# Developing relevant measurement science and technology: The new system of units and the future of metrology

### Diederik S. Wiersma

1 Introduction

One can perform an extremely accurate measurement but when the unit of measure is misunderstood, the outcome is useless or can have disastrous effects. NASA lost a spacecraft due to a misunderstanding amongst engineers about the units used in the design of the propulsion system, Air Canada managed to have a passenger aircraft run out of fuel in mid-air due to a confusion about metric units, and, in medicine, expressing blood sugar levels in the wrong units can have fatal effects for a patient. These are some examples of mistakes caused by mixing up units. But how about the problems that arise when the unit of measure itself has a size that is ill-defined? We often take for granted that the meter is simply the meter and the kilogram the kilogram, but what is the meter actually and how is the kilogram defined? And can we be sure that everyone in the world agrees on their size?

Recently a newly defined international system of units – known by many simply as the SI – has come into force, signed in Versailles by representatives of most countries in the world (fig. 1). One of the major changes in the new system resides in the definition of the kilogram, which up till recently has always been defined with respect to a physical object (artefact), while in the new system it is defined with respect to a natural constant – the Planck constant h. Using a natural constant as “unit of measure” for our measurements is a brilliant concept. The natural constants appear in the laws of physics which express our current understanding of the way our universe works.

2 A very short history of lenght

Finding the right reference for performing reliable measurements is a problem with a long history. The Egyptians took the approach of using the body as reference standard with the cubit, palm, and digit being defined as the length from elbow to tip of finger, width of hand, and width of finger. To assure standardization not just any body was chosen as reference, but that of the Pharaoh. Since one cannot disturb a Pharaoh very often to compare the length of objects to his body, primary copies of reference values were made in granite and secondary copies in wood. The resulting, surprisingly modern, system based on monthly recalibration of instruments – further strengthened by imposing the death penalty for non-compliance – functioned with amazing success and accuracy. Similar systems based on artefacts as reference for length, weight, and volume have been used throughout Europe over the centuries with varying levels of accuracy and practicality. A massive downside of this type of system is the inconsistency of reference values in various locations, even within a single country. The value of one foot, for instance, could vary up to nearly a factor two from one city to another.

It was the French revolution that changed this situation forever. While initial ideas of a metric system can be traced back to the age of enlightenment, it was during the French revolution that a practical realization of a metric system was implemented.de Maybe even more importantly, the basic units were taken from the natural world so that they would not be owned by anyone and, in principle, accessible to all peoples and constant for all times. In particular, the metre was defined as one ten-millionth of the distance from the North Pole to the Equator (along the meridian going through Paris – after all the idea of this new system was launched by the French revolutionists). The new decimal system had various advantages and is still used today in most parts of the world. In an attempt to express every measurement in decimal numbers, even decimal time was introduced in the end of the 18th century, although it never gained the success of the other decimal units of measure.

The size of the Earth was clearly a more stable and universal reference with respect to the Pharaos forearm, but it was clearly not easy to measure the distance from the North Pole to the Equator. The technology used for measuring distances was that of triangulation in which unknown distances were inferred from angular measurements on clearly visible objects like towers and hill tops. Amongst the various triangulation studies, a famous one was performed by Méchain and Delambre between 1792 and 1798 – hence in the midst of the French revolution and therefore not without several practical difficulties. As the two men climbed domed volcanoes, churches, and cathedral towers to perform their triangulation measurements, they were sometimes imprisoned as spies, royalists and accused of being sorcerers, while Méchain ended up being trapped in Barcellona when Spain declared war on France. The results of their heroic effort to measure the distance between Dunkerque and Barcelona resulted in a surprisingly accurate result which was only 0.02 percent off with respect to the currently known value. Various previous and successive triangulations to determine the size and shape of the Earth have been performed in different parts of the world, including the massive Great Trigonometrical Survey of India that started in 1802 and which finished nearly seventy years later. The Earth as reference was stable and universal but clearly not very practical. Hence again an artefact had to be produced as primary standard, consisting in a Platinum Iridium bar conserved in a safe at the BIPM in Sèvres (Paris), which served as the standard of the metre until well into the 20th century.

Light can be used to determine length much more accurately than what can be achieved using a platinum iridium bar. People therefore started to use a krypton lamp and interferometry to determine length and this became the de facto standard of length while the official definition of the metre – in an attempt to keep up with developments – was only redefined in 1960 in terms of the wavelength in vacuum of the radiation corresponding to the transition between the levels $2p10$ and $5d5$ of the krypton 86 atom. The accuracy that could be achieved with this definition was again limited by technology – namely that of krypton lamps – and was soon superseded by the invention of the laser. The helium neon laser became the new de facto standard, with the definition of the metre again running behind technological developments.

