*Reference: Einstein’s 1920 Book*

*This paper presents Part III, Chapter 1 from the
book RELATIVITY: THE SPECIAL AND GENERAL THEORY by A. EINSTEIN. The
contents are from the original publication of this book by Henry Holt and
Company, New York (1920).*

*The paragraphs of the original material (in black) are accompanied
by brief comments (in color) based on the present understanding. Feedback
on these comments is appreciated.*

*The heading below is linked to the original materials.*

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## Cosmological Difficulties of Newton’s Theory

Apart from the difficulty discussed in Section XXI, there is a second fundamental difficulty attending classical celestial mechanics, which, to the best of my knowledge, was first discussed in detail by the astronomer Seeliger. If we ponder over the question as to how the universe, considered as a whole, is to be regarded, the first answer that suggests itself to us is surely this: As regards space (and time) the universe is infinite. There are stars everywhere, so that the density of matter, although very variable in detail, is nevertheless on the average everywhere the same. In other words: However far we might travel through space, we should find everywhere an attenuated swarm of fixed stars of approximately the same kind and density.

*We may assume the whole
universe to be flat like a galaxy rotating whirlpool like. It extends outwards
beyond it relatively solid core. Therefore, it is unlikely to have a uniform
density of matter.*

This view is not in harmony with the
theory of Newton. The latter theory rather requires that the universe should
have a kind of centre in which the density of the stars is a maximum, and that
as we proceed outwards from this centre the group-density of the stars should
diminish, until finally, at great distances, it is succeeded by an infinite
region of emptiness. The stellar universe ought to be a finite island in the
infinite ocean of space. *[Proof.—According
to the theory of Newton, the number of “lines of force” which come from
infinity and terminate in a mass m is proportional to the mass m. If, on the
average, the mass-density P _{0} is constant throughout the universe,
then a sphere of volume V will enclose the average mass P_{0}V. Thus
the number of lines of force passing through the surface F of the sphere into
its interior is proportional to P_{0}V. For unit area of the surface of
the sphere the number of lines of force which enters the sphere is thus
proportional to P_{0} · v/F} or P_{0}R. Hence the intensity of
the field at the surface would ultimately become infinite with increasing
radius R of the sphere, which is impossible.]*

*The universe as a
whirlpool is in harmony with both the theory of Newton and the general theory
of relativity.*

This conception is in itself not very satisfactory. It is still less satisfactory because it leads to the result that the light emitted by the stars and also individual stars of the stellar system are perpetually passing out into infinite space, never to return, and without ever again coming into interaction with other objects of nature. Such a finite material universe would be destined to become gradually but systematically impoverished.

*On an infinite scale,
light shall not be traveling in a straight line. It has some amount of inertia,
so its path shall be curved. It will be part of an infinite whirlpool.*

In order to escape this dilemma, Seeliger suggested a modification of Newton’s law, in which he assumes that for great distances the force of attraction between two masses diminishes more rapidly than would result from the inverse square law. In this way it is possible for the mean density of matter to be constant everywhere, even to infinity, without infinitely large gravitational fields being produced. We thus free ourselves from the distasteful conception that the material universe ought to possess something of the nature of centre. Of course we purchase our emancipation from the fundamental difficulties mentioned, at the cost of a modification and complication of Newton’s law which has neither empirical nor theoretical foundation. We can imagine innumerable laws which would serve the same purpose, without our being able to state a reason why one of them is to be preferred to the others; for any one of these laws would be founded just as little on more general theoretical principles as is the law of Newton.

*Seeliger’s conception of
the situation is not very satisfactory. Therefore, his recommended solution is
not very satisfactory either.*

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## FINAL COMMENTS

*Einstein is considering
Seeliger’s paradox in this section. He finds Seeliger’s conception of the
problem to be unsatisfactory.*

*Interestingly enough the
general relativity provides a solution in terms of the universe being an infinite
whirlpool-like field. On an infinite scale, The path of light shall be curved
because it has finite amount of inertia. It will form a part of the infinite
whirlpool.*

*Newton’s theory is modified in the sense that the path of light also has infinitesimal curvature.*

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