Pagina 48 van 212

Place a metre-rod in the x′-axis of K′ in such a manner that one

end (the beginning) coincides with the point x′ = 0 whilst the

other end (the end of the rod) coincides with the point x′ = 1.

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

image006

the distance between the points being

image007

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

image008

of a metre. The rigid rod is thus shorter when in motion than

when at rest, and the more quickly it is moving, the shorter is

the rod. For the velocity v = c we should have

image009