At that point the metrology community could have used laser light to redefine the metre but they did not. The brilliant decision was taken to define the speed of light instead, that is to assign a fixed number to the speed of light (and hence without uncertainty) and build the definition of the metre on that. In 1983 at the 17th Conférence Générale des Poids et Mesures (CGPM) – the meeting in which representatives from governments world-wide take decisions on the International System of Units (SI) – it was decided that the new definition of the metre would be: “The metre is the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 second.” which was reworded in 2019 to become: “The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299792458 when expressed in the unit m·s-1, where the second is defined in terms of the caesium frequency $\Delta \nu_{Cs}$.”

3 The last artefact

The definition of the metre – based on the speed of light – is so clever since it incorporates automatically any future technological developments. By fixing the speed of light and using that as reference for the definition of length, the accuracy of the unit is only limited to the accuracy by which a practical realization can be achieved, incorporating thereby in the definition all future technological improvements. With the metre defined in this new way, the only base unit that had remained behind, still defined with respect to an artefact, was the kilogram. It was the recent redefinition of the SI units during the 26th CGPM in 2018 in Versailles that finally overcame this imperfection and embedded a redefinition of the kilogram in terms of a natural constant, in particular the Planck constant.

Until that moment there were clear problems with the definition of the kilogram. The International Prototype of the Kilogram, or IPK, as kept in a safe in Sèvres and only occasionally taken out following a complex protocol to make comparisons with national copies, was diverging from its replicas by approximately 50 micrograms since its manufacture in the late 19th century. This was clearly unacceptable since it introduced an inaccuracy in the definition of the unit of mass much greater than what can be measured with current and future technology. Hence a redefinition was in place. Various strategies have been explored by the international metrology community in the last decades to achieve this goal. One possible redefinition, pursued by the International Avogadro Coordination, was based on fixing the value of the Avogadro constant and defining the kilogram in terms of the mass corresponding to a well-defined number of silicon atoms or a physical object of well-defined size made of silicon. While this type of definition was based on a natural constant, it still had difficulties for its practical realization in that it required to either count large numbers of silicon atoms or determine the mass of a physical object with possible inaccuracies arising from surface oxidation, impurities, lattice deformations, amongst others.

After careful consideration, the international metrology community opted for a different redefinition based on fixing the value of the Planck constant (see fig. 2). The Planck constant is related to the quantization of light and matter and equals the energy of a photon divided by its frequency. It can be seen as a subatomic-scale constant of nature and as such plays a fundamental role. Since energy and mass are equivalent through Einstein’s relativity theory, the Planck constant can be used as reference for the definition of mass. When an atom emits a photon of frequency $\nu$ it loses the amount of energy $E = h\nu$, and hence its mass is reduced by the (tiny) amount $E=m/c^{2}$. As we saw above, the definition of the metre fixes the value of the velocity of light $c$, while the definition of the kilogram fixes the value of h. (See also Box 1.)

While the new definition of the kilogram as chosen by the international metrology community might seem, at first sight, somewhat more difficult to understand than the proposal based on counting silicon atoms, it has important advantages regarding its practical realization. In particular, it is now possible to realize the kilogram without creating a physical object. The mass of an object can be determined by a so-called Watt balance, or Kibble balance – named after its inventor Bryan Kibble – in which the weight of an object is compared to the force generated by an electrical current in a magnetic field. This can be done very accurately since excellent quantum standards are available for both electrical current and voltage. Also the local gravitation acceleration g has to be known, but technology exists with which this can be determined with great accuracy. In the new definition the Kibble balance is first used to determine the Planck constant and, later on, becomes a realization of the kilogram, without the use of any artefact.

Even though the alternative pursued by the International Avogadro Coordination was not chosen as new definition, the work performed in this context still provided a crucial contribution to the determination of the Planck constant, required for the new SI (see fig. 3). This collaboration provided a value for the Planck constant, measured with a technology totally independent of the Kibble balance, and consistent with the Kibble balance work with a relative uncertainty of the order of 10-9. That is an amazing achievement and only possible thanks to decades of painstaking improvement of accuracies, analysis, and reduction of systematic errors. Much passion and time of metrologists around the world went into this effort. I still remember the meeting of the Consultative Committee for Units (CCU) in Sèvres in 2018, in which results on the Planck constant were discussed and the decision was taken to move forward with the redefinition of the kilogram. Enrico Massa, who worked with Giovanni Mana at the Istituto Nazionale di Ricerca Metrologica (INRiM) in a lifetime effort to measure the lattice constant of silicon – a value crucially important for the value of the Planck constant using the Avogadro approach and a measurement in which the entire international community put its trust – confessed that he was truly worried the evening before this crucial meeting: “What if, after 40 years of work, there is still some systematic error or mistake that we did not notice?”.

