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Relativity: The Special and General Theory
Albert Einstein: Relativity
Part I: The Special Theory of Relativity
The Apparent Incompatibility of the
Law of Propagation of Light with the
Principle of Relativity
There is hardly a simpler law in physics than that according to which light is propagated in empty
space. Every child at school knows, or believes he knows, that this propagation takes place in
straight lines with a velocity c= 300,000 km./sec. At all events we know with great exactness that
this velocity is the same for all colours, because if this were not the case, the minimum of emission
would not be observed simultaneously for different colours during the eclipse of a fixed star by its
dark neighbour. By means of similar considerations based on observa− tions of double stars, the
Dutch astronomer De Sitter was also able to show that the velocity of propagation of light cannot
depend on the velocity of motion of the body emitting the light. The assumption that this velocity of
propagation is dependent on the direction "in space" is in itself improbable.
In short, let us assume that the simple law of the constancy of the velocity of light c (in vacuum) is
justifiably believed by the child at school. Who would imagine that this simple law has plunged the
conscientiously thoughtful physicist into the greatest intellectual difficulties? Let us consider how
these difficulties arise.
Of course we must refer the process of the propagation of light (and indeed every other process) to
a rigid reference−body (co−ordinate system). As such a system let us again choose our
embankment. We shall imagine the air above it to have been removed. If a ray of light be sent
along the embankment, we see from the above that the tip of the ray will be transmitted with the
velocity c relative to the embankment. Now let us suppose that our railway carriage is again
travelling along the railway lines with the velocity v, and that its direction is the same as that of the
ray of light, but its velocity of course much less. Let us inquire about the velocity of propagation of
the ray of light relative to the carriage. It is obvious that we can here apply the consideration of the
previous section, since the ray of light plays the part of the man walking along relatively to the
carriage. The velocity W of the man relative to the embankment is here replaced by the velocity of
light relative to the embankment. w is the required velocity of light with respect to the carriage, and
we have
w = c−v.
The velocity of propagation ot a ray of light relative to the carriage thus comes cut smaller than c.
But this result comes into conflict with the principle of relativity set forth in Section V. For, like every
other general law of nature, the law of the transmission of light in vacuo [in vacuum] must,
according to the principle of relativity, be the same for the railway carriage as reference−body as
when the rails are the body of reference. But, from our above consideration, this would appear to
be impossible. If every ray of light is propagated relative to the embankment with the velocity
c, then for this reason it would appear that another law of propagation of light must necessarily hold
with respect to the carriage — a result contradictory to the principle of relativity.
In view of this dilemma there appears to be nothing else for it than to abandon either the principle
of relativity or the simple law of the propagation of light in vacuo. Those of you who have carefully
followed the preceding discussion are almost sure to expect that we should retain the principle of