Special theory of relativity > The slowing down of time and the reduction in the size of bodies in motion; the Lorentz Transformations > Problem 14.2.10

Statement

$14.2.10.$ At a longitudinal velocity of $\beta c$, the length of a pencil is equal to the length of a pencil case $l$. As the pencil flies into the pencil case, the lid of the case slams shut, and the pencil comes to an instantaneous stop. Describe this process in the reference frame of the pencil.

Solution

Answer

During the time between the two events, the pencil case “reaches” the other end of the pencil, propagating a deformation wave and compressing it to its proper length, after which the lid closes without hindrance.