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

TL;DR

This paper examines the rod and slit paradox, emphasizing the crucial role of Silberstein/Thomas/Wigner-rotation in understanding the relativistic effects involved, correcting previous misconceptions and providing clearer explanations.

Contribution

It highlights the significance of STW-rotation in the paradox and clarifies misunderstandings in earlier analyses.

Findings

STW-rotation is essential to the paradox's outcome

Clarification of previous misconceptions about relativistic effects

Additional figures aid in understanding the role of rotation

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.