The Problem with ‘Dimensionless Quantities’

B. Hall

2022

Abstract

Many different quantities can be described as ‘dimensionless’ and have the same SI unit “one”, so their different natures cannot be determined from the unit name alone. In scientific unit systems like the SI, a set of base quantities and associated units can lead to such many-to-one relationships between quantities, dimensions, and units. So, it is necessary to understand how the mechanism of dimensions in unit systems works before trying to design more general formats for the expression of quantities. In the familiar expression of physical quantities, like mass, energy, etc, dimensions play a role when converting between unit systems or changing unit prefixes. So, it is often assumed that the notion of dimension is general. However, this paper explains that is not so: dimensions do not apply to all expressions of quantities. By recognising that there different types of measurement scale, the role played by dimensions in systems like the SI can be seen as secondary to the importance to the kind of quantity being expressed. There is a need to provide a unique way of identifying each kind of quantity: dimensions and unit names are not able to fulfil this requirement.

Paper Citation

in Harvard Style

Hall B. (2022). The Problem with ‘Dimensionless Quantities’. In Proceedings of the 10th International Conference on Model-Driven Engineering and Software Development - Volume 1: MODELSWARD, ISBN 978-989-758-550-0, pages 116-125. DOI: 10.5220/0010960300003119

in Bibtex Style

@conference{modelsward22,
author={B. Hall},
title={The Problem with ‘Dimensionless Quantities’},
booktitle={Proceedings of the 10th International Conference on Model-Driven Engineering and Software Development - Volume 1: MODELSWARD,},
year={2022},
pages={116-125},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0010960300003119},
isbn={978-989-758-550-0},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 10th International Conference on Model-Driven Engineering and Software Development - Volume 1: MODELSWARD,
TI - The Problem with ‘Dimensionless Quantities’
SN - 978-989-758-550-0
AU - Hall B.
PY - 2022
SP - 116
EP - 125
DO - 10.5220/0010960300003119