterious ratio in the fine-grained structure of the continuum."
From these extracts it will be seen that as early as 1920 Eddington's mind was tentatively and vaguely reaching out towards a fusion of the very great and the very small, a fusion of the macroscopic theory of relativity and the microscopic atomic physics. It was at about this time (1921) that he conceived the conviction that the true foundation of physics must be in epistemology-the theory of knowledge. The stage was being set for the last great act in Eddington's career and the curtain rang up when in 1928 there appeared Dirac's celebrated paper on the wave equation of the electron, in which it was shown that the power of the quantum theory to explain atomic phenomena could be greatly increased by introducing relativistic ideas. Eddington at once realised the importance of Dirac's wave equation, and he felt that the time had come to construct a comprehensive theory combining and transcending both quantum mechanics and relativity. His line of attack was to find a common meeting-point of the two-to consider a problem which could be solved rigorously by both methods. Such a problem is that of an Einstein radiationless universe (in the relativity sense) consisting of hydrogen, i.e. of protons and electrons. This system forms on the one hand a closed macroscopic system with a definite radius and on the other a quantised system in its ground state. The two answers must agree; and since the relativity solution will be expressed in terms of the gravitational constant and the cosmical constant, whereas the quantum solution will be expressed in terms of Planck's constant and other microscopic constants, it is evident that a comparison of the two will yield a relation between the constants of Nature.
This idea started Eddington off on a long and difficult journey which led him to a Fundamental Theory of Physics, some of the philosophical aspects of which have already been mentioned. He was led to numerical values for four fundamental dimensionless constants of Nature. Two of these are the fine structure constant and the ratios of the masses of the proton and electron. Another dimensionless constant is the ratio of the constant of gravitation to a constant of similar dimensions obtained from other physical constants, and the total number N of protons and electrons in the radiationless Einstein universe of hydrogen is the fourth. These four dimensionless constants having been deduced, then if the experimentally determined values of three physical constants (possessing dimensions) are adopted, the values of other physical constants can be calculated in terms of grammes, centimetres and seconds. Eddington adopts the experimentally determined values of the velocity of light, the Rydberg constant for hydrogen and the Faraday constant for hydrogen. He deduces the values of the electronic charge, the Planck constant, the constant of gravitation, the speed of recession of the galaxies, the forces between protons in the nucleus, the masses of the electron, the proton, the neutron and the cosmic ray meson, the mass defects of deuterium and helium, the separation constant of isobaric doublets, the lifetime of the cosmic ray meson, and the magnetic moments of the hydrogen atom and the neutron. In all cases the values so found agree with the observed values within the margin of observational error. Eddington's own attitude to this agreement has been indicated above; to him the agreement probably seemed merely inevitable and constituted "the same kind of perfunctory verification that we apply sometimes to theorems in geometry". But to many scientists it is the agreement between theory and experiment which will still make the strongest appeal, and they will accept the agreement as indicating that Eddington's work is firmly based on physical truth.
One of the four fundamental dimensionless constants is the total number of protons and electrons in the ideal radiationless Einstein universe of hydrogen. This number N is the "cosmical number"; as defined it is perfectly definite, but it has unfortunately been loosely described as the "number of particles in the universe"; and this description, which obscures the point that N is defined with respect to a very definite idealised universe and not with regard to the actual universe, has led to much misunderstanding. It may be asked: Why define a fundamental constant in such an artificial way? Why not frame the definitions with respect to actual physical existence? This kind of question misses the real point, which is that we must approach the whole matter by selecting a problem which is capable of treatment both by relativistic and quantum methods. The ideal universe considered provides such a problem, and our questioner is probably subject to some mental confusion between actual physical existence and physical possibility. The following is quoted from Eddington's Relativity Theory of Protons and Electrons (page 280):
"Although the relations between the natural constants have here been calculated for a special distribution of matter, they must hold for the irregular distribution in the actual universe. In determining the constant of gravitation experimentally, the physicist is not forbidden to arrange the matter in his laboratory in any way that suits the experiment; similarly the theoretical physicist is not forbidden to arrange the matter of the universe in any way that makes his calculation easier. In either case the value found for the constant will apply to all distributions, however widely they may differ from those used in the experiment or the calculation. Only we must take note that, in rearranging the matter to suit his purpose, the experimenter cannot, and the theorist must not, violate any law of nature. Thus we have had to defend our rearrangement of the universe as a static configuration, by showing that the matter of the universe is necessarily such that it possesses a static configuration."
The number N, as defined, is actually a very important constant for which Eddington has derived the value 3/2 .136.2256.It enters into many physical formulae, e.g. it determines the ratio of the electrical to the gravitational force between a proton and an electron, the range and magnitude of the non-Coulombian forces between the heavy particles in atomic nuclei, etc. It takes its place as one of the fundamental numbers of physics and may well be known as "Eddington's Number".
Eddington's treatment of gravitation is of some interest as illustrating the unifying nature of the new fundamental physics. The proper-energy (which is the same as proper-mass) of an observed. particle depends on the highest energy level of the Einstein world. If, however, the system which is observed contains a large number of particles, the uppermost energy levels would have become exhausted in supplying them, and it would be necessary to include some particles from deeper levels, which have a lower proper-energy. This fact, that the proper-energy of n particles is less than n times the proper-energy of one particle, is identified by Eddington with the phenomenon of gravitation, the difference in energy being what is ordinarily described as gravitational potential energy. Gravitation is thus a consequence of the exclusion principle, which forbids multiple occupation of energy levels. But Eddington went beyond this; he linked gravitation and exclusion with two other physical principles, namely interchange and Coulomb energy.
The results of Eddington's researches in this field up to the year 1936 were presented systematically in his book Relativity Theory of Protons and Electrons, which was based almost entirely on what he called the "spin extension" of relativity theory. After this he approached the same problems by a different method, which he called the "statistical extension" of relativity theory; an account of this was given in his Dublin lectures of 1942, The Combination of Relativity Theory and Quantum Theory (published in 1943), in which he showed that the new principle permitted the calculation of all the fundamental physical constants except the cosmical number. In the last months of his life he planned, and almost completed, a book in which both methods were combined, and which was intended to replace all his previous writings on the theory; this will be published by the Cambridge University Press.
The Fellows of our Society will join with the whole scientific world in lamenting the loss caused by Eddington's untimely death on November 22, 1944. Indeed we in the Royal Society of Edinburgh are ourselves directly bereaved, for Eddington has been a member of our body since his election to Honorary Fellowship in 1930. Astronomers and physicists can only console themselves with the reflection that there are those in their ranks today who will assuredly develop the territories gained by a great master of theoretical physics. No man's work can be fully judged until the lapse of time supplies the proper perspective, but we may rest assured that in the future adjudication of his scientific merit Arthur Stanley Eddington will be awarded a high place. It may well be that he will be recognised as the greatest Natural Philosopher of our age.
Arthur Stanley Eddington's RSE obituary by W M H Greaves appeared in Royal Society of Edinburgh Year Book 1946, 22-30.
See also Obituary Notices of Fellows of the Royal Society, V, 1945, 113-125.
See also Obituary Notices of Fellows of the Royal Society, V, 1945, 113-125.