Extent of VIM 'Quantity' Extension to Vectors and Tensors

Clarify to what extent the JCGM 200:2012 International Vocabulary of Metrology (VIM) definition of "quantity," which is defined as a scalar, can be extended to include vectors and tensors, specifying the scope and limits of this extension within metrological terminology and practice.

Background

The paper examines tensions between the scalar-focused definition of "quantity" in VIM and widespread scientific usage involving vectors and tensors. Note 5 to the VIM quantity definition suggests that vectors or tensors whose components are quantities are also considered quantities, but the paper highlights that this raises unresolved issues about ordering, comparability, units, and uncertainty for multivariate objects.

This ambiguity affects both metrological consistency (e.g., uncertainty propagation and unit comparability) and educational alignment with physics, motivating a precise articulation of how far the VIM definition is intended to extend beyond scalars.