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Relativity: The Special and General Theory

A Few Inferences from the General Principle of
Relativity
The considerations of Section 20 show that the general principle of relativity puts us in a
position to derive properties of the gravitational field in a purely theoretical manner. Let
us suppose, for instance, that we know the space-time " course " for any natural process
whatsoever, as regards the manner in which it takes place in the Galileian domain relative
to a Galileian body of reference K. By means of purely theoretical operations (i.e. simply
by calculation) we are then able to find how this known natural process appears, as seen
from a reference-body K1 which is accelerated relatively to K. But since a gravitational
field exists with respect to this new body of reference K1, our consideration also teaches
us how the gravitational field influences the process studied.
For example, we learn that a body which is in a state of uniform rectilinear motion with
respect to K (in accordance with the law of Galilei) is executing an accelerated and in
general curvilinear motion with respect to the accelerated reference-body K1 (chest). This
acceleration or curvature corresponds to the influence on the moving body of the
gravitational field prevailing relatively to K. It is known that a gravitational field
influences the movement of bodies in this way, so that our consideration supplies us with
nothing essentially new.
However, we obtain a new result of fundamental importance when we carry out the
analogous consideration for a ray of light. With respect to the Galileian reference-body K,
such a ray of light is transmitted rectilinearly with the velocity c. It can easily be shown
that the path of the same ray of light is no longer a straight line when we consider it with
reference to the accelerated chest (reference-body K1). From this we conclude, that, in
general, rays of light are propagated curvilinearly in gravitational fields. In two respects
this result is of great importance.
In the first place, it can be compared with the reality. Although a detailed examination of
the question shows that the curvature of light rays required by the general theory of
relativity is only exceedingly small for the gravitational fields at our disposal in practice,
its estimated magnitude for light rays passing the sun at grazing incidence is nevertheless
1.7 seconds of arc. This ought to manifest itself in the following way. As seen from the
earth, certain fixed stars appear to be in the neighbourhood of the sun, and are thus
capable of observation during a total eclipse of the sun. At such times, these stars ought
to appear to be displaced outwards from the sun by an amount indicated above, as
compared with their apparent position in the sky when the sun is situated at another part
of the heavens. The examination of the correctness or otherwise of this deduction is a
problem of the greatest importance, the early solution of which is to be expected of
astronomers.1)
In the second place our result shows that, according to the general theory of relativity, the
law of the constancy of the velocity of light in vacuo, which constitutes one of the two
fundamental assumptions in the special theory of relativity and to which we have already
frequently referred, cannot claim any unlimited validity. A curvature of rays of light can
only take place when the velocity of propagation of light varies with position. Now we
might think that as a consequence of this, the special theory of relativity and with it the
whole theory of relativity would be laid in the dust. But in reality this is not the case. We
can only conclude that the special theory of relativity cannot claim an unlimited domain
 
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