Metrological Infrastructure 9783110715835, 9783110715682

Table of contents :
Foreword
Preface
Contents
List of Contributing Authors
International system of units: Concept and current design
Measurement uncertainty and metrological traceability
The structure and organization of metrology
International recognition
Impacts of metrology
Metrology for the digital age
Index
List of acronyms

Citation preview

Metrological Infrastructure

De Gruyter Series in Measurement Sciences

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Edited by Klaus-Dieter Sommer and Thomas Fröhlich

Metrological Infrastructure �

Edited by Beat Jeckelmann and Robert Edelmaier

Editors Dr. Beat Jeckelmann Form. Federal Institute of Metrology METAS Switzerland [email protected]

Robert Edelmaier Bundesamt für Eich- und Vermessungswesen Arltgasse 35 1160 Wien Austria [email protected]

ISBN 978-3-11-071568-2 e-ISBN (PDF) 978-3-11-071583-5 e-ISBN (EPUB) 978-3-11-071590-3 ISSN 2510-2974 Library of Congress Control Number: 2023933231 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2023 Walter de Gruyter GmbH, Berlin/Boston Cover image: Wassily and the World of Metrology, Susanna Beyer, llmenau, Deutschland Aus der Sammlung: Measurement lmpressions (Privatbesitz) Typesetting: VTeX UAB, Lithuania Printing and binding: CPI books GmbH, Leck www.degruyter.com

Foreword The De Gruyter Book Series on Measurement Science (DGSM) includes monographs ranging from the mathematical foundations to the connection between metrology and information theory to current developments such as quantum sensing and cognitive sensors and measurement systems. The present volume “Metrological Infrastructure,” which was produced under the leadership of the internationally renowned metrologists Beat Jeckelmann (Switzerland) and Robert Edelmaier (Austria), is the first monograph in the DGSM series. The other planned volumes of the book series will be available within a period of 24 months after the publication of this first volume. The metrological infrastructure is one of the supporting pillars of the quality infrastructure. Although it is not in the first place in the public perception, its importance for the economic success of a country and the safeguarding and promotion of the quality of life should not be underestimated. The metrological infrastructure forms a solid basis for trade and transport, a competitive innovative industry, a secure energy supply, the protection of the environment and health and, last but not least, for areas of security and defense. The two editors of the volume have succeeded in winning proven experts with many years of experience in metrology and its environment as authors for the individual chapters of the book. This fact alone would guarantee the attractiveness of the book volume. The consistently chosen structure of the book starting with the basics of metrology with the International System of Units and the concept of measurement uncertainty, the structure and international organization of metrology, the mutual recognition of measurement and calibration results up to current developments in the digitalization of metrology make the book an important companion and reference work for all metrologists worldwide. This book should be at least as important for university teaching in metrology and information technology as for their industrial application. We firmly believe that this book will become a standard work in metrology. We congratulate the editors and authors on a successful and highly topical monograph and wish it a wide readership. Klaus-Dieter Sommer Technische Universitaet Ilmenau (Germany) Editor of the DGSM Book Series

https://doi.org/10.1515/9783110715835-201

Frank Haertig Vice President of the Physikalisch-Technische Bundesanstalt (Germany) President of the International Measurement Federation (IMEKO)

