A. S. Eddington

The End of the World: from the Standpoint of Mathematical Physics*

THE world—or space-time—is a four-dimensional continuum, and consequently offers a choice of a great many directions in which we might start off to look for an end; and it is by no means easy to describe “from the standpoint of mathematical physics” the direction in which I intend to go. I have therefore to examine at some length the preliminary question, Which end?

The Internal Constitution of the Stars

LAST year at Bournemouth we listened to a proposal from the President of the Association to bore a hole in the crust of the earth and discover the conditions deep down below the surface. This proposal may remind us that the most secret places of Nature are, perhaps, not 10 to the nth miles above our heads, but 10 miles below our feet. In the last five years the outward march of astronomical discovery has been rapid, and the most remote worlds are now scarcely safe from its inquisition. By the work of H. Shapley the globular clusters, which are found to be at distances scarcely dreamt of hitherto, have been explored, and our knowledge of them is in some respects more complete than that of the local aggregation of stars which includes the sun. Distance lends not enchantment, but precision, to the view. Moreover, theoretical researches of Einstein and Weyl make it probable that the space which remains beyond is not illimitable; not merely the material universe, but also space itself, is perhaps finite; and the explorer must one day stay his conquering march for lack of fresh realms to invade. But to-day let us turn our thoughts inwards to that other region of mystery—a region cut off by more substantial barriers, for, contrary to many anticipations, even the discovery of the fourth dimension has not enabled us to get at the inside of a body. Science has material and non-material appliances to bore into the interior, and I have chosen to devote this address to what may be described as analytical boring devices —absit omen!

On the Value of the Cosmical Constant

1. The cosmical constant λ occurs in Einstein’s law of gravitation G μv = λ g μv . In the resulting equations of motion the term containing λ represents a scattering force which tends to make all very remote bodies recede from one another; this phenomenon is the basis of the theories of de Sitter and Lemaitre concerning the “expansion of the universe.” If the observed recession of the spiral nebulae is a manifestation of this effect the value of λ can be found from the astronomical observations. In this paper I put forward a simple geometrical interpretation of the term in the wave equation which contains the mass m of an electron; this interpretation provides an alternative expression for the term. The new expression involves λ, and by equating it to the ordinary expression we find a theoretical value of λ, viz., 9⋅8.10-55 cm.-2. This agrees satisfactorily with the value found from the observed recession of the spiral nebulae (8).

Philosophy of Physical Science

I HAVE terminated my correspondence on the philosophical controversy; but since Dr. Swanns letter deals with a purely scientific question regarding the relations of relativity theory and quantum theory, I venture to offer some remarks.

The theoretical values of the physical constants

The principal physical constants are calculated by the theory developed in Relativity Theory of Protons and Electrons and subsequent papers, and are compared with the values given by Birge (1942) in Reports on Progress in Physics, 8. There is satisfactory agreement with Birges values as they stand. But the theory also indicates that small corrections are required in the computation of certain constants from experimental data; when these corrections are included, the small discordance between the spectroscopic and deflection values of e/mec disappears, and the agreement of observation and theory is complete. It is concluded that there ought to be no difference between the direct and indirect values of h/e. The calculated constant of gravitation is 6.6665.10-8; and it is pointed out that the expected agreement of the calculated and observed values is not affected by the mean chemical constitution of the universe or the free radiant energy in space - a point previously left doubtful. As the purpose is not to justify or explain the theory but to compare it with observation, theoretical explanation is limited to the points which arise in adapting the theory to practical comparisons.

Physics and Philosophy

I think it will be agreed that there is a domain of investigation where physics and philosophy overlap. There are branches of philosophy which do not approach the subject-matter of physics, and a great part of the work of practical and theoretical physicists is not aimed at extending our knowledge of the fundamental nature of things; but questions which concern the general interpretation of the physical universe and the significance of physical law are claimed by both parties. I suppose that ideally the physicist should be allowed to elucidate his own universe up to a point, and then hand it over to the philosopher to ascertain its exact status in relation to a wider outlook.

The Interior of a Star

The first “saucy look” into the fiery regions lying deep below the visible surface of the sun and stars is contained in a paper published by Homer Lane in 1870 “On the Theoretical Temperature of the Sun’’. His theory was further developed by A. Ritter, Lord Kelvin, and others; in particular the masterly work of R. Emden in his book Gas- kugeln has been invaluable as a basis of recent advances. Progress in thermodynamics and atomic physics has led to modifications of the original theory and to further opportunities of advance, so that we now appear to have reached a stage at which the study of the deep- lying conditions enables us to predict to some extent the surface features accessible to observation, and we may appeal to experiment to declare that our professed knowledge of the interior is something more than “base authority from others’ books”.

The Philosophy of Physical Science

Preface 1. Scientific epistemology 2. Selective subjectivism 3. Unobservables 4. The scope of epistemological method 5. Epistemology and relativity theory 6. Epistemology and quantum theory 7. Discovery or manufacture 8. The concept of analysis 9. The concept of structure 10. The concept of existence 11. The physical universe 12. The beginnings of knowledge 13. The synthesis of knowledge Index.

The Mass of the Universe

UNDOUBTEDLY, the mass of the radiation should be added to the mass of the stars and of the nebulous matter in computing the total mass of the universe. But the general belief is that its contribution is comparatively small—less than 1 per cent of the whole. This is not inconsistent with the figures cited by Admiral Beadnell. With radiation at the rate of 4 × 1028 tons per second, it would take 5 × 1018 seconds, or more than 1011 years, to accumulate to 1 per cent of the total mass 2 × 1049 tons. According to cosmological theory, the age of the stars can scarcely exceed 1010 years.

New Pathways in Science

Preface 1. Science and experience 2. Dramatis personae 3. The end of the world 4. The decline of determinism 5. Indeterminacy and quantum theory 6. Probability 7. The constitution of the stars 8. Subatomic energy 9. Cosmic clouds and nebulae 10. The expanding universe 11. The constants of nature 12. The theory of groups 13. Criticisms and controversies 14. Epilogue Index.