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Intended Vector/Tensor Space Context in VIM

Determine whether references to vectors and tensors in JCGM 200:2012 VIM are intended to apply specifically to three-dimensional Euclidean space, four-dimensional Minkowski spacetime, or an arbitrary vector space, and specify the implications for metrological definitions and usage.

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Background

The paper observes that VIM mentions vectors and tensors only sporadically and without specifying the underlying space, which is critical because dimensions and unit structures differ across 3D space, 4D spacetime, and more general parameter spaces.

Clarifying the intended context would guide the consistent treatment of components, dimensions, and operations (e.g., scalar products, distances) within metrological definitions.

References

Returning to the vectors and tensors, we have to mention that from their sporadic appearances in VIM it is impossible to understand whether the authors mean ‘our’ 3d space or 4d [Minkowsky] space-time, or an arbitrary one.

— Quantity and quantitative properties in physics and metrology (2404.04294 - Karshenboim, 4 Apr 2024) in Main text, discussion of vectors and tensors referenced in VIM