Dimensionless units in the SI
Abstract
The International System of Units (SI) is supposed to be coherent. That is, when a combination of units is replaced by an equivalent unit, there is no additional numerical factor. Here we consider dimensionless units as defined in the SI, e.g. angular units like radians or steradians and counting units like radioactive decays or molecules. We show that an incoherence may arise when different units of this type are replaced by a single dimensionless unit, the unit ‘one’, and suggest how to properly include such units into the SI in order to remove the incoherence. In particular, we argue that the radian is the appropriate coherent unit for angles and that hertz is not a coherent unit in the SI. We also discuss how including angular and counting units affects the fundamental constants.
 Publication:

Metrologia
 Pub Date:
 February 2015
 DOI:
 10.1088/00261394/52/1/40
 arXiv:
 arXiv:1409.2794
 Bibcode:
 2015Metro..52...40M
 Keywords:

 Physics  Data Analysis;
 Statistics and Probability;
 Physics  Classical Physics;
 Physics  History and Philosophy of Physics
 EPrint:
 19 pages