Quantity calculus

Quantity calculus is the formal method for describing the mathematical relations between abstract physical quantities.[1] Despite the name, it is more analogous to a system of algebra than calculus in the mathematical sense of the term. Measurements are expressed as products of a numeric value with a unit symbol, e.g. "12.7 m". Unlike algebra, the unit symbol represents an actual quantity such as a meter, not an algebraic variable.

The basic axiom of quantity calculus can, for most purposes, be taken to be Maxwell's description[2] of a physical quantity as the product of a "numerical value" and a "unit of measurement", although the roots can be traced to Fourier's concept of dimensional analysis (1822)[3] and a full axiomatization has yet to be completed.[1]

A careful distinction needs to be made between abstract quantities and measurable quantities. The multiplication and division rules of quantity calculus are applied to SI base units (which are measurable quantities) to define SI derived units, but if the units are algebraically simplified, it has been suggested that they then are no longer units of that quantity.[4]

References

  1. ^ a b de Boer, J. (1995), "On the History of Quantity Calculus and the International System", Metrologia 31 (6): 405–429, Bibcode 1995Metro..31..405D, doi:10.1088/0026-1394/31/6/001 
  2. ^ Maxwell, J. C. (1873), A Treatise on Electricity and Magnetism, Oxford: Oxford University Press, http://www.archive.org/details/electricandmagne01maxwrich 
  3. ^ Fourier, Joseph (1822), Théorie analytique de la chaleur 
  4. ^ Emerson, W.H. (2008), "On quantity calculus and units of measurement", Metrologia 45 (2): 134–138, Bibcode 2008Metro..45..134E, doi:10.1088/0026-1394/45/2/002 

Further reading