Realization

In metrology, the realization (or embodiment) of a measurement unit or a measurement scale is the practical method by which the unit can be measured (or the scale put into practice) according to its definition. The realization of a unit or of a scale creates one or more measurement standards against which an unknown physical quantity of the same kind can be compared.

There are three general methods of realizing a unit or a scale. The first and most obvious is simply to follow the definition of the unit or scale, for example by measuring the distance travelled by light in vacuum in ¹⁄_299,792,458 of a second to realize the metre. The second method is to use a physical phenomenon which is accepted to be equivalent to the definition, for example realizing the metre by laser interferometry with a measured frequency of light. The third method is to have a physical standard, technically known as a prototype standard, for example the now-obsolete International Prototype Metre. A realization is distinct from a representation of a unit, such as a metre ruler.

As a realization is a measurement, it is associated with a measurement uncertainty, which is called the standard measurement uncertainty. The standard measurement uncertainty is a component of the uncertainty in any measurement result which relies on the measurement standard, although it is often (indeed usually) negligeable compared to other components of the uncertainty.

International System of Units

The realizations of the base units in the International System of Units (SI) are known as mises en pratique (literally, "putting into practice"), and are approved by the International Committee for Weights and Measures (CIPM).

Unit	Principle of realization	ur	Link
Metre	laser interferometry using standard wavelengths	10−12	[1]
Kilogram	mass of the International Prototype Kilogram immediately after cleaning and washing	<10−7	[2]
Second	caesium-fountain atomic clock	<10−15	[3]
Ampere	SI watt, ohm and volt (two out of three suffice) conventional volt and ohm with SI values of KJ and RK	<10−6 10−7	[4]
Kelvin	International Temperature Scale (ITS-90)		[5]
Mole	molar mass	<10−6	[6]
Candela	radiometry with absolutely calibrated detectors		[7]

The relative standard measurement uncertainties (u_r) are given for the best realizations, such as those carried out in national physical laboratories. Routine realizations may have uncertainites which are several orders of magnitude larger.

Standard measurement uncertainty

A practical measurement will be made against a "laboratory" or "local" standard, and will be associated with a measurement uncertainty. Part of that uncertainty is the question of whether the standard is really an accurate representation of the unit in question: for example, is the laboratory metre bar really one metre long? For accurate work, it is necessary to use laboratory standards which have been calibrated (often through a series of intermediate steps) to a recognized realization of the unit in question. For example, the chain of calibration for a laboratory standard 100 g mass might be

laboratory 100 gram standard

calibrated against

manufacturer's 100 gram standard

calibrated against

national 100 gram standard

calibrated against

national kilogram working standard

calibrated against

national prototype kilogram

calibrated against

International Prototype Kilogram

Each step in the calibration chain introduces a measurement uncertainty, but no measure of the unit can be more precise than the uncertainty in the primary realization used in the calibration chain. Calibrations and intercomparisons of national standards are organized by the International Bureau of Weights and Measures (BIPM) in Sèvres, near Paris, France, which also holds the International Prototype Kilogram.

Prototype standards

The situation of units defined by a prototype standard is slightly different from that of units defined in relation to physical phenomena. The main example in modern practice is the kilogram: the kilogram is defined (since 1889) as the mass of the International Prototype Kilogram, so the IPK always has a mass of exactly 1 kg, without uncertainty. The standard measurement uncertainty arises with the first step in the calibration chain, that of the national prototype kilograms, and was long thought to be u_r < 10⁻⁹. The use of a prototype standard with no uncertainty in the realization might appear at first sight to reduce the measurement uncertainties in subsequent measurements. However, in practice, calibration chains for units based on prototype standards tend to be longer than those for units based on physical phenomena: there are many laboratories which can perform a realization of the metre by interferometry to high accuracy, but there is only one laboratory in the world (the BIPM) which can perform a calibration against the International Prototype Kilogram.

A further problem with prototype standards is that they might not represent a constant physical quantity. This was found to be a problem with bronze standard yard-sticks in the United States in the late nineteenth century: the standard yards were found to be getting shorter, and at varying rates. The discovery prompted the United States to switch to a metric basis for the yard and the pound with the Mendenhall Order of April 5, 1893. The same phenomenon was later noticed in the United Kingdom primary standard of the yard, which was shortening at a rate of one part per million (or about 1 µm) every 23 years when the UK officially adopted the metric basis for Imperial units in 1964.

A recalibration and intercomparison of national standard kilograms from 1988 to 1992 suggested that the stability of the mass of these standards is less than had been assumed, and that their mass is steadily diverging. The reason for the instability is unclear, but it strongly suggests that the standard measurement uncertainty for the realization of the kilogram is higher than that implied by the periodic calibrations at the BIPM: a conservative estimate of the uncertainty is u_r ≈ 8 × 10⁻⁸.

History

The very earliest units of measurement were undoubtedly based on the dimensions of the human body, but these suffer from the obvious disadvantage that the dimensions differ between individuals. Standardized units of length and mass appear to have been introduced around the time of the first sedentary civilizations (about 8,000 years ago), length units being reproduceable to about one part in a thousand. Roman length units appear to have been reproduceable to about one part in ten thousand.

The introduction of gold coinage required the definition of standard masses to ensure the quality of minting. Indeed, the mass of coins became a convenient practical standard for small masses in many cultures. Larger masses were usually standardized at the marketplace, which gave rise to considerable variation between different locations even though the reproduceability at any given location was much better.

Prior to the introduction of the metric system at the end of the eighteenth century, both length and mass standards were based on "prototypes": that is, one yard was defined as the length of the standard yardstick and one pound was defined as the mass of the standard pound weight. The metric system made a philosophical break in deciding to use universal physical constants for the definitions of length and mass unit: ¹⁄_10000000 of the distance from the Equator to the North Pole for the metre, and the mass of one cubic decimetre of water at maximum density for the kilogram. The realizations of these definitions were carried out, and a metre bar and a kilogram weight were made as a permanent record of the measurements and stored in the National Archives in Paris. Nevertheless, when the original realizations were found to be slightly in error, it was the permanent records which prevailed as the basis of the metric system, converting them into prototype standards. New prototypes were made at the time of the international adoption of the metric system through the Metre Convention of 1875, and the International Prototype Kilogram is still the standard of mass measurements under the International System of Units (SI).