The kilogram and three other metric units are about to be revamped

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THROUGHOUT MUCH of human history, man has been the measure of many, if not all, things. Lengths were divided up into feet, palms, spans and smaller units derived from the human hand. Other measures were equally idiosyncratic. Mediterranean traders for centuries used the weight of grains of wheat or barley to define their units of mass. The Roman libra, forerunner of the pound, was 1,728 siliqua (carats), each the weight of a carob seed (possibly because they were thought, erroneously, to be less variable in mass than the seeds of other species).

The sizes of similarly named units could also differ. The pied du roi (king’s foot), used in France for nearly 1,000 years after its introduction by Charlemagne in around 790AD, was, at 32.5cm, around a centimetre shorter than the Belgic foot, used in England until 1300. The talent was the mass of water required to fill an amphora (approximately 28kg), but Greek, Egyptian and Babylonian versions varied from one another by a few kilos. Nor was there agreement on such things within countries. In France, where there was no unified measurement system at the national level, the situation was particularly dire. The lieue (league), for example, varied from just over 3km in the north to nearly 6km in the south.

Although John Wilkins, an Englishman, first proposed a decimal system of measurement in 1668, it was the French, full of revolutionary zeal, who in 1799 made it law. Standards for the metre and kilogram were duly cast in solid platinum, and while Napoleon lampooned the new units, the Système international d’unités (SI, or the metric system, as it is better known) descended from them and became the official measurement in all countries except Myanmar, Liberia and the United States. Now the International Bureau of Weights and Measures (BIPM) in Paris is set to give the metric system its biggest shake-up yet.

At a meeting in Versailles on November 16th, the world’s measurement bodies are almost certain to approve a resolution that will mean four out of the seven base SI units, including the kilogram, will follow the other three, including the metre, in being redefined in terms of the values of physical constants. Each of the chosen constants has been measured incredibly precisely. Furthermore, they represent fundamental characteristics of the universe that are not expected to change (at least on the sorts of earthly timescales likely to concern the human race). This would mean that from May 20th 2019 the constants will themselves be fixed at their current values for ever. Any laboratory in the world will then be able to measure, for example, the mass of an object as precisely as the accuracy of their equipment will allow.

Plus ça change

In 1967 the redefinition of time, in the form of the second, led to the current overhaul. Rather than pegging the second to the rotation of the Earth about its axis, the second is now defined by the ticking of a caesium atomic clock. This neither loses nor gains more than a second in 1.4m years. This clock relies on microwaves, which at a frequency of 9,192,631,770Hz are known to make electrons jump between two particular energy levels, known as the hyperfine ground states of caesium. The microwaves are tuned to this frequency and the pulses used to measure out a second of time, just as the regular oscillations of quartz crystals are used to calibrate electronic watches.

The candela, a unit of luminosity originally based on the brightness of a candle flame, was redefined in 1979 to be based on the brightness of a source emitting light at a specific frequency in the green part of the spectrum, to which the human eye is most sensitive. In 1983 it was the turn of the metre, which by virtue of the fact that light travels at a fixed speed (299,792,458 metres per second) through a vacuum, was redefined that way. Now it is the turn of the units of mass (kilogram), current (ampere), temperature (kelvin) and the amount of a chemical substance (mole) to be redefined so that they too can, in theory, be reproduced at any time and in any place.

The change is most significant for the kilogram, physically defined by a cylinder of platinum-iridium alloy housed under nested bell jars in a vault at the BIPM in Paris. Known as the International Prototype of the Kilogram, or Le Grand K, this was made in 1889 to be of about the same mass as the original Napoleonic-era ingot. The problem is that the masses of the six official copies have drifted a little from that of Le Grand K over the years (see chart). Why that is so is not known, but since the copies have changed, it is likely that the mass of the original has, too. Because Le Grand K is the standard against which the copies are measured, it is meaningless to ask whether it has gained or lost weight. And despite all the security, there is an outside chance that should the prototype ever be stolen or destroyed, as the Imperial Standard Pound was when the Palace of Westminster in London burnt down in 1834, there would be no official measure.

How to Kibble it

The new definition of the kilo will turn Le Grand K into a museum relic. The role will instead fall to a piece of kit called the Kibble balance, formerly known as the Watt balance, but renamed in 2016 after its inventor, Bryan Kibble of the National Physical Laboratory in Britain.

The Kibble balance measures a mass by looking at the amount of energy it takes to balance its weight using electromagnetic forces. The amount of energy required to measure 1kg will depend on a value known as the Planck constant, which is depicted by the letter h. The constant is a number from the weird world of quantum physics that, for example, links the energy of a photon of light to its frequency.

To calibrate all the Kibble balances in the world, it is necessary to first measure the Planck constant using a known reference mass, such as Le Grand K. Scientists around the world have been doing that in a series of elaborate tests. These involve placing a mass in a pan suspended on a length of wire within what is known as an ambient magnetic field. When an appropriate current is run through a coil of wire attached to the pan, it generates another magnetic field, which interacts with the ambient field to produce a force upwards that exactly balances the weight of the mass. The current flowing through the wire is easy to determine accurately, but the strength of the ambient magnetic field is not. Measuring that involves removing the mass, turning the current off and moving the coil at a fixed velocity through the ambient field. This movement induces a voltage across the wire that is directly related to the strength of the ambient magnetic field. This voltage, like the current, can be measured stringently. As both are related by the Planck constant, it will allow scientists to come up with an agreed value for it.

That value is set to be fixed on May 20th 2019, after which any lab with a Kibble balance handy will be able to determine the mass of an object without recourse to Le Grand K or its near-clones. There is a certain irony that a constant arising from quantum mechanics, famous for its uncertainty principle, will thenceforth bring more certainty to measurements of mass.

Similar efforts with the ampere, kelvin and mole will link them, respectively, to the elementary charge, e; the Boltzmann constant, k; and the Avogadro constant, N{-A}. Like the Planck constant, their values will be fixed next year if the vote in Versailles goes as planned. Those who need to determine such things can then measure a current by counting single electrons (each bearing a charge, e) passing a point in a circuit; temperature by measuring the average speed (and thus the heat energy) of an assembly of molecules; and the amount of stuff by determining the number of particles (usually atoms or molecules) composing it. For those with the expertise and cash, the apparatus for making such measurements is available.

Those hoping, however, to effortlessly shed some weight before the festive season as a result of these changes will be disappointed. As the determinations of the Planck constant used the prototype kilogram, there will be no difference between the new and old kilo.

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