Answer
(a) The result is a contradiction since the paint stripes can not both be painted below the other paint nozzle.
(b) We can conclude that objects perpendicular to the motion are not contracted.
Work Step by Step
(a) An experimenter in frame S finds that the S' nozzle, as it goes past, is less than 1 m above the x-axis. Therefore, the blue paint stripe will be painted below the red paint nozzle.
An experiment carried out in two different inertial reference frames will have the same outcome in both.
Therefore, an experimenter in frame S' finds that the S nozzle, as it goes past, is less than 1 m above the x-axis. Therefore, the red paint stripe will be painted below the blue paint nozzle.
Clearly, this result is a contradiction since the paint stripes can not both be painted below the other paint nozzle.
(b) According to the contradiction, the assumption that objects perpendicular to the motion are contracted is an incorrect assumption. Therefore, we can conclude that objects perpendicular to the motion are not contracted.