The values for the Planck constant matched and all approvals were obtained to go forward with the redefinition of the SI. It was voted unanimously in favour by the representatives of all member states during the Conférence Générale des Poids et Mesures in 2018 and brought into force on May 20th 2019, the date of the world metrology day. Together with the kilogram, all base units were either redefined or reworded, including the kelvin which became defined using a fixed value of the Boltzmann constant (fig. 4). With the redefinition we now have an international system of units, recognized by nearly all countries in the world through the metre convention, in which the base units are defined with respect to natural constants (fig. 5) (see also Box 2). While there is still an improvement to come in future years regarding the definition of the second, a milestone in the definition of the base units has been achieved and the metrology community – rightfully proud of this results – can move forward from here. Important things to be taken care of in the future include the implementation of the new SI and the development of new metrology science and technology for industry, society, and scientific research in general.

4 Towards the future

Our industry and society are rapidly changing. The recent progress in neural networks has allowed efficient implementation of machine learning algorithms which will change, for instance, the way we drive cars, perform medical diagnoses, control industrial processes and take strategic decisions in general. The full impact that the current digital revolution will have on our lives in the near future is difficult to oversee.

At the same time humanity has put unprecedented pressure on the resources offered by our planet, which means we have to deal with important global challenges including climate change induced by global warming, environmental pollution on various scales, and potential scarcity of resources such as energy, food, and drinking water. Within this rapidly changing context one can ask the question how metrology research and technology can and should develop such that its impact for industry and society, as well as for other fields of science, can be maintained and further improved.

4.1 Focus points for future metrology research

A. Monitoring the environment and supporting the development of clean technologies

The state of our environment poses a major concern in our rapidly changing world. Research programs at national, European, and worldwide level dedicate special attention to environment technologies and the protection of the fragile environment in which we are living. Metrology can play an important role, for instance in assessing climate change and pollution.

Monitoring the environment requires a huge amount of data, collected by different sources (satellites, air-based, marine-based, terrestrial networks, etc.), which require careful traceability, calibration, uncertainty evaluation, and conformity assessment for instruments and procedures. Moreover, the global environment is very complex and hence monitoring initiatives must deal with the specific requirements of atmosphere, sea, and land under investigation, including those under extreme environments (e.g. mountains, polar regions, etc.).

Monitoring the environment is not only a scientific challenge per se, but it is also a trigger to supporting the development of clean technologies. Efficient and reliable assessments of pollution and greenhouse gas emissions in each step of a value chain or during a product life cycle is crucial. In recent years, various methodologies have been developed to quantify and report greenhouse gases emissions, among other things, i) for companies during the whole value chain, ii) for products life cycles, iii) for emission-mitigation projects. Standard protocols are important for planning, comparisons of strategies, products and companies, and for transparent public reporting. However, whereas such a holistic approach is becoming ever more common at the corporate level, end-users tend to focus on very few steps, neglecting large parts of the product life cycle. Faithful measurements of the emissions and clear communication and explanation to the citizens is therefore very important.

B. Supporting sustainable energy conversion and clean storage

The public concern with environmental consequences of energy conversion and storage has increased rapidly in recent years. Effects on the environment happen at all stages, from extraction of raw materials, through manufacturing, distribution, consumption and disposal, and include the depletion of natural resources, pollution, and the degradation of soil and forests.

A limit to the energy that can be made available from renewable sources, which are intermittent and partially unpredictable, is given by the distribution grid and the storage capacity. Various storage approaches are under development that allow for an increase of self-consumption of electricity by small-scale photovoltaic systems, support frequency and voltage regulation of the distribution grid, and decouple energy generation from demand over the time scale of one day. However, batteries play a prominent role because they are particularly suited for the car industry, which canalizes large resources for research and development. Battery production is rather expensive and emits large amounts of greenhouse gases, but the longer the life cycle of a battery the lower is the pollution over the whole life cycle, especially if this allows replacing fossil fuels by renewable sources. Introducing renewable sources into the energy infrastructure is extremely challenging for the grids, because of the need to compensate energy intermittency and to balance energy users and producers. This is typically achieved also by smart metering. Smart electrical, thermal, and fluid grids open new challenges, also because they require new paradigms in distributed metrology and user data protection. Thus, the problem is complex and its solution does not depend only on mere technical improvements but also on social habits, organization, and coordination on a national and international level. Hence the metrological challenge includes the development of methods to measure advantages for the community in such a complex context, and measurements of habits of citizens.

