On the Real and Apparent Positions of Moving Objects in Special Relativity: The Rockets-and-String and Pole-and-Barn Paradoxes Revisited and a New Paradox

TL;DR

This paper clarifies the distinction between real and apparent positions of moving objects in special relativity, revisiting classic paradoxes and introducing a new paradox to elucidate the effects of Lorentz transformations.

Contribution

It provides a detailed analysis of well-known paradoxes, showing the string remains unstressed and the pole never fits, and introduces a new paradox related to causality and Lorentz contraction.

Findings

The string in the Rockets-and-String paradox remains unstressed.

The pole in the Barn-and-Pole paradox never actually fits into the barn.

A new paradox related to causality and Lorentz contraction is proposed.

Abstract

The distinction between the real positions of moving objects in a single reference frame and the apparent positions of objects at rest in one inertial frame and viewed from another, as predicted by the space-time Lorentz Transformations, is discussed. It is found that in the Rockets-and-String paradox the string remains unstressed and does not break and that the pole in the Barn-and-Pole paradox never actually fits into the barn. The close relationship of the Lorentz-Fitzgerald Contraction and the relativity of simultaneity of Special Relativity is pointed out and an associated paradox, in which causality is apparently violated, is noted.