A brief history of metrology: past, present, and future

In this paper, we take the freedom to paraphrase Stephen Hawking's well-known formula and approach, for a reflection about metrology. In fact, metrology has a past, a present, and a future. The past is marked by a rich series of events, of which we shall highlight only those which resulted in major turns. The impact of the French Revolution is indisputably one of them. The present corresponds to a significant evolution, which is the entry of metrology into the world of quantum physics, with the relevant changes in the International System of units (SI). An apercu of the actual state of the art of metrological technology is given. The future is characterised by a persisting need for a still enhanced metrology, in terms of performance and domain covered. In this respect, soft metrology seems to constitute a promising field for research and development.


Introduction
In these times where significant changes in the International System of units (SI) are taking place, it may be worth to establish a short assessment about when and why the question of metrology has emerged. As a matter of fact, the history of metrology has included plenty of events. Since enough books and courses already have thoroughly treated this subject [1,2], we shall highlight here only the most significant of them. It is especially interesting to try to understand what have been the difficulties encountered, and which answers have then been found to overcome them.
We shall conclude by an overview of what are today the metrological performance attained for the different physical quantities and contexts, and what are our current expectations for the future.
Concrete examples to illustrate our remarks will be taken from the domain of electricity.
What is a kilogram? A kilogram is that sort of thing which, most of us when over 40 years old, would like to lose a few ones ...

The choice of a numeration base
Measuring consists in assigning numerical values to quantities in play, i.e. give an experimental, and quantified, description of the reality. This means that a clear numeration system should have been previously defined.
We are today accustomed to a decimal numeration basis, and we even consider it sometimes as natural. By the way, humans have ten fingers.
But a great number of other possibilities could have been considered. Base 12, accepting sub-multiples 2, 3, 4, and 6, would have been more practical. Also if our ancestors had known computer science, they would possibly have chosen either an octal base (8) or a hexadecimal one (16).
A given numeration base being chosen, a rational associated unit system must use consistent multiples and sub-multiples, i.e. in our case a decimal system. But a decimal system has long been considered unpractical, in some commercial issues, for instance to operate sharing of a given object, may it be land, bread, tissue, etc. Thus, many ancient unit systems used non-decimal values for subquantities, such as 12, 20, or even 60.
Same considerations also applied in parallel, outside the domain of physical quantities, to the domain of currencies.
3 Some historical confusions, having hampered metrology

The confusion between weight and volume
The difference between weight and volume was not so clear in the remote past. Actually, the measurement value associated to weight, for a given amount of goods, is exact, whereas the measurement of volume is approximate; it remains today something of this, would it be only in the today non-modifiable name "Bureau des Poids ET Mesures".
For most goods, the equivalence between weight and volume remained sufficient for commercial operations during centuries, at least, for instance, for liquid goods. But an important sector for trade was seeds. It is clear that in this field the confusion may lead to inaccuracy, and moreover to treachery.
Legal institutions made their best to take into account the consequence of this confusion. For instance in France, Minister Colbert (1670) clarified the notions of "mesure rase" (flat surface of a seed barrel) and "mesure comble" (curved surface of a seed barrel). Even so, the seed quantity remained dependant on the pressure exerted on the upper surface of the barrel, and on the barrel cross-area [3].

The confusion between weight and mass
Still today in current life, the distinction between the two parameters is often ignored, whereas the weight is a force, depending on the location, and the mass is a scalar, and intrinsic to an object. The no longer used unit kilogramforce was in this respect not helpful to raise the ambiguity.

The confusion between temperature and heat flux
A similar observation, i.e. a distinction still today ignored, concerns temperature and heat flux. But it should be noted that a scientific interpretation of both concepts took place very early in history. At the time of Boltzmann, very little was yet known about the intimate structure of matter, in terms of atoms and particles; and despite of this, a theory for thermodynamics based on statistical distribution of kinetic energies could be elaborated.
Anyway, we shall always hear people complaining "I cannot bear HEAT", etc.

Does physics obey to political power?
For the quantities most important for trade, i.e. weight and length, the definition of units was extremely diverse, regarding geographic dispersion. This was an obvious obstacle to equitable and efficient transactions.
As we shall see, in many countries political authorities tried, therefore, to impose their views on the subject, so as, in the same time, to confirm their authority. In China, archaeological discoveries demonstrate the use of a decimal metric system as soon as 1600 B.C. Around 200 B.C., at the same time the whole country was unified, a unique unit system was also spread into it.
The accurate dimensioning of Egyptian pyramids witnesses of an advanced mastery.
Significant research works on the subject have been led by University Paris 7 [4].

