The New Kilogram & Quantum Standards
One year ago today, on the 16th of November 2018, on the last day of the 26th meeting of the General Conference on Weights and Measures (26e CGPM) in Versailles, a momentous record in the history of measurement was achieved. With a historic vote, all the base units of “metric system”, the Système International (SI) were cast in the form of operational(rather than artefact) standards. This brought to completion a more than 200-year quest in measurement science (known as metrology), bringing us into a new era, in which the everyday units we use for measuring time, length and mass are all now linked to quantum phenomena.
Historically, units of measurement such as the inch, foot, cubit and pound were defined on a human scale. No particular order or design was required, and no attempt was made to link different quantities such as mass and length. As a result, a wide array of measurement standards was developed. Each was different; different countries and even city-states might have their own definition of a given standard unit, such as a pound, or a yard.
The rising demands of international commerce, and the requirements for higher precision imposed by the machine tools being developed in the nascent industrial revolution, made the need for a more rational system obvious. The first coherent response to this emerged in the time of the French Revolution. Against a general backdrop of revolutionary fervour, old standards were case aside, including even the names of the months of the year. In terms of lengths, the base unit of the metric system was made the metre; it was defined as one ten-millionth of the distance from the pole of the Earth to the equator along a line of longitude. This was the first example of a universal unit, based on a rational formula, rather than an arbitrary artefact. In principle every citizen of France (and indeed of the entire world) had access to the Earth as a standard and the metre could therefore be accessed universally. The actual determination of this metre standard required of course a serious piece of engineering; a geodetic survey team led by Pierre Méchain and Jean-Baptiste Joseph Delambre travelled from Dunkirk in the north to Barcelona in the south, surveying accurately as they went, in order to correctly establish the unit. In the context of the general revolutionary disruptions of the times, this was a heroic event. Of course, there was a need for secondary standards which could actually be used on a day-to-day basis. For this purpose, platinum metre-length bars (starting with the “metre des archives” in 1799) were used. This was an early example of the mise-en-pratique, or “putting into practice” a scientifically defined standard.
The situation for the unit of mass was similar. The gram was defined as the mass of a 1 cm x 1 cm x 1 cm cube of water, and by extension the kilogram was the mass of 1000x bigger volume, namely a 10 cm x 10 cm x 10 cm cube. For practical purposes the kilogram became the base unit of mass. Again the spirit of rationality was employed; a sample with known dimensions of a universally available substance (water) was chosen as the mass standard, thus inexorably linking mass and length, and ensuring that anyone with access to the length standard and water could manufacture their own kilogram secondary standard. In practice, things were a bit more complicated of course; the apparently “universal” substance water actually has a density which varies with temperature and (slightly) with pressure, and also could incorporate dissolved salts, which will affect the final mass. Thus despite the simplicity of the original definition, there was a practical need for an artefact standard which would capture the sense of and match the original definition, but which would be more robust, This was found in the form of the International Protoype Kilogram (“le grand K”), a kilogram standard made of 90% platinum 10% iridium alloy, cast in London and delivered to the Bureau International des Poids et Mesures (BIPM) in the Parc St. Cloud, just outside Paris in 1879.
The modern era of measurement science began with the best measured standard of all, namely time. As with length, the Earth had played a role as the prime artefact for time as well, with the units of time being based on the earth’s rotation rate; however this is subject to variability as well as an overall slowing down due to tidal friction, resulting in a small but measureable uncertainty of around 1 second every 3 years. A much better solution was a time standard based on a cesium atomic clock, resulting in the modern definition of the second via the statement that the unperturbed ground-state hyperfine splitting frequency of cesium-133 is exactly 9 192 631 770 cycles per second. For the first time, an SI base unit was defined in terms of an inherently quantum mechanical atomic property.
The invention of the laser in 1960 (originally framed by one witty scientist as “a solution in search of a problem”) and its subsequent rapid development led to the realization that a precision, quantum linked standard of length could be developed, by linking distance and time via the universal speed of light. The decision taken in 1983 at the 17th CGPM to define the speed of light to exactly 299 792 458 m/s was in fact a redefinition of the metre in terms of the atomic time standard. With this new definition rooted in modern physics, the artefact metre bar standard could be thrown away! Now the standard of length became an “operational standard” which could in principle be implemented by anyone anywhere in the world who had suitable laser and atomic clock technology, without reference to a master artefact standard kept in a vault. This was the ultimate democratic development in the standard of length.
In this grand historical development the kilogram mass standard was the laggard; for more than 100 years le Grand K and its copies at the BIPM and in National Measurement Institutes (NMIs) around the world served as the primary and secondary standards of mass. Infrequent comparisons of these mass standards to one another revealed a clear issue with drifts and variations, but for a long time there was no better way. The variations of the kilogram standard were believed to be of the order of 50 parts per billion, embarrassingly large compared to the ultra-high precision of cesium atomic clocks and the linked metre standard.
This situation began to change in 1976, when Brian Kibble at the National Physical Laboratory in the UK came up with a new way to link mass to other fundamental units, in this case the SI units of electric current and voltage, the Ampere and the Volt. These units had also undergone progressive improvements in how well they could be measured, and today they are linked to quantum standards via the Quantum Hall Effect and the Josephson effect.
Kibble realized that by connecting the mass standard to force measurements in a “watt balance” configuration, the mass on the balance pan could linked directly to electrical standards. It took about 4 decades of continuous development for the proposal to reach fruition. Encouraging results from multiple watt balance experiments of different design around the world confirmed the possibility of replacing the kilogram artefact standard by an operational standard. In the fall of last year, this was finally done; we now live in a world in which the SI base units of time, length, and mass are operational standards, linked to invariant quantum quantities. Brave new world indeed!