Preface Whether it is a mundane everyday activity, looking at the body weight readout on the scales in the morning, trying out a new cooking recipe, or adjusting the tyre pressure on a vehicle: There is hardly an activity that does not involve a measurement. Our everyday life without measurements is unthinkable. Not only in everyday life, but also in the whole industrialized and increasingly globalized world are we dependent on measurements. Many sectors rely on correct and comparable measurements: Be it in the expansion of knowledge, the accurate efficient and reliable production of goods, the reliability of medical diagnoses, the monitoring of the environment or the guarantee of data quality in the regulated sector. With a measurement, we quantify the property of an object by comparing the selected property with an agreed reference quantity, and thus assigning it a number that we can communicate to others. For the receiver to make use of this information, a well-established and broadly coordinated infrastructure is needed. This functions largely unnoticed by public perception; we take it for granted. This book is about this infrastructure and the associated science: metrology. In order to be able to measure all the required quantities without contradiction, we first need a system of units of measurement that is valid and accepted worldwide and across all disciplines. After a 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 towards 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 then became the International System of Units (SI) with seven base units today. The SI can be used in all scientific and practical measurement tasks and is rightly regarded as the technical language of science. It 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. Thus, measuring instruments based on quantum sensors become possible, which directly provide the end user with intrinsically stable, accurate measurement results that are directly traceable to the SI. The cumbersome periodic recalibrations of the instrument are thus eliminated. The contribution 1 of the book gives a brief outline of the history and background of the SI, explains the revision of the SI and outlines the resulting possibilities. The concept of measurement uncertainty is closely linked to the concept of measurement. No measurement is exact. A measurement result depends on the properties https://doi.org/10.1515/9783110715835-202

VIII � Preface of the measurement system and the object being measured, on the environmental conditions and on the skill of the operator. A measurement result without information on its uncertainty is useless. Measurement results are the basis for conformity decisions, be it in quality control in the manufacturing of products, in trade or in health and safety protection. Since every measurement result is associated with uncertainty, conformity decisions are always associated with risk. For example, if a driver is caught speeding during a road traffic speed check, the question arises of whether or not a fine is justified based on the knowledge of the measured value and its uncertainty. Only a careful characterization of the measurement system and the resulting probability distribution of the possible measured values makes it possible to quantitatively determine the risk of a false report. With the help of suitable tolerance deductions on the measured speed value, the risk for a wrong decision can be reduced to an acceptable level. Only a broadly supported, standardized procedure for determining and stating measurement uncertainties can ensure that measurement uncertainty data are interpreted uniformly and can be adopted and further used by external bodies. The “Guide to the expression of uncertainty in measurement (GUM),” prepared by a committee of representatives from seven international organizations, provides such a procedure. The GUM is now firmly established and is widely used in standardized measurement, testing and conformity assessment procedures. The concept of measurement uncertainty, the GUM and the concept of metrological traceability are covered in the second part. The third part is dedicated to the structures and organizations at national, regional, and international level that together make up the metrological infrastructure. Along with accreditation, standardization and conformity assessment, this is one of the pillars of the quality infrastructure, and thus an essential element for sustainable economic development and environmental and social well-being. Based on the spirit of the Metre Convention, all industrialized countries have gradually built up a national metrology system that, supported by the International System of Units, strengthens the competitiveness of their own economies, enables fair trade, and provides basic support for maintaining and improving the quality of life. With increasing globalization, the decentralized manufacturing of products and the associated worldwide trade but also the exchange and harmonization of processes and procedures came to the fore. To support and facilitate this development, the member states of the World Trade Organization signed an agreement to reduce technical barriers to trade. In the field of metrology, this led to the claim “once measured or tested, everywhere accepted.” This goal can only be achieved if countries recognize the equivalence of their national measurement standards among themselves. Until the end of the 20th century, this mutual recognition was regulated by a multitude of bilateral agreements. Unification was achieved in 1999 with the signing of the agreement “Mutual recognition of national measurement standards and of calibration and measurement certificates issued by national metrology institutes” within the framework of the Metre Convention. For the first time, a worldwide uniform approach to mutual recognition was achieved. The

