fourth equations of the Lorentz transformation give for these two ticks :
t = 0
and
eq. 07: file eq07.gif
As judged from K, the clock is moving with the velocity v; as judged from this
reference-body, the time which elapses between two strokes of the clock is not
one second, but
eq. 08: file eq08.gif
seconds, i.e. a somewhat larger time. As a consequence of its motion the clock
goes more slowly than when at rest. Here also the velocity c plays the part of an
unattainable limiting velocity.
THEOREM OF THE ADDITION OF VELOCITIES. THE
EXPERIMENT OF FIZEAU
Now in practice we can move clocks and measuring-rods only with velocities
that are small compared with the velocity of light; hence we shall hardly be able
to compare the results of the previous section directly with the reality. But, on
the other hand, these results must strike you as being very singular, and for that
reason I shall now draw another conclusion from the theory, one which can
easily be derived from the foregoing considerations, and which has been most
elegantly confirmed by experiment.
In Section 6 we derived the theorem of the addition of velocities in one direction
in the form which also results from the hypotheses of classical mechanics- This
theorem can also be deduced readily horn the Galilei transformation (Section
11). In place of the man walking inside the carriage, we introduce a point
moving relatively to the co-ordinate system K1 in accordance with the equation
x1 = wt1