Angles in the SI: a detailed proposal for solving the problem

TL;DR

This paper proposes redefining the status of radians and steradians in the SI to create a more consistent and unambiguous unit system, with minimal disruption to current practices.

Contribution

It introduces a detailed proposal to treat radians and steradians as dimensionless within the SI, enhancing clarity and consistency in physical units.

Findings

Improved units for torque, angular momentum, and moment of inertia

Explicit conventions for equations involving angles

Use of different symbols for h-bar in quantum physics

Abstract

A recent Letter proposed changing the dimensionless status of the radian and steradian within the SI, while allowing the continued use of the convention to set the angle 1 radian equal to the number 1 within equations, providing this is done explicitly. This would bring the advantages of a physics-based, consistent, and logically-robust unit system, with unambiguous units for all physical quantities, for the first time, while any upheaval to familiar equations and routine practice would be minimised. More details of this proposal are given here. The only notable changes for typical end-users would be: improved units for the quantities torque, angular momentum and moment of inertia; a statement of the convention accompanying some familiar equations; and the use of different symbols for h-bar the action and h-bar the angular momentum, a small step forward for quantum physics. Some features of the proposal are already established practice for quantities involving the steradian such as radiant intensity and radiance.