Preface � IX

agreement is based on transparent, strict, and consistently applied technical criteria. All data collected in the processes can be viewed in a publicly accessible database. Detailed information on this is described in Part 4. The metrological actors from the National Metrology Institutes to the calibration laboratories and the associated organizational structures play an underpinning role. The output consists of realized units of measurement, the measurement, and calibration possibilities based on them and, therefore, the traceability chains from each measurement to the SI. The output also consists of metrological tools such as instruments, software, reference materials, and measurement methods, of best practice guides and standards, and finally of metrological know-how imparted. All these outputs are necessary to ensure that measurement data are robust, comparable and resilient, and to help make evidence-based and informed policy decisions, reduce barriers to trade and build trust in trading partners, enable robust and sustainable health care, secure energy supplies and reliably measure the state of the environment. Part of the impact chain is also supporting industry’s ability to compete and innovate and, finally, the constant shifting of our knowledge horizon in science. Part 5 of this book gives some selected examples of the concrete impact of metrology, and thus attempts to make its rather hidden infrastructure role more visible. We live in the age of digitalization. A key feature of this development is exponentially growing volumes of data that are evaluated and made usable with algorithms, increasingly using artificial intelligence methods. Trust in the data and algorithms is a basic prerequisite for their sustainable and reliable application. This opens up new tasks for metrology. Through the development of reference procedures and the provision of reference data, metrology can enable quantifiable statements on the reliability and trustworthiness of simulations, algorithms, and AI methods in the future. In general, the consistent application of metrological principles in dealing with data promotes data security, and thus trust in these data. Consequently, this creates added value. Modern communication technologies enable the use of large-scale multisensor, multiparameter, and multinode systems, and thus the availability of networked information. In the “Internet of Things,” physical objects can be seamlessly integrated into the global information network. The networks are characterized by the use of novel sensors based on quantum-, bio-, and nanotechnologies, by the use of a large number of sensors of different types and by the integration of data from different systems. The metrological characterization of such networks requires a new interpretation of the concept of traceability and the development of new procedures for calibration. This represents an expansion of the scope for metrology triggered by digitalization. The last part of this book deals with these new aspects and ventures an outlook into the near future. This volume is intended to provide users of metrology and the general public with a broad overview of the infrastructure aspects of metrology. It is aimed both at those who are not familiar with the subject and are looking for an introduction, and at those who are involved in metrology at various levels but would like to get more insights about the subject or simply obtain specific information.

X � Preface As editors of this volume, we would like to thank the authors of the individual parts for their competent contributions. Beat Jeckelmann Robert Edelmaier

Contents Foreword � V Preface � VII List of Contributing Authors � XIII Beat Jeckelmann International system of units: Concept and current design � 1 Walter Bich Measurement uncertainty and metrological traceability � 23 Beat Jeckelmann and Ulrike Fuchs The structure and organization of metrology � 57 Andy Henson International recognition � 81 Robert Edelmaier Impacts of metrology � 111 Sascha Eichstädt Metrology for the digital age � 131 Index � 155 List of acronyms � 159

List of Contributing Authors Walter Bich Istituto Nazionale di Ricerca Metrologica 10135 Torino Italy E-mail: [email protected]

Ulrike Fuchs Bundesministerium für Arbeit und Wirtschaft Vienna Austria

Robert Edelmaier Bundesamt für Eich- und Vermessungswesen (BEV) Vienna Austria E-mail: [email protected]

Andy Henson Retired from Bureau international des poids et mesures (BIPM) Exeter United Kingdom E-mail: [email protected]

Sascha Eichstädt Physikalisch Technische Bundesanstalt (PTB) Braunschweig Germany E-mail: [email protected]

Beat Jeckelmann Self-employed 3286 Muntelier Switzerland E-mail: [email protected]

Beat Jeckelmann

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.” [28]

Beat Jeckelmann, Self-employed, 3286, Muntelier, Switzerland, e-mail: [email protected] https://doi.org/10.1515/9783110715835-001

2 � B. Jeckelmann 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.

International system of units: Concept and current design

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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 Q = {Q} [Q].

(1)

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 size and dimension depend on the conventionally-fixed base units.

4 � B. Jeckelmann This dependence is determined by a mathematical equation. This equation also contains a constant to which one can assign any value and any dimensions. A system of units is called coherent if the derived units for a given system of magnitudes and a chosen set of base units are products of powers of base units, with the proportionality factors taking the value 1.

