SI definitions, traceability and calibration

For most of the twentieth century the kilogram was a cylinder of platinum-iridium in a vault outside Paris, and the kilogram was whatever that cylinder weighed. It was a workable definition with an uncomfortable property: the official copies drifted relative to it by tens of micrograms over a century, and there was no way to say which of them had changed. Since May 2019 no SI unit rests on an object. Each is defined by declaring the numerical value of a constant to be exact — the caesium hyperfine frequency for the second, the speed of light for the metre, the Planck constant for the kilogram, the elementary charge for the ampere, Boltzmann's constant for the kelvin, the Avogadro constant for the mole.

Two things follow. The definitions are now permanent in a way an artefact never was, and they are democratic: any laboratory with a Kibble balance or an optical clock can realise the unit from the definition, rather than sending a mass to France for comparison. And crucially, nothing measurable changed at the moment of the switch. Continuity was designed in, so the new kilogram matches the old one within the uncertainty to which the old one was known, and no earlier measurement needed revising.

Realising a unit is specialist work; using one is not, and the bridge between them is traceability. A measurement is traceable when its result can be related to a realisation of the definition through an unbroken chain of comparisons, each documented and each contributing its own uncertainty. In practice: a national metrology institute realises the unit, calibrates a reference standard, which calibrates a working standard, which calibrates the meter on your bench, and the uncertainty grows a little at every step. This is why a calibration certificate reports a deviation and an uncertainty rather than a verdict, why calibrations expire, and why an instrument with a great many digits and no chain behind it tells you only what it is repeating, not what is true.