The middle ages and monarchic times
Although very different, these two long history periods present common features concerning metrology.
The political power was very disseminated in the middle ages, and was on the contrary very centralised under monarchy, which sometimes confined to absolutism. The feudal system, characterised by dispersion, subsisted in some way under monarchy. The problem regarding metrology was the same in both cases: the affirmation of authority. Every king, lord, town council, monastery, etc. had a tendency to define its own units, as a sign of its power, according to the principle "a king, a law, a weight, a measure".
Hence, a great number of different units, also different according to the nature of the goods, measured. Thus, a pound of weight was different for wheat, barley, or flour. Just to illustrate the problem (but, in fact, innumerable examples of this could be given), the measurement of surfaces in the Généralité de Paris (the surroundings of Paris), in 1780-although a late date À made use of the unit arpent, for which existed at least 48 definitions. Moreover, each of these definitions used specific subunits, the length perche being worth here 20 feet, there 25 feet, and yet elsewhere 22 feet 6 inches [3].
Very complicated transactions resulted of this, voluminous manuals and many calculations were required for the unavoidable conversions.

The progress brought by illuminism and the French Revolution
The intervention of the French Revolution in the field of measurement and metrology had social and ethical purposes. The unit system should be unique and equal for all, a goal consistent with the motto of the Republic, and with the expectations of the population as collected by the cahiers de doléances (peoples' claim books).
The use of the decimal system introduced drastic simplifications, especially for the determination of surfaces and volumes. These simplifications applied to any citizen, enabling him to proceed to easier exchanges with others, and hence increasing in general welfare.
In fact, the Revolution imposed both things, still unfamiliar, which were decimal numeration and a simplified measurement unit system.
In most domains the proposed reforms were successful, and progressively adopted by other countries, first in Europe, and later beyond (Fig. 2).
However, it should be noted that the attempts of revolutionists in the domain of time were unsuccessful. The goal was to implement, in addition to the revolutionary calendar, weeks of 10 days, hours of 100 min, and minutes of 100 s. But the way to count and display hours and days is something so familiar to everyone, that this reform has always remained unpopular and was finally never applied.
Also, the proposition to use the quarter of the tenth million part of the terrestrial meridian was not due to the Revolution, but was much older, first made by French mathematician Gabriel Mouton a century before (1670). This occurred just two years before French theatre author Moliere described, in the Learned Ladies, the current state of the minds about women willing access to science: not very advanced at that time.

From 17th to 21th century
The main evolutions in the field of metrology during this last period have been the development of scientific discoveries, the intensification of exchanges, and the settlement of international institutions. Table 1 proposes an overview of these events, in a summary of 14 steps.

