The role of the Silberstein/Thomas/Wigner-rotation in the rod and slit paradox

Abstract

The rod and slit paradox, as first proposed by R. Shaw, is revisited. In this paradox, a rod of rest length $l_0$ moves parallel to the horizontal x-axis. Simultaneously, a thin sheet parallel to the horizontal xz-plane with a rod-shaped slit of rest length $d < l_0$ moves along the vertical y-axis. The rod passes through the slit due to relativistic effects. Earlier papers do not link the thought experiment to the Silberstein/Thomas/Wigner-rotation (STW-rotation), which is essential to its outcome. In this paper the role of the STW-rotation is discussed, and additional clarifying figures are provided. Some misleading aspects of earlier treatments are pointed out and corrected.