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Book by David Michalets

Review of Einstein's 1920 Book on Relativity  (from Translation)

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A (remark) line precedes my remark from my review of the preceding original content.

My remark applies to only this section of the original.

Section XXX of 35


PART from the difficulty discussed in Sec tion 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,  lthough 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.
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  y an infinite region of emptiness. The stellar universe ought to be a finite island in the infinite ocean of space.
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.
1 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 ρ0 is constant throughout the universe, then a sphere of volume V will enclose the average mass . ρ0V Thus the number of lines of force passing through the surface F of the sphere into its interior is proportional to . ρ0V For unit area of the surface of the sphere the number of lines of force which enters the sphere is thus proportional to F V ρ0
or . ρ0R Hence the intensity of the field at the surface would ultimately become infinite with increasing radius   of the sphere, which is impossible.

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  rom 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 a 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  aws would be founded just as little on more general theoretical principles as is the law of Newton.


It is just wrong to mention difficulties with Newton's theory, when Newton's theory is misunderstood.

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last change 05/07/2022