3 Historical background to the International System of Units 3.1 From ancient measures to metric units Fair trade in goods has always required units of measurement for length, weight, and volume set by the state or local authorities. Measures from ancient times in the form of artefacts have been preserved until today. The oldest known yardstick dates back to the 3rd millennium BC, was found in Nippur, Mesopotamia, and is called the Nippur cubit [8]. It is an impressive object, made of copper and with a weight of 45.5 kg. The markings on the scale represent the units cubit, foot, and finger. The cubit is equal to 51.8 cm. All premetric units of length can be derived from the Nippur cubit. In Egypt, around the same time, the royal cubit was introduced, a primary scale made of granite. Wooden copies of it served as working standards; they were periodically compared with the royal cubit. Even then, the principle of traceability applied, which is still the basic prerequisite for comparable measurements today. In the Middle Ages, too, measurements were used that could be derived from body masses. In the eighteenth century, however, there was still a great deal of chaos with regard to units of measurement. Every region had its own units. A measurement was inseparably linked to the measured object; it referred to a certain locally existing standard. To make matters worse, the technique of measuring also depended on local customs. This made trade more difficult and encouraged abuse and fraud. In his book, “The Measure of the World” [1], Ken Alder vividly describes the variety of designations in use and the incredible number of weight and measurement units in France during the Ancien Régime. The impetus for improving this situation came from France. At the time of the French Revolution, the idea matured to trace the unit of length back to a quantity given by nature. Two proposals were discussed in the Académie des Sciences. One idea was to derive the unit of length from the length of the seconds pendulum. In this pendulum, the half oscillation T1/2 lasts one second. According to the model equation for the mathematical pendulum, the length is linked to the oscillation period by L=g(

T1/2 2 ) . π

(2)

Unfortunately, the length also depends on g, the locally acting acceleration due to gravity. This varies depending on the position of the observer. With an average value of

International system of units: Concept and current design

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9.806 m/s2 , the length of the pendulum is 0.994 m, quite close to 1 m. The dependence on g is the main disadvantage of this proposal, but the big advantage is that the unit of length can be reproduced anytime and anywhere by building a seconds pendulum. The 2nd proposal was to base the unit on the circumference of the earth at the equator or on the length of a meridian. The choice finally fell on the earth’s meridian in 1793. The unit of length, called the meter, was to be fixed as the ten-millionth part of the meridian arc running through Paris between the equator and the North Pole. Two of the best astronomers of the time, Jean-Baptiste Delambre and Pierre-François-André Méchains were entrusted with the survey. In the midst of the turmoil of the French Revolution, the two scientists surveyed the part of the meridian between Barcelona and Paris (Méchains) and between Paris and Dunkirk (Delambre) in separate expeditions. The mission lasted six years, between 1792 and 1798, and is described in detail in the very readable book by Ken Alder [1]. In order to gain acceptance for the new unit of longitude beyond France, an international expert commission was convened to assess and analyze the geodetic data collected. This met in Paris and established the meter in 1799. For the mass unit, which was initially named grave, the mass of a cubic decimeter of water was chosen. Later the name was changed to kilogram, and in 1799 the kilogram was finally defined by the mass of a platinum cylinder, which corresponded to one cubic decimeter of water at its highest density (4 ∘C). The meter derived from the measurement of the Earth’s circumference was transferred to a cuboid platinum rod. The new original meter was brought to the Archives of the Republic in Paris on June 22, 1799. This event can be seen as the first step in the development of today’s International System of Units. Today, we know that the meter was set 0.2 mm too short. On the one hand, because Méchains had made a mistake when determining the latitude in Barcelona and, on the other hand, because the possibilities of data analysis were not yet sophisticated enough at that time to take into account the actual shape of the meridian arc. It turned out that, in addition to the well-known flattening at the poles, the Earth has other deviations from the ideal shape. Every meridian is different, and thus the original idea, namely to trace the meter back to a universally valid reference measure, could not be fully realized. In 1832, Gauss strongly advocated the use of the metric system in physics. He introduced a system of units based on the millimeter, the gram and the second defined in astronomy. Gauss and Weber later extended the system to electrical units. In the 1860s, Maxwell and Thomson developed the concept for a coherent system of units with base and derived units, which finally led in 1874 to a system based on the three mechanical units centimeter, gram and second, the so-called CGS system. As described in the section above, the term “coherent” in this context means that the derived units are derived from the base units by multiplication and division without the use of additional numerical factors. For a long time thereafter, the development of experimental physics was based on this system. In electricity, however, the CGS system was not initially very popular because the coherently derived electrical CGS units were perceived as impractical. For this reason,

