Relativity - The Special and General Theory | Page 7

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 relativity, which appeals so convincingly to the intellect
because it is so natural and simple. The law of the propagation of light in vacuo would
then have to be replaced by a more complicated law conformable to the principle of
relativity. The development of theoretical physics shows, however, that we cannot pursue
this course. The epoch-making theoretical investigations of H. A. Lorentz on the
electrodynamical and optical phenomena connected with moving bodies show that
experience in this domain leads conclusively to a theory of electromagnetic phenomena,
of which the law of the constancy of the velocity of light in vacuo is a necessary
consequence. Prominent theoretical physicists were theref ore more inclined to reject the
principle of relativity, in spite of the fact that no empirical data had been found which
were contradictory to this principle.
At this juncture the theory of relativity entered the arena. As a result of an analysis of the
physical conceptions of time and space, it became evident that in realily there is not the
least incompatibilitiy between the principle of relativity and the law of propagation of
light, and that by systematically holding fast to both these laws a logically rigid theory
could be arrived at. This theory has been called the special theory of relativity to
distinguish it from the extended theory, with which we shall deal later. In the following
pages we shall present the fundamental ideas of the special theory of relativity.

ON THE IDEA OF TIME IN PHYSICS
Lightning has struck the rails on our railway embankment at two places A and B far
distant from each other. I make the additional assertion that these two lightning flashes
occurred simultaneously. If I ask