.1 The international institutions
The context today for metrology is fortunately more cooperative than competitive. A set of international institutions, closely linked to one another, have taken place: These institutions have received authority to act in matters of world metrology from the Convention of the Metre (a diplomatic treaty between 51 nations initially, but today approved by almost all nations).
This particularly concerns the demand for measurement standards of ever increasing accuracy, range, and diversity, and the need to demonstrate equivalence between national measurement standards. The Convention was signed in Paris in 1875 by representatives of 17 nations.
The National Metrology Institutes (NMIs), such as PTB in Germany, or LNE in France, constitute the local relays of the international institutions.
The global organisation is completed by World Regional Institutes (RMOs), according to the map in Figure 3.
The regional institutes are less known than NMIs; however, their role is important. They have responsibilities: to facilitate traceability to primary realisations of the SI; to coordinate comparisons of national measurement standards; to make mutual reviews of technical competencies and quality systems; to cooperate in metrology research and development; to operate joint training and consultation; and to share technical capabilities and facilities.  Proposition for a new length unit based on the terrestrial meridian 1799 Creation of the decimal metric system Two platinum standards, representing the metre and the kilogram manufactured 1832 Austrian mathematician Gauss strongly promotes the application of the metric system, together with the second defined in astronomy, as a coherent system of units for the physical sciences; first measurements of the Earth's magnetic field take place 1860 Maxwell and Thomson formulate the requirement for a coherent system of units with base units and derived units 1880 Approval by IEC of a mutually coherent set of practical units. Among them were the Ohm for electrical resistance, the Volt for electromotive force, and the Ampere for electric current 1875 Signing of the Metre Convention, which created the BIPM, established the CGPM and the CIPM, and adopted the MKS system 1889 The first conference of CPGM takes place 1901 The so-called rationalised proposal of Giorgi, for a single coherent four-dimensional system, by adding to the three base units a fourth unit, of an electrical nature such as the Ampere or the Ohm, and rewriting the equations occurring in electromagnetism 1939 Adoption of a four-dimensional system based on the metre, kilogram, second, and Ampere, and the MKSA system, a proposal approved by the CIPM in 1946 1954 Introduction of the Ampere, the Kelvin, and the Candela as base units, respectively, for electric current, thermodynamic temperature, and luminous intensity 1960 The name International System of Units, with the abbreviation SI, is given to the system 1971 Introduction of the last SI base unit: the mole, as the base unit for amount of substance, bringing the total number of base units to seven 1999 Signature of the CIPM-MRA (Mutual Recognition Agreement), for international recognition of national measurement standards 2018 New definition adopted concerning four base units on 7 (see hereunder Sect. 6.3) The significant role of CAFMET (African Committee of Metrology) is also to be mentioned, as a key factor in the creation of AFRIMET.
Among other tasks, the international institutions have issued a set of fundamental documents: the VIM (International Metrology Vocabulary) [5], the GUM (Guide to the expression of Uncertainty in Measurement) [6], and defined the rules for mutual recognition between NMIS, for national measurement standards, and for calibration and measurement certificates (CIPM Mutual Recognition Arrangement À 1999).

The unit system
The 11th CGPM (1960) adopted the name Système International d'Unités (International System of Units, abbreviation SI), for the recommended practical system of measurement units. SI units are divided into two classes: base units (7) and derived units.
To have a realistic approach of practices, these two unit sets are completed by the so-called SI-compatible units, SI-temporarily compatible units, and SI-non-compatible units [7].
It can be seen that in this arrangement, many units were dependent from other units as shown in Figure 4.

The most recent changes
The 26th CGPM has taken place in November 2018, and has approved several significant changes through its Resolution A [8]. Goals of this evolution have been recalled, i.e. to build a system that would be "uniform and accessible world-wide for international trade, hightechnology manufacturing, human health and safety, protection of the environment, global climate studies and basic science . . . , stable in the long term, internally selfconsistent, and practically realizable".
Thus, values of seven general constants, as described hereunder, whose numerical value was initially obtained by experimentation, have been defined as exact values.
The definition of each of the seven base units of the SI relies on one of these constants, according to the diagram of Figure 5. Older definitions are said abrogated by [8].
The physical process used for the definition of four of the seven base units is renewed. Former references which were the international prototype of the kilogram (IPK), an electromagnetic force for the Ampere, the triple point of water for the Kelvin, and the carbon 12 atom for the mole are no longer used.   An in-depth analysis of the nature and consequences of the planned changes may be found in [9]. Attention is especially drawn in paper [9] on some remaining criticalities about the consistency of the SI logical edifice. To give just a brief look into the problem: in which units should the fundamental constants themselves be expressed? Future research works will have to investigate this, sooner or later, to overwhelm these difficulties.
Prior to the last revision of the SI, major evolutions have concerned the domain of electricity: a new technique has emerged to represent the volt: this technique is based on the Josephson effect; and another new technique has emerged to represent the ohm: this technique is based on the Quantum Hall Effect (QHE).
Both techniques require cryogenic setups (T ∼ 3 K) for practical implementation of superconductive environments; both are also based on quantum mechanics considerations.
The revision of the SI, in connection with the changes concerning the Ampere, has allowed to reintegrate the volt and the ohm, which were in practical outside the SI since CIPM Recommendations 1 and 2 of 1988, into a consistent system.
The three main electrical parameters, voltage, intensity, and resistance, through their relations with exact constants h and e, form the Quantum Metrological Triangle.
This progress in coherence constitutes one of the major advances related to SI revision [10].
It has also been underlined that "the new definitions do not prescribe particular realization methods" [11].

