The direct use of a physical law for the purpose of measurement creates a problem of circularity: the law needs to be empirically tested in order to ensure the reliability of measurement, but the testing requires that we already know the value of the quantity to be measured. This problem is discussed through some detailed examples of energy measurements in quantum physics; three major methods are analyzed in their interrelation, with a focus on the method of “material retardation.” It seems (...) that the only reasonable solution is to establish the law needed for the measurement by relying on an alternate method of measurement. This solution is also circular, since it amounts to letting different measurement methods justify each other. However, this circularity can be fruitful for the process of concept building; meaning can be created in a web of interconnected measurement methods. (shrink)

According to the realist interpretation, measurement commits us not just to the logically independent existence of things in space and time, but also to the existence of quantitatively structured properties and relations, and to the existence of real numbers, understood as relations of ratio between specific levels of such attributes. Measurement is defined as the estimation of numerical relations (or ratios) between magnitudes of a quantitative attribute and a unit. The history of scientific measurement, from antiquity to the present may (...) be interpreted as revealing a progressive deepening in the understanding of this position. First, the concept of ratio was broadened to include ratios between incommensurable magnitudes; second, the concept of a quantitative attribute was broadened to include non-extensive quantities; third, quantitative structure and its relations to ratios and real numbers were elaborated; and finally, the issue of empirically distinguishing between quantitative and non-quantitative structures was addressed. This interpretation of measurement understands it in a way that is continuous with scientific investigation in general, i.e., as an attempt to discover independently existing facts. (shrink)