**Length contraction**

Moving objects appear shorter in the dimension
parallel to their velocity, again by the factor
**g**
introduced previously.
To derive the contraction we again consider a light clock; only in this case
let the clock be on its side so the motion of the light pulse is parallel to the clock's
velocity. If the clock has length * L_{0}* in its rest
frame, the time for light to bounce from one side of the clock and back
is:

However to an observer who sees the clock pass
at velocity * v*, the light takes more time to
traverse the length of the clock when the pulse is traveling in the same direction as the
clock, and it takes less time for the return trip.

We know from the time dilation that

The above three equations can be used
to eliminate * t* and

** Thus moving meter sticks and all other moving objects appear shorter along
their direction of motion. Like the time dilation effect, this happens as a result of
the nature of space and time. It occurs equally for all objects, independent of what they
are made of; it is not caused by forces, since as you well know, the force is
zero when the velocity is constant.**