The impact of new definitions
New definitions of units will have an impact on reproducibility data, according to [9] (Tab. 2): In fact, this impact is weak and will be visible mainly for NMIs. The badly understood distinction between volume and weight has long been, as already said, a factor for progress slowdown. This problem may be regarded as solved today.
However, the unit stère for a volume of 1 cubic meter of wood is still in use, although a quite inaccurate measure of the quantity concerned, but practical, because it allows visual estimation of the quantity.

Resistance to changes also has often impacted progress
The human mind presents some inertia. Understanding of new discoveries is sometimes difficult; daily ways of thought and habits can be hard to change.
This resistance explains the upkeep of SI-compatible units (angle degrees, litre, electron-volt, etc.) and even SInon-compatible units (carat in jewellery, faraday in chemistry, bar in meteorology, horsepower in mechanics, calorie for food, and all the Anglo-Saxon units).
We certainly would not, in the future, express distances in seconds, although it would be quite logical: 1 m corresponds to 3.335 ns, referring to the speed of light in vacuum. This state of things will persist. In the same time, we currently accept the light year as a distance.

Economic competition has sometimes played a negative role
Specific unit systems have À or still are À in some cases to be considered as a tool for the protection of trade. This probably explains the (rare) cases of countries still resisting to the use of the metric system. Even in these cases, the local standards institutions, such as IEEE, do so as to provide appropriate guidance documents [12].
8 The next steps 8

.1 What means metrological performance?
This performance relies on the following factors: the range accessible to measurement; and the accuracy of such measurement, i.e. the associated uncertainties.

Performance aimed at fundamental research
About accuracy, a present state of the art for the different physical quantities may be established as follows. Table 3 gives indicative values of currently attainable relative uncertainties (indicative means outside the It can be observed that the most accurate quantities are "mechanical" ones, i.e. time, length, and mass. Among these, time is the most precise.
Performance of electrical quantities comes after, and is quite good; thermal quantities are somehow under, and lastly luminous quantities have rather limited accuracy, due to the fact that physiological aspects necessarily enter into the measurement process.
Nonetheless, the need for accuracy is not the same for fundamental research, for industry, and for trade.

Performance aimed at industry
Considering industry in general, it may be observed that provisions are progressively taken to anticipate and implement the new SI definitions [13,14].
Concerning, more precisely, electrical industries, it can be regularly observed, during accreditation assessments of test laboratories, that the designers of a product have used as little as possible of costly materials, such as copper. Hence, product characteristics sometimes very close to the limits permitted by international standards.
Conformity decisions, taken in such situations, may be difficult. Accurate measuring equipment can help in some way to raise the difficulty, but in any case if the measurement uncertainty is not taken into account, the decision remains doubtful.
Hence, a true need for a performing metrology, to associate with uncertainties treatment.
Anyway, strictly speaking, a measurement value without uncertainty remains meaningless.
The Fluke 5730A calibrator represents a good example of a modern equipment, providing extended capabilities and a good safety margin for calibration laboratories (Fig. 6).
Such modern equipments allow to handle the risk of wrong conformity decisions, thanks to a Bayesian approach, using the notion of "guard bands".

A farther future
The domains covered by fundamental and applied physics extend every day. So must do metrology [15].
Beyond its traditional goal to help specification and understanding of objective reality, metrology today also investigates the domain of human perception (i.e. the socalled "soft metrology") (Fig. 7). This is to be applied for instance to: psychometric measurement or perceived feeling (colour, taste, odour, and touch); qualitative measurements (perceived quality, customer satisfaction, etc.); econometrics and sociometry (opinion); and measurements related to human sciences: biometry, behaviour, intelligence, etc.   Soft metrology sections are already active at NIST (USA) and NPL (UK). Also the European Commission has funded some research within the N.E.S.T. programme "Measuring the Impossible" [16].
There is likely a wide future for such works.

A conclusion proposal
Metrology at start has been developed to support human economic activities (trade and exchanges). The level of metrological performance attained today largely exceeds the actual needs in this field; further progress is now more requested to facilitate scientific progress. A still higher accuracy level is necessary today for specific domains of science such as spatial, astrophysics, medical care, etc.; all these domains contribute in fact to human welfare. It is also encouraging to observe that metrology is one of the (rare) domains where an efficient and sincere cooperation takes place between the nations of the world (Fig. 8). Almost all nations acknowledge the metric system (with the remaining exception of the USA); and more than 100 laboratories worldwide have signed the document quoted above, called CIPM-MRA agreement.
Going forward with metrology is a path to a more peaceful world.