A new graphical depiction of the barn and pole paradox

Abstract

A novel graphical depiction of the relativistic barn and pole paradox is constructed in such a way that the space-time plot axes are dimensionless for both observers. Times of events over the entire range of pole-to-barn length ratio and relative speeds can be displayed in one plot for each observer. That for the barn frame clearly depicts the range of pole-to-barn length ratio over which the paradox appears, while that for the pole frame shows that the pole vaulter will only see the pole within the barn if the proper length of the pole is smaller than the contracted length of the barn.