Space geometry of rotating platforms: an operational approach

TL;DR

This paper defines the physical space of a rotating disk operationally, demonstrating its non-Euclidean geometry and resolving Ehrenfest's paradox through a consistent relativistic framework.

Contribution

It introduces the concept of relative space as the operationally meaningful space of a rotating platform and clarifies its non-Euclidean geometry within relativity.

Findings

The space of a rotating disk is non-Euclidean, matching Einstein's early intuition.

The Born metric is derived as the natural geometry of the rotating platform.

Relativistic kinematics resolve Ehrenfest's paradox without additional assumptions.

Abstract

We study the space geometry of a rotating disk both from a theoretical and operational approach, in particular we give a precise definition of the space of the disk, which is not clearly defined in the literature. To this end we define an extended 3-space, which we call relative space: it is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the 'physical space of the rotating platform'. Then, the geometry of the space of the disk turns out to be non Euclidean, according to the early Einstein's intuition; in particular the Born metric is recovered, in a clear and self consistent context. Furthermore, the relativistic kinematics reveals to be self consistent, and able to solve the Ehrenfest's paradox without any need of dynamical considerations or ad hoc assumptions.