Angles are inherently neither length ratios nor dimensionless

TL;DR

This paper argues that angles should not be considered dimensionless or as length ratios within the SI system, clarifying a fundamental conceptual issue in measurement theory.

Contribution

It clarifies that angles are not inherently length ratios and distinguishes between defining a quantity and measuring it, addressing a key controversy in SI units.

Findings

Angles are not necessarily length ratios.

Distinction between definition and measurement of angles.

Clarifies SI treatment of angles.

Abstract

The status of angles within The International System of Units (SI) has long been a source of controversy and confusion. We address one specific but crucial issue, putting the case that the idea of angles necessarily being length ratios, and hence dimensionless, is not valid. By making a clear distinction between the definition of a quantity and the process of making a measurement of that quantity, we show that the usual arguments for angles being length ratios are problematic. An appreciation of this point should clear away a major obstacle preventing a more proper treatment of the angle problem.