6 � B. Jeckelmann practical electrical units were defined in the 1880s. These were based on practical, easily repeatable artefact standards adapted to the needs of the emerging electrical industry. Parallel to the development in physics, the metric system with kilogram and meter did not really become established in everyday life in France until 1840. Other countries gradually followed the French system and finally agreed to introduce the metric measure in 1875 in the Metre Convention. New prototypes for the meter and the kilogram were produced from a platinum-iridium alloy. These new standards, known as International Prototypes, were officially adopted by the 1st General Conference on Weights and Measures (Conférence Genérale de Poids et Mesures: CGPM) in 1889. Together with the second, these units formed a system of units with three base units, the MKS system. It is interesting to note that the unit of time, the second, was not a subject of discussion in the Metre Convention at that time. It was a matter for astronomers and defined as the 1/86’400th part of a day. This fraction is derived from the division of the day into 24 hours at 60 minutes, and finally at 60 seconds each. This sexagesimal division of the day existed since the 3rd millennium BC. But it was not until the seventeenth century that clocks were able to count seconds accurately. In 1901, Giorgi showed a way to connect the MKS system with the practical electrical units. He proposed a coherent system that, in addition to the mechanical base units m, kg, and s, included an additional base unit of an electrical nature, the ampere or the ohm. It took until the 1920s before Giorgi’s proposal was also discussed in the bodies of the Metre Convention and in other international organizations. In 1939, the Consultative Committee for Electricity (CCE), a technical body under the Metre Convention, proposed an expanded system of units with the ampere as an additional base unit, the MKSA system. It was not until 1954 that the ampere was finally officially introduced by the 10th CGPM, together with the kelvin as the base unit for thermodynamic temperature and the candela for luminous intensity. The name “International System of Units (SI),” which is still valid today, was introduced by the 11th CGPM in 1960. Finally, in 1971, the 14th CGPM defined the mole as the unit for the quantity of a substance, and thus increased the number of base units in the SI to seven.

3.2 Characteristics of the SI The SI is a coherent system of units. It has seven base units, the last one, the mole, was introduced in 1971 and opens the way for measurement quantities outside the physical world. The expansion of the number of base units in the course of time shows that practicality for the widest possible circle of users was a priority in the development of the system of units. According to the traditional approach going back to C. F. Gauss, the three basic dimensions of length, time, and mass are necessary and sufficient to express the dimension of each physical quantity. It is not mandatory, as in the SI, to define dimensions for electricity, temperature, luminous intensity, and quantity of

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Table 1: SI base units.

Name

Base quantity

time length mass electric current thermodynamic temperature amount of substance luminous intensity

Typical symbol

Base unit Name Symbol

Dimension

t l, x, r, etc. m I, i T n Iv

second meter kilogram ampere kelvin mole candela

T L M I Θ N J

s m kg A K mol cd

matter with the corresponding base units. It is practical considerations that led to this choice: – The introduction of the ampere, as already mentioned, was about integrating the practical electrical units in use for application reasons into a coherent system. – The thermodynamic temperature corresponds to the average energy of an ensemble of particles. It is thus proportional to the thermal energy and can therefore be measured in energy units. Until recently, however, this was not possible with sufficient accuracy, so that an independent temperature scale with its own dimension had to be defined and the proportionality factor between temperature and energy, the Boltzmann constant had to be determined experimentally. – There would also be no need for a separate base unit for measuring the intensity of light. Light is electromagnetic radiation and can be measured in the already known units. However, because of the central importance of the human sense of sight, it was agreed to define separate units for the subjective effect of electromagnetic radiation on the human organ of sight, and for historical reasons, also a separate base unit. With the photometric units and the candela as the base unit, light is thus not only measured according to its physical nature, but also according to the perception of the human eye. – Finally, the mole allows the number of particles in a substance to be indicated in a handy way. Here, too, the assignment of a dimension to a simple conversion from a very large number to a small number is done for practical reasons. Table 1 gives an overview of the base quantities and units of the SI.

