Angles in the SI: treating the radian as an independent, unhidden unit does not require the redefinition of the term frequency or the unit hertz

TL;DR

This paper argues that treating the radian as an independent unit in the SI system clarifies the role of angles without redefining fundamental units like frequency or hertz, addressing issues caused by the current Radian Convention.

Contribution

It proposes minimal changes to SI definitions to explicitly treat the radian as a separate unit, improving clarity without redefining frequency or hertz.

Findings

The current SI treats the radian as dimensionless, causing conceptual issues.

Explicitly defining the radian as a separate unit clarifies its role in measurements.

No redefinition of frequency or hertz is necessary with this approach.

Abstract

Some recent papers have argued that frequency should have the dimensions of angle/time, with the consequences that 1 Hz = $2\pi$ rad/s instead of 1 s$^{-1}$, and also that $\nu = \omega$ and $h = \hbar$. This letter puts the case that this argument redefines the quantity frequency and then draws conclusions from equations that rely on the standard definition being used. The problems that this redefinition is designed to address arise from the widespread unstated adoption of the Radian Convention, which treats the radian as a dimensionless quantity equal to the number 1, in effect making the radian a hidden unit. This convention is currently built-in to the SI, when it should be separable from it. The unhelpful status of angles in the SI can be remedied with minimal disruption by (1) changing the definition of the radian from a radian equals 1 m/m to e.g. a right angle equals $\pi/2$ radians, and (2) acknowledging that the adoption of the Radian Convention is acceptable, when made explicit. The standard definitions of frequency and the hertz should remain unchanged.