Einstein Albert Relativity

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Next: Part III: Considerations on the Universe as a Whole
Footnotes
1)
First observed by Eddington and others in 1919. (Cf. Appendix III, pp. 126-129).
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Relativity: The Special and General Theory
2)
Established by Adams in 1924. (Cf. p. 132)
Relativity: The Special and General Theory
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Relativity: The Special and General Theory
Albert Einstein: Relativity
Part III: Considerations on the Universe as a Whole
Part III
Considerations on the Universe as a Whole
Cosmological Difficulties of Netwon's Theory
Part from the difficulty discussed in Section 21, 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 approrimately 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 by an infinite region of emptiness. The stellar universe ought to be
a finite island in the infinite ocean of space. 1)
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.
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 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 laws would be founded just as little on
more general theoretical principles as is the law of Newton.
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Relativity: The Special and General Theory
Footnotes
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 p0 is constant throughout tithe universe, then a sphere of volume V will enclose the average
man p0V. Thus the number of lines of force passing through the surface F of the sphere into its
interior is proportional to p0 V. For unit area of the surface of the sphere the number of lines of force
which enters the sphere is thus proportional to p0 V/F or to p0R. Hence the intensity of the field at
the surface would ultimately become infinite with increasing radius R of the sphere, which is
impossible.
Relativity: The Special and General Theory
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Relativity: The Special and General Theory
Albert Einstein: Relativity
Part III: Considerations on the Universe as a Whole
The Possibility of a "Finite" and yet "Unbounded" Universe
But speculations on the structure of the universe also move in quite another direction. The
development of non-Euclidean geometry led to the recognition of the fact, that we can cast doubt
on the infiniteness of our space without coming into conflict with the laws of thought or with
experience (Riemann, Helmholtz). These questions have already been treated in detail and with
unsurpassable lucidity by Helmholtz and Poincar�, whereas I can only touch on them briefly here.
In the first place, we imagine an existence in two dimensional space. Flat beings with flat
implements, and in particular flat rigid measuring-rods, are free to move in a plane. For them
nothing exists outside of this plane: that which they observe to happen to themselves and to their [ Pobierz całość w formacie PDF ]

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