Implications of adopting plane angle as a base quantity in the SI

TL;DR

This paper discusses the potential benefits and challenges of redefining plane angle as a base quantity in the SI system, aiming to improve consistency and conceptual clarity in physics and mathematics.

Contribution

It proposes a formal framework for including angle as a base quantity in SI, outlining the resulting changes in fundamental equations and units.

Findings

Enhanced consistency in physical quantities

Revised fundamental equations with angle as base

Potential for clearer conceptual understanding

Abstract

The treatment of angles within the SI is anomalous compared with other quantities, and there is a case for removing this anomaly by declaring plane angle to be an additional base quantity within the system. It is shown that this could bring several benefits in terms of treating angle on an equal basis with other metrics, removing potentially harmful ambiguities, and bringing SI units more in line with concepts in basic physics, but at the expense of significant upheaval to familiar equations within mathematics and physics. This paper sets out the most important of these changes so that an alternative unit system containing angle as a base quantity can be seen in the round, irrespective of whether it is ever widely adopted. The alternative formulas and units can be treated as the underlying, more general equations of mathematical physics, independent of the units used for angle, which are conventionally simplified by implicitly assuming that the unit used for angle is the radian.