Talk:Quantity calculus

Vague
"It has been suggested that if the units of a quantity are algebraically simplified, they then are no longer units of that quantity" is not clear. Example? Is this a claim that e.g. mass fraction has unit kg/kg and is not dimensionless?--Patrick (talk) 09:47, 1 May 2012 (UTC)

Yes, it's hard to summarise even this short paper in one sentence. You're welcome to try.

Here's a typical paragraph: "It is when we assign units to the more complex derived quantities that the concept of unit algebra most obviously becomes untenable [10]. Dynamic viscosity (abstract) is the ratio of shear stress in a Newtonian fluid to the velocity gradient in the direction orthogonal to the plane of shear. Its unit must be a unit of stress, per unit of velocity per unit of length. The punctuation is important. By convention, using SI units it can be expressed as Pa (m s−1 m−1)−1 or N m−2 (m s−1 m−1)−1, or kgms−2 m−2 (m s−1 m−1)−1. If the units in those expressions are treated as algebraic variables (which they are not) the expressions reduce to respectively Pa s, Nm−2 s and kgm−1 s−1. The first is what the SI gives as its unit for dynamic viscosity; the last is what the SI Brochure calls the SI unit ‘expressed in terms of SI base units.’ The last is also the ‘dimension’ of dynamic viscosity with symbols for base units substituted for the symbols for the base dimensions. None is recognizable as a viscosity, though a unit is supposed to be an example of the quantity to which it is assigned. A kilogram per metre per second has no physical meaning in the context"

The author's conclusion is: "The convention of presenting derived units of measurement in an algebraic format does not, or should not, imply that units are variables subject to algebraic manipulation. Some of the SI’s derived units which are the result of such manipulation are not in fact quantities of the kinds to which they are assigned. Differences between intensive quantities of the same kind are not themselves quantities of that kind and have a different unit, even though it may bear the same name."

Adamtester (talk) 07:15, 7 May 2012 (UTC)

Careful Distinctions
The VIM (BIPM, IEC, et al. "International vocabulary of metrology—Basic and general concepts and associated terms (VIM), 3rd edn. JCGM 200: 2008.") is an international standard that maintains careful definitions of "physical quantity", "unit", "dimension" and so forth, in French and English. It also defines the terms "quantity system" and the "International Quantity System" which would be well worth mentioning here.

The careful definitions and distinctions in the VIM may not completely address every objection to quantity calculus, but they address the most common ones. They are a consensus opinion derived from a structured standard development process, rather than the idiosyncratic opinion of a single scholar.

Some mention of the VIM and even some use of its definitions might be worthwhile.Antiskid56 (talk) 15:53, 29 July 2020 (UTC)