The dimensions of physical quantities

Abstract

As a basis for the discussion of the dimensions of physical quantities, the three usual quantities (length, time and mass) are taken as indefinables and the mechanical quantities are defined in terms of these. The dimensions follow directly from the definition of a quantity and indicate the type of measurements that have to be made to determine the magnitude of those quantities. It is shown that a further indefinable is necessary for defining electrical and magnetic quantities, and reasons are given for choosing electric charge for this purpose. It is pointed out that when the dielectric constant and the permeability are equated to unity for a vacuum it amounts to using these two quantities as indefinables, which, although in some cases convenient from practical considerations, is not necessary. For defining thermodynamical quantities, only the three indefinables, mass, length and time, are used. The introduction of Boltzmann's constant, as a numerical scale factor, is not necessary, but gives a more convenient unit of temperature. The significance of the introduction of such scale factors is also discussed from a more general point of view. Finally, it is shown that three indefinables are not necessary for measuring the magnitude of mechanical, and hence thermodynamical quantities, and that these can be quite adequately defined in terms of length and time only, while electrical and magnetic quantities are measured in terms of length, time and charge.

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