International system of units: Concept and current design

Abstract

Measurement processes determine our everyday life. A system of measurement units that is valid and accepted worldwide and across all disciplines, is the prerequisite for measurement results to be comparable and interpreted correctly everywhere. After great confusion in the Middle Ages, the decisive impulse for the design of such a system came from France. At the time of the French Revolution, the foundations for the decimal metric system were laid by tracing the unit of length, the meter, back to part of the Earth’s meridian. Finally, with the signing of the Metre Convention in 1875, the step was taken toward standardizing the units of measurement beyond national borders. After that, the metric system was able to expand and develop over the years according to the increasing needs of science and technology. It became the International System of Units (SI) with seven base units today. It can be used in all scientific and practical measurement tasks and is rightly regarded as the technical language of science. The SI remains adaptable to the needs of all areas of science and adjustments are made when necessary. In 2018, a fundamental revision of the SI took place. For the first time, the SI became free of artefacts. The realization of units is now conceptually detached from the definition. A unit defined by the fixed value of natural constants can be realized in accordance with the laws of physics. Improvements in realization are possible without having to redefine the unit.

In this chapter, a brief outline of the history and background of the SI is given, the 2018 revision of the SI is explained, and the resulting possibilities are outlined.

1 Introduction

Measurement determines our everyday life. There is hardly any activity that does not involve a measurement task in some way, be it in the private sphere, in the practice of a craft, in industry or in research. William Thomson, later Lord Kelvin, expressed the importance of measuring at the end of the eighteenth century as follows:

“ I often say that when you can measure what you are speaking about and express it in numbers you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge of it is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts advanced to the stage of science, whatever the matter may be.”

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Measurement processes seem so self-evident to us that the underlying concepts remain hidden and are often not questioned. Yet there are still different views and controversial debates in measurement theory today, precisely because measurement is applied very broadly in almost all disciplines. A recent review of the state and developments in measurement theory can be found, for example, in a book by D. J. Hand [13].

Metrology is the science of measurement and its applications. It deals, among other things, with the definition of units of measurement and the conceptual aspects of measurement. A key component is the International System of Units SI, which claims for itself (SI brochure, 9th edition [5]):

“ ….The International System of Units, the SI, has been used around the world as the preferred system of units, the basic language for science, technology, industry, and trade since it was established in 1960….”

“ The SI is a consistent system of units for use in all aspects of life, including international trade, manufacturing, security, health and safety, protection of the environment, and in the basic science that underpins all of these…”

The term measurement used in the context of the SI is described in the latest version of the International Vocabulary of Metrology|see VIM [4]:

measurement

process of experimentally obtaining one or more quantity values that can reasonably be attributed to a quantity.

Note 1:

Measurement does not apply to nominal properties.

Note 2:

Measurement implies comparison of quantities or counting of entities.

Note 3:

Measurement presupposes a description of the quantity commensurate with the intended use of a measurement result, a measurement procedure, and a calibrated measuring system operating according to the specified measurement procedure, including the measurement conditions.

The history of the SI is shaped by the physical sciences. This may explain that the concept of measurement used in the VIM is limited to quantities that can be represented by numerical values arranged in an ordinal sequence. Nominal properties are explicitly excluded (Note 1). This also excludes notions of measurement as used in sciences other than the physical sciences. Prominent examples of measurements with nominal character are the identification of chemical species or agents, the identification of DNA bases, stellar spectral types, and many others [31].

An extension of the concept of measurement will be necessary in future developments if the SI is to truly live up to its claim to be the universal language for all sciences.

This chapter provides an overview of the roots, development, and current status of the SI; it is limited to the measurement concept used in the VIM.

2 Quantities and units

Measurement means assigning numbers to aspects of an object that we want to describe. Aspects such as the length of a table can be made quantifiable by dividing it into quanta that can be counted. So, if we want to determine the length of a table, we take a short rod as a reference measure and count how many of these rods are necessary to encompass the whole length of the table. So, to assign a number to an aspect of our object, the physical quantity, we need a reference (the short rod), which we call a unit. For example, comparing the table with the rod used as a measuring rod gives the number 3.5. We can share this result with a colleague. If this person has an exact copy of our reference rod or has a recipe with which such a rod can be made, he or she can make length measurements themselves that are comparable with ours. By converting the observations of our environment (the length of a table) into numerical form, we map part of the real world into an abstract model to which we can apply mathematical tools. The characteristic of the object to be described is called the “ dimension”: the length, the mass, the time, and so on. So, an object is described by a set of numbers; some of them are dimensional, others are pure numbers. Each dimensional physical quantity Q can be represented as

Here, {Q} is a pure number and [Q] denotes the unit used. This representation can be traced back to J. C. Maxwell [14]. The formal method for describing the mathematical relations between abstract physical quantities is called “ quantity calculus.” The most important elements in the history of quantity calculus are presented in an article by J. de Boer in 1995 [6].

Physics maps the real world into abstract models. The physical quantities play the essential role. They are linked by mathematical equations that express the mutual relationships and the physical laws. In mathematical equations, the objects that are related must have the same dimension. This means that quantities with different dimensions can be multiplied but not added. To ensure the balance of dimensions in an equation, dimensional proportional factors (constants) are introduced. It would be impractical to include such constants in every equation. Therefore, in a system of units, only a few selected quantities have an independent dimension. Here, the system of units means the set of units and the rules that are needed to make all quantities measurable. Let us take the volume of a body as an example. It can be expressed as the product of three lengths l, measured in the unit meter (m). The volume is in general form V=kl3. We can now choose k=1. This makes the unit of volume m3 and the dimension L3. We do not need a new independent unit to characterize the volume. This brings us to the important features of a system of units. It is characterized by a set of conventionally defined dimensions and the base units associated with them. The sizes of the base units are arbitrarily and independently fixed. In addition, there is an arbitrary number of derived units whose...