Pagina 184 van 212

Furthermore, the principle of relativity teaches us that, as

judged from K, the length of a unit measuring-rod which is at

rest with reference to K′ must be exactly the same as the length,

as judged from K′, of a unit measuring-rod which is at rest

relative to K. In order to see how the points of the x′-axis

appear as viewed from K, we only require to take a "snapshot" of

K′ from K; this means that we have to insert a particular value

of t (time of K), e.g. t = 0. For this value of t we then obtain

from the first of the equations (5)

x′ = ax

Two points of the x′-axis which are separated by the distance Δx′

= 1 when measured in the K′ system are thus separated in our

instantaneous photograph by the distance

image043

But if the snapshot be taken from K′(t′ = 0), and if we eliminate

t from the equations (5), taking into account the expression (6),

we obtain

image044