4 The development of the SI using the unit of length as an example The Metre Convention of 1875 laid the foundations for a globally valid system of units. This system specifies the units of measurement with which the properties of objects can

8 � B. Jeckelmann be measured. Measurement results are identical or comparable, regardless of where and with what equipment measurements are made. It is clear that the result of a measurement cannot be more accurate than the scale used. The definition or determination of a unit will therefore not last forever. Adjustments over time are necessary to keep pace with the progress of science and technology. The development of the unit of length, the meter, over time is a good illustration of this process.

4.1 Representation of an unit through an artefact: The 1889 prototype meter The aim of the meridian expedition was to realize a measure of length that could be traced back to a constant of nature and was thus independent of human arbitrariness. The goal was only partially achieved. It turned out that the meridian arc was not really a constant. Also, a repetition of the meter realization over the meridian was very complex and time-consuming. In addition, precision metrology was also developing rapidly. The Mètre des Archives, which was made of platinum, soon no longer met the requirements as an embodiment of measurement. For these reasons, it was decided in 1872 to replace the meter with a newly manufactured artefact made of a more stable platinumiridium alloy (90 % platinum, 10 % iridium). The new artefact was designed as a bar with an X-shaped cross-section (see Figure 1). The distance between the lines marked on the bar corresponded to the length of the Mètre des Archives derived from the meridian. The new original meter was introduced in 1889. The definition of the meter in the 1927 version was as follows: “The unit of length is the meter, defined by the distance, at 0 °, between the axes of the two central lines marked on the bar of platinum-iridium kept at the Bureau International des Poids et Mesures and declared Prototype of the meter by the 1st Conférence Générale des Poids et Mesures, this bar being subject to standard atmospheric pressure and supported on two cylinders of at least one centimeter diameter, symmetrically placed in the same horizontal plane at a distance of 571 mm from each other.”

Thus, the relationship to the length of the meridian arc exists only indirectly, the unit of length is defined by the prototype meter, an artefact made of platinum-iridium. This step corresponded to the state of the art at the end of the nineteenth century. Characteristic of an artefact-based unit definition is: – The unit of measurement depends on a number of external parameters. For example, the meter prototype changes its length by approx. 0.3 mm when it is heated from 0 ∘C to 20 ∘C. External influences or aging processes in the alloy can result in a change in length. – The artefact is only available at one location. It is imperative that copies of the artefact are used to pass on the unit. – The artefact can be damaged or even lost.

International system of units: Concept and current design

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Figure 1: Left picture: National copy of the meter prototype; used to represent the unit meter from 1889 to 1960 (source: Physikalisch-Technische Bundesanstalt). Right picture: Iodine stabilized He-Ne laser, provides light of exact frequency for interferometric length measurements; realization of the meter since 1983 (source: Federal Institute of Metrology METAS).

4.2 Light as a measuring standard The development of quantum mechanics at the beginning of the 20th century opened up the world of atoms. Atoms have the property that the electrons are in quantized energy states around the atomic nucleus. During the transition from one state to another, electromagnetic radiation with a defined wavelength is emitted. This wavelength represents a natural measuring standard. A. A. Michelson took up this idea and as early as 1887 he proposed using an optical interferometer to measure length. Michelson subsequently succeeded in making a first comparison between the prototype meter and the wavelength of a red cadmium spectral line [20]. After that, the Physikalisch-Technische Bundesanstalt in particular led the way in the development of an interference comparator and suitable spectral lamps. With the realization of a krypton 86 spectral lamp, which produced orange-red light with the most stable and most reliably reproducible wavelength at the time, the precision of the original meter was surpassed in 1951. Subsequently, the meter was redefined in 1960: “The meter is the length equal to 1 650 763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton 86 atom.”

With this new definition, and thus the connection of the unit to a natural constant, an improvement of the measurement accuracy by a factor of 10 could be achieved [3]. Compared to the earlier, artefact-based definition, there are a number of advantages: – The realization of the unit is independent of place and time. – Each krypton atom has the same properties. – A suitable experimental set-up is sufficient to realize the unit of length. As a limitation, it should be mentioned that the definition is bound to a selected atomic transition. The properties of this transition, such as its line width, thus set a natural limit to the accuracy of the meter definition.

