The Relative Space: Space Measurements on a Rotating Platform

TL;DR

This paper introduces the concept of relative space for rotating disks, explaining how space measurements are performed and resolving Ehrenfest's paradox through relativistic kinematics.

Contribution

It defines relative space as the operational framework for measuring space in rotating systems and provides a relativistic explanation for Ehrenfest's paradox.

Findings

Relative space is the only meaningful space for rotating disks.

Ehrenfest's paradox is resolved through relativistic kinematics.

Tangential dilation explains the paradox's resolution.

Abstract

We introduce here the concept of relative space, an extended 3-space which is recognized as the only space having an operational meaning in the study of the space geometry of a rotating disk. Accordingly, we illustrate how space measurements are performed in the relative space, and we show that an old-aged puzzling problem, that is the Ehrenfest's paradox, is explained in this purely relativistic context. Furthermore, we illustrate the kinematical origin of the tangential dilation which is responsible for the solution of the Ehrenfest's paradox.