Relativity - The Special and General Theory | Page 6

must grant it a considerable measure of " truth," since it supplies us
with the actual motions of the heavenly bodies with a delicacy of detail little short of
wonderful. The principle of relativity must therefore apply with great accuracy in the

domain of mechanics. But that a principle of such broad generality should hold with such
exactness in one domain of phenomena, and yet should be invalid for another, is a priori
not very probable.
We now proceed to the second argument, to which, moreover, we shall return later. If the
principle of relativity (in the restricted sense) does not hold, then the Galileian
co-ordinate systems K, K1, K2, etc., which are moving uniformly relative to each other,
will not be equivalent for the description of natural phenomena. In this case we should be
constrained to believe that natural laws are capable of being formulated in a particularly
simple manner, and of course only on condition that, from amongst all possible Galileian
co-ordinate systems, we should have chosen one (K[0]) of a particular state of motion as
our body of reference. We should then be justified (because of its merits for the
description of natural phenomena) in calling this system " absolutely at rest," and all
other Galileian systems K " in motion." If, for instance, our embankment were the system
K[0] then our railway carriage would be a system K, relative to which less simple laws
would hold than with respect to K[0]. This diminished simplicity would be due to the fact
that the carriage K would be in motion (i.e."really")with respect to K[0]. In the general
laws of nature which have been formulated with reference to K, the magnitude and
direction of the velocity of the carriage would necessarily play a part. We should expect,
for instance, that the note emitted by an organpipe placed with its axis parallel to the
direction of travel would be different from that emitted if the axis of the pipe were placed
perpendicular to this direction.
Now in virtue of its motion in an orbit round the sun, our earth is comparable with a
railway carriage travelling with a velocity of about 30 kilometres per second. If the
principle of relativity were not valid we should therefore expect that the direction of
motion of the earth at any moment would enter into the laws of nature, and also that
physical systems in their behaviour would be dependent on the orientation in space with
respect to the earth. For owing to the alteration in direction of the velocity of revolution
of the earth in the course of a year, the earth cannot be at rest relative to the hypothetical
system K[0] throughout the whole year. However, the most careful observations have
never revealed such anisotropic properties in terrestrial physical space, i.e. a physical
non-equivalence of different directions. This is very powerful argument in favour of the
principle of relativity.

THE THEOREM OF THE ADDITION OF VELOCITIES EMPLOYED IN
CLASSICAL MECHANICS
Let us suppose our old friend the railway carriage to be travelling along the rails with a
constant velocity v, and that a man traverses the length of the carriage in the direction of
travel with a velocity w. How quickly or, in other words, with what velocity W does the
man advance relative to the embankment during the process ? The only possible answer
seems to result from the following consideration: If the man were to stand still for a
second, he would advance relative to the embankment through a distance v equal
numerically to the velocity of the carriage. As a consequence of his walking, however, he
traverses an additional distance w relative to the carriage, and hence also relative to the

embankment, in this second, the distance w being numerically equal to the velocity with
which he is walking. Thus in total be covers the distance W=v+w relative to the
embankment in the second considered. We shall see later that this result, which expresses
the theorem of the addition of velocities employed in classical mechanics, cannot be
maintained ; in other words, the law that we have just written down does not hold in
reality. For the time being, however, we shall assume its correctness.

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