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4.3 The fundamental constant as the ultimate natural unit In the year of the meter definition with reference to the krypton transition, the laser was discovered. This turned out to be an excellent light source for interferometry thanks to the high temporal and spatial coherence of the laser light. Different wavelengths were possible and soon it was also possible to stabilize the laser frequency to a transition in selected molecules. The iodine-stabilized He-Ne laser with a wavelength of 633 nm was particularly successful (see Figure 1). Lasers made it possible to determine the speed of light. The wavelength of light is related to the speed of light c via the equation λ=

c ν

(3)

where ν stands for the frequency of light. Soon the accuracy of the meter realization became the limiting factor in determining the speed of light. An obvious step would have been to use a more suitable transition for a redefinition of the meter instead of the krypton transition. Instead of this not very far-sighted strategy, the responsible bodies of the Metre Convention chose a new visionary approach. They fixed the value of the speed of light numerically and redefined the meter on the basis of the speed of light and the definition of the time unit second. The 17th General Conference on Weights and Measures established in 1983, only 23 years since the last revision of the meter definition: “The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.”

This definition fixes the value of the speed of light in vacuum at 299 792 458 m s−1 . This definition has important advantages. – The speed of light is one of the most important constants in physics. It appears as a connecting point in countless physical equations. – The constant describes a fundamental limiting principle (special theory of relativity). – By choosing c as the natural unit, the meter definition is detached from a specific physical state (atomic transition) with its natural and experimental limitations. – New physical discoveries and new technologies may allow a more precise unit realization without changing the definition of the unit. We have seen how the definition of the unit of length meter has evolved from being an artefact, to being based on a physical state, to being based on a fundamental natural constant. In recent decades, many metrologists have worked to apply this strategy to the other units of the International System of Units.

International system of units: Concept and current design

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5 The 2018 revision of the SI 5.1 Replacement of the last artefact With the introduction of the mole in 1971 as the 7th base unit, the International System of Units opened up to measurement quantities outside the physical world and established itself as a universally valid measurement system for all measurements relevant in science, industry, and worldwide trade. Nevertheless, more than 100 years after Maxwell, a weak point remained in the system: the unit of mass, the kilogram, was still represented by an artefact, the Prototype of the kilogram, introduced in 1889. The Prototype kilogram is carefully preserved at the BIPM. Copies of the Prototype are guarded at National Metrology Institutes around the world and used to disseminate the unit in their respective countries. Comparisons with the Prototype of the kilogram were carried out at astonishingly long intervals to ensure the traceability of the unit. The results of this so-called “periodic verification” are shown in Figure 2 [12], [26]. Since the standards compared are artefacts, it is not surprising that the absolute differences in mass increase over time. On average, the mass of the national copies seems to increase by 50 µg per 100 years compared to the Prototype of the kilogram. Although this is quite small and speaks for the high quality of the artefacts, it must also be noted that this is a relative

Figure 2: Relative change in mass of the six official copies and seventeen national prototypes with respect to the mass of the International Prototype kilogram. The zero line is for the assumed constant value of the prototype according to the definition. The solid green line is the average mass drift (50 µg in 100 years) of the national prototypes. The gray band of ±20 µg represents the uncertainty that was to be achieved for the redefinition of the kilogram.

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Figure 3: Principle of the X-ray crystal density experiment. The volume of a single crystal sphere made of enriched 28 Si is measured geometrically. The lattice constant of the crystal is determined by X-ray interferometry. The experiment establishes the link between the mass of the sphere and the mass of a silicon atom.

movement. How the mass of the Prototype kilogram changes absolutely over time is not known. This uncertainty is not limited to the unit of mass. The electrical units are linked to the kilogram via the ampere definition. A drift in the unit of mass therefore also means the same relative drift in the electrical units. In the last few decades, metrologists have spared no effort to remedy this significant weakness of the SI. The goal was to realize a link between the kg and a natural constant with a relative uncertainty of