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Einstein's theory. A beam of light that passes near the sun should be deflected by its
gravitational field. The deflection has been found experimentally by Freundlich in the right order
of magnitude; but whether the deflection agrees quantitatively with the value predicted by
Einstein's theory has not yet been decided. The best evidence for the validity of the theory of
general relativity seems to be the procession in the orbital motion of the planet Mercury, which
apparently is in very good agreement with the value predicted by the theory.
Though the experimental basis of general relativity is still rather narrow, the theory contains
ideas of the greatest importance. During the whole period from the mathematicians of ancient
Greece to the nineteenth century, Euclidean geometry had been considered as evident; the
axioms of Euclid were regarded as the foundation of any mathematical geometry, a foundation
that could not be disputed. Then, in the nineteenth century, the mathematicians Bolyai and
Lobachevsky, Gauss and Riemann found that other geometries could be invented which could be
developed with the same mathematical precision as that of Euclid; therefore, the questions as to
which geometry was correct turned out to be an empirical one. But it was only through the work
of Einstein that the question could really be taken up by the physicists. The geometry discussed
in the theory of general relativity was not concerned with three-dimensional space only but with
the four-dimensional manifold consisting of space and time. The theory established a connection
between the geometry in this manifold and the distribution of masses in the world. Therefore,
this theory raised in an entirely new form the old questions of the behavior of space and time in
the largest dimensions; it could suggest possible answers that could be checked by observations.
Consequently, very old philosophic problems were taken up that
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had occupied the mind of man since the earliest phases of philosophy and science. Is space finite
or infinite? What was there before the beginning of time? What will happen at the end of time?
Or is there no beginning and no end? These questions had found different answers in different
philosophies and religions. In the philosophy of Aristotle, for instance, the total space of the
universe was finite (though it was infinitely divisible). Space was due to the extension of bodies, it
was connected with the bodies; there was no space where there were no bodies. The universe
consisted of the earth and the sun and the stars: a finite number of bodies. Beyond the sphere of
the stars there was no space; therefore, the space of the universe was finite.
In the philosophy of Kant this question belonged to what he called `antinomies' questions
that cannot be answered, since two different arguments lead to opposite results. Space cannot be
finite, since we cannot imagine that there should be an end to space; to whichever point in space
we come we can always imagine that we can go beyond. At the same time space cannot be
infinite, because space is something that we can imagine (else the word `space' would not have
been formed) and we cannot imagine an infinite space. For this second thesis the argument of
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Kant has not been verbally reproduced. The sentence space is infinite' means for us something
negative; we cannot come to an end of space. For Kant it means that the infinity of space is really
given, that it `exists' in a sense that we can scarcely reproduce. Kant's result is that a rational
answer to the question whether space is finite or infinite cannot be given because the whole
universe cannot be the object of our experience.
A similar situation is found with respect to the problem of the infinity of time. In the
Confessions of St Augustine, for instance, this question takes the form: What was God doing
before He created the world? Augustine is not satisfied with the joke: `God was busy preparing
Hell for those who ask foolish questions.' This, he says, would be too cheap an answer, and he
tries to give a rational analysis of the problem. Only for us is time passing by; it is expected by us
as future; it passes by as the present moment and is remembered by us as past. But God is not
in time; a thousand years are for Him as one day, and one day as a thousand years. Time has
been created together with the
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world, it belongs to the world, therefore time did not exist before the universe existed. For God
the whole course of the universe is given at once. There was no time before He created the world.
It is obvious that in such statements the word `created' at once raises all the essential difficulties.
This word as it is usually understood means that something has come into being that has not been
before, and in this sense it presupposes the concept of time. Therefore, it is impossible to define
in rational terms what could be meant by the phrase `time has been created.' This fact reminds
us again of the often discussed lesson that has been learned from modern physics: that every
word or concept, clear as it may seem to be, has only a limited range of applicability.
In the theory of general relativity these questions about the infinity of space and time can be
asked and partly answered on an empirical basis. If the connection between the four-dimensional
geometry in space and time and the distribution of masses in the universe has been correctly
given by the theory, then the astronomical observations on the distribution of galaxies in space
give us information about the geometry of the universe as a whole. At least one can build
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models' of the universe, cosmological pictures, the consequences of which can be compared with
the empirical facts.
From the present astronomical knowledge one cannot definitely distinguish between several
possible models. It may be that the space filled by the universe is finite. This would not mean that
there is an end of the universe at some place. It would only mean that by proceeding farther and
farther in one direction in the universe one would finally come back to the point from which one
had started. The situation would be similar as in the two-dimensional geometry on the surface of
the earth where we, when starting from a point in an eastward direction, finally come back to
this point from the west.
With respect to time there seems to be something like a beginning. Many observations point to
an origin of the universe about four billion years ago; at least they seem to show that at that time
all matter of the universe was concentrated in a much smaller space than it is now and has
expanded ever since from this small space with different velocities. The same time of four billion
years is found in many different observations (e.g., from the age of meteorites, of minerals
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on the earth, etc.), and therefore it would be difficult to find an interpretation essentially
different from this idea of an origin. If it is the correct one it would mean that beyond this time
the concept of time would undergo essential changes. In the present state of astronomical
observations the questions about the space-time geometry on a large scale cannot yet be
answered with any degree of certainty. But it is extremely interesting to see that these questions
may possibly be answered eventually on a solid empirical basis. For the time being even the
theory of general relativity rests on a very narrow experimental foundation and must be
considered as much less certain than the so-called theory of special relativity expressed by the
Lorentz transformation.
Even if one limits the further discussions of this latter theory there is no doubt that the theory of
relativity has deeply changed our views on the structure of space and time. The most exciting
aspect of these changes is perhaps not their special nature but the fact that they have been
possible. The structure of space and time which had been defined by Newton as the basis of his
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