Why dimensionless units should not be used in physics

TL;DR

This paper argues against the use of dimensionless units in physics, advocating for their avoidance except for the mathematical identity, to ensure coherence in SI units and reduce ambiguities.

Contribution

It provides new arguments and coherence to SI units by recommending the exclusion of physical dimensionless units, clarifying conflicts between mathematical and physical conventions.

Findings

Recommends avoiding physical dimensionless units

Clarifies the role of the identity element in units

Enhances coherence in SI units

Abstract

The quantities of dimension one - known as the dimensionless quantities - are widely used in physics. However, the debate about some dimensionless units is still open. The paper brings new interrelated arguments that lead to the conclusion to avoid physical dimensionless units, except one for the mathematical multiplication identity element that should not be introduced into a system of physical units. It brings the coherence to the International System of Units (SI) and it will remove ambiguities rising from the conflict between the mathematical properties and the physical conventions.