About continuity and discreteness of quantities: examples from physics and metrology

Abstract

The VIM3 defines a quantity as a “property of a phenomenon, body, or substance”, leaving the characteristics of the term ‘quantity’, related to the chosen characteristics of the relevant properties. The question is: does necessarily a property also necessarily refer to the possible granularity of a phenomenon, body, or substance? Take, for example, for the quantity “mass”: it does not always have to take into account whether or not a phenomenon, body, or substance is subdivided into discrete entities? It depends of the frame of the analysis and also on the chosen measurement unit. In other cases, like temperature, the macroscopic properties are related to the statistical properties of granular substances like atoms and molecules are, so the present meaning of ‘temperature’ is generally lost at the numerical level where the entity’s statistics become meaningless. Yet another case is quantum physics. The paper illustrates the issue and possible solutions under development. Keywords: continuous; granular; quantity; magnitude; quanta; integer number; real number; counting; function