A clearer approach for defining unit systems

TL;DR

This paper introduces a clear framework for defining and relating various unit systems, emphasizing the independence of base units and the role of conventions, including a new perspective on the radian and the Gaussian system.

Contribution

It proposes a unified framework for defining unit systems with independent base units and conventions, clarifying their interrelations and the treatment of angles and electromagnetic units.

Findings

Clarifies how different unit systems are interconnected.

Proposes the radian as an independent unit with modified dimensional status.

Identifies key information needed to define and use various unit systems.

Abstract

We present the SI and other unit systems, including cgs-em and cgs-es, in a framework whereby a system of fully independent and dimensionally orthogonal base units is modified by conventions designed to simplify the equations that are used within each system. We propose that the radian can be seen as an independent unit whose dimensional status is modified in the SI and other unit systems for this purpose. This framework clarifies how different unit systems are interrelated, and identifies the key pieces of information that are needed to define both a unit system and the equations that are to be used with it. Specifically, these are the size of the base units in the unsimplified system, together with sufficient equations to identify all the conventions adopted by the particular unit system. The appropriate extra information for the revised SI is presented. We do not propose that the treatment of angles as dimensionless within the SI is changed. It is also proposed that the Gaussian unit system is best seen as identical to cgs-es, but with the B and H symbols in equations used to represent relativistic versions of B and H, which should properly be treated as different quantities. These different versions of B and H can similarly be used within the SI, with many of the advantages of the Heaviside-Lorentz system.