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particular phenomena that are possible in this part of nature. In this way the mathematical
scheme represents the group of phenomena so far as the correlation between the symbols and the
measurements goes. It is this correlation which permits the expression of natural laws in the
terms of common language, since our experiments consisting of actions and observations can
always be described in ordinary language.
Still, in the process of expansion of scientific knowledge the language also expands; new terms
are introduced and the old ones are applied in a wider field or differently from ordinary language.
Terms such as `energy,"electricity,"entropy' are obvious examples. In this way we develop a
scientific language which may be called a natural
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extension of ordinary language adapted to the added fields of scientific knowledge.
During the past century a number of new concepts have been introduced in physics, and in
some cases it has taken considerable time before the scientists have really grown accustomed to
their use. The term `electromagnetic field,' for instance, which was to some extent already
present in Faraday's work and which later formed the basis of Maxwell's theory, was not easily
accepted by the physicists, who directed their attention primarily to the mechanical motion of
matter. The introduction of the concept really involved a change in scientific ideas as well, and
such changes are not easily accomplished.
Still, all the concepts introduced up to the end of the last century formed a perfectly
consistent set applicable to a wide field of experience, and, together with the former concepts,
formed a language which not only the scientists but also the technicians and engineers could
successfully apply in their work. To the underlying fundamental ideas of this language belonged
the assumptions that the order of events in time is entirely independent of their order in space,
`
that Euclidean geometry is valid in real space, and that the events happen' in space and time
independently of whether they are observed or not. It was not denied that every observation had
some influence on the phenomenon to be observed but it was generally assumed that by doing
the experiments cautiously this influence could be made arbitrarily small. This seemed in fact a
necessary condition for the ideal of objectivity which was considered as the basis of all natural
science.
Into this rather peaceful state of physics broke quantum theory and the theory of special
relativity as a sudden, at first slow and then gradually increasing, movement in the foundations of
natural science. The first violent discussions developed around the problems of space and time
raised by the theory of relativity. How should one speak about the new situation? Should one
consider the Lorentz contraction of moving bodies as a real contraction or only as an apparent
contraction? Should one say that the structure of space and time was really different from what it
had been assumed to be or should one only say that the experimental results could be connected
mathematically in a way corresponding to this new structure, while space and time, being
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the universal and necessary mode in which things appear to us, remain what they had always
been? The real problem behind these many controversies was the fact that no language existed
in which one could speak consistently about the new situation. The ordinary language was based
upon the old concepts of space and time and this language offered the only unambiguous means
of communication about the setting up and the results of the measurements. Yet the
experiments showed that the old concepts could not be applied everywhere.
The obvious starting point for the interpretation of the theory of relativity was therefore the
fact that in the limiting case of small velocities (small compared with the velocity of light) the new
theory was practically identical with the old one. Therefore, in this part of the theory it was
obvious in which way the mathematical symbols had to be correlated with the measurements and
with the terms of ordinary language; actually it was only through this correlation that the Lorentz
transformation had been found. There was no ambiguity about the meaning of the words and
the symbols in this region. In fact this correlation was already sufficient for the application of the
theory to the whole field of experimental research connected with the problem of relativity.
Therefore, the controversial questions about the `real' or the `apparent' Lorentz contraction, or
`
about the definition of the word simultaneous' etc., did not concern the facts but rather the
language.
With regard to the language, on the other hand, one has gradually recognized that one should
perhaps not insist too much on certain principles. It is always difficult to find general convincing
criteria for which terms should be used in the language and how they should be used. One
should simply wait for the development of the language, which adjusts itself after some time to
the new situation. Actually in the theory of special relativity this adjustment has already taken
place to a large extent during the past fifty years. The distinction between `real' and `apparent'
contraction, for instance, has simply disappeared. The word `simultaneous' is used in line with
the definition given by Einstein, while for the wider definition discussed in an earlier chapter the
term `at a space-like distance' is commonly used, etc.
In the theory of general relativity the idea of a non-Euclidean geometry in real space was
strongly contradicted by some philosophers
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who pointed out that our whole method of setting up the experiments already presupposed
Euclidean geometry.
In fact if. a mechanic tries to prepare a perfectly plane surface, he can do it in the following
way. He first prepares three surfaces of, roughly, the same size which are, roughly, plane. Then
he tries to bring any two of the three surfaces into contact by putting them against each other in
different relative positions. The degree to which this contact is possible on the whole surface is a
measure of the degree of accuracy with which the surfaces can be called `plane.' He will be
satisfied with his three surfaces only if the contact between any two of them is complete
everywhere. If this happens one can prove mathematically that Euclidean geometry holds on the
three surfaces. In this way, it was argued, Euclidean geometry is just made correct by our own
measures.
From the point of view of general relativity, of course, one can answer that this argument
proves the validity of Euclidean geometry only in small dimensons, in the dimensions of our
experimental equipment. The accuracy with which it holds in this region is so high that the above
process for getting plane surfaces can always be carried out. The extremely slight deviations from
Euclidean geometry which still exist in this region will not be realized since the surfaces are made
of material which is not strictly rigid but allows for very small deformations and since the concept
of `contact' cannot be defined with complete precision. For surfaces on a cosmic scale the
process that has been described would just not work; but this is not a problem of experimental
physics.
Again, the obvious starting point for the physical interpretation of the mathematical scheme in
general relativity is the fact that the geometry is very nearly Euclidean in small dimensions; the
theory approaches the classical theory in this region. Therefore, here the correlation between the
mathematical symbols and the measurements and the concepts in ordinary language is
unambiguous. Still, one can speak about a non-Euclidean geometry in large dimensions. In fact a
long time before the theory of general relativity had even been developed the possibility of a
non-Euclidean geometry in real space seems to have been considered by the mathematicians,
especially by
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