The same result is obtained for rays of light advancing in
any other direction whatsoever. Of cause this is not surprising, since
the equations of the Lorentz transformation were derived conformably
to this point of view.
Notes
*) A simple derivation of the Lorentz transformation is given in
Appendix I.
THE BEHAVIOUR OF MEASURING-RODS AND CLOCKS IN MOTION
Place a metre-rod in the x1-axis of K1 in such a manner that one end
(the beginning) coincides with the point x1=0 whilst the other end
(the end of the rod) coincides with the point x1=I. What is the length
of the metre-rod relatively to the system K? In order to learn this,
we need only ask where the beginning of the rod and the end of the rod
lie with respect to K at a particular time t of the system K. By means
of the first equation of the Lorentz transformation the values of
these two points at the time t = 0 can be shown to be
eq. 05a: file eq05a.gif
eq. 05b: file eq05b.gif
the distance between the points being eq. 06 .
But the metre-rod is moving with the velocity v relative to K. It
therefore follows that the length of a rigid metre-rod moving in the
direction of its length with a velocity v is eq.
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