C. Supporting the quality of life and health

Supporting life quality and heath requires that medicines and therapies are assessed, that chronic diseases are monitored over time, and that our food chain is properly protected. If physical metrology has reached its maturity, the situation is much more challenging for chemical metrology and even more for agri-food and biological metrology. In particular, the latter is still actively working on identifying biological markers (biomarkers), which are objective and measurable indicators of normal biological processes, pathogenic processes or pharmacological responses to therapeutics. Once these biomarkers are identified, it is essential to define reference materials, which can be used to ensure the traceability and reproducibility of biological measurements, and to store them in biobanks, namely repositories that store biological samples for use in research and medicine. Similar considerations hold for the traceability and quality assessment of food and medicines.

D. Accelerating digital transformation and supporting industrial transitions

Industrial transitions have significantly changed our society throughout the centuries – from the introduction of steam engines, then mass production, and more recently electronics-based automation. Nowadays industry is facing a new transition based on (large amounts of) data and partially autonomous machines – a concept often referred to as Industry 4.0. Metrology can help to make Europe more competitive in this transition.

Clearly better sensors (smarter, cheaper, and more robust) will play a key role for assessing the quality of measurements. Cheap sensors pave the way towards large-scale sensor networks, which can bring new levels of quality assessment and traceability to primary standards throughout the whole value chain. The use of sensor networks provides a challenge for metrology since it requires a paradigm shift from single, high-quality sensors with extremely low measurement uncertainty to the analysis of large amount of data produced by many lower-quality sensors. These large amounts of data will also require new types of data processing, analysis, and (automated) decision making. At the same time the data and information infrastructure has to be protected against cyber security threads. Digital transformation is much more than collecting data: it is a way to redesign the industrial production (even dynamically) in order to match a wider set of requirements by the customers.

E. Developing technology for space applications and research

Europe manages today the second largest public space budget (Member States, EU, ESA, and EUMETSAT) in the world with programs and facilities spanning different European countries. Because of this investment, Europe can rely on its own space systems like Copernicus for Earth observations, the European Geostationary Navigation Overlay Service (EGNOS), and Galileo for satellite navigation and geo-positioning. Space technologies, data, and services have become indispensable in the daily lives of European citizens. In particular, Copernicus is the most advanced Earth observation system in the world and Galileo is the first civilian-run navigation satellite system, providing highly accurate global positioning data. In spite of this excellent positioning, Europe has to face new challenges due to global competition and the pervasive integration with digital technologies.

The combination of space data and digital technologies allows to develop novel space services for the benefit of society and the European economy. For these reasons, the new EU space program will integrate current activities and will synergically drive them during the next decade. The European Commission envisions to promote the uptake of Copernicus, EGNOS, and Galileo solutions in EU policies. In particular, the Commission aims to facilitate the use of Copernicus data and information by strengthening data dissemination and setting up platform services, promoting interfaces with non-space data and services. From the metrological point of view, this strategic goal requires a careful assessment of the data quality and their improvement by advanced sensors and their integration. Moreover, the Commission intends to promote measures for introducing the use of Galileo for mobile phones, and critical infrastructures using time synchronization.

F. Improving the quality and impact of fundamental scientific research

Properly designed and executed experiments constitute an essential pillar of both fundamental and applied scientific research. While much investigation is done to improve metrology, the use of – often very advanced and reliable – metrology tools to improve the quality of measurements in other fields of research is less common. Yet there is a golden opportunity for scientific progress by strengthening cross fertilization between research communities. Science – in addition to industry and society – constitutes in that respect a customer for metrology.

Certain areas of fundamental science intrinsically require high-precision measurements. Examples include ultra-sensitive quantum physics experiments, time synchronization in fundamental physics experiments, and the determination of fundamental constants. In addition to the research areas that intrinsically require metrology to achieve the extreme accuracy required for their experiments, there are several fields of research that do not require metrology know-how intrinsically, but that can still benefit enormously from the above-described synergy.

5 Conclusions

With the new SI in place and the implementation on its way, the world-wide metrology community has reached an important milestone. All base units are now defined with reference to natural constants, which means that all future technological developments are automatically built into the system. A new chapter opens now in which metrology can help to address some of the current fundamental challenges of our society, including energy, environment, and health. Also an important role for metrology tools to improve scientific research in general can be foreseen. The road to the redefined SI has been exciting and many more dreams are bound to become real.