Relativity: The Special and General Theory
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 observations 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.