Redefining the kilogram

Why did the world's laboratories replace a real lump of metal with a fixed number?

Until 2019, the kilogram was a cylinder of platinum-iridium in a vault near Paris. Not a representation of the kilogram — the thing itself. Every mass measurement on Earth traced back through a chain of comparisons to that object.

It was then replaced by a sentence containing a fixed number: the Planck constant is exactly 6.62607015 times ten to the minus thirty-fourth joule seconds, and the kilogram is whatever follows. A physical object was swapped for a convention. That looks like a step away from concreteness, so it is worth asking what problem a lump of metal has that a number does not.

Begin by asking what a unit is actually for. Not for being true — there is no fact about how heavy a kilogram ought to be. A unit exists so that a mass measured in Lisbon and a mass measured in Osaka mean the same thing. It is a coordination device, and the only question that matters about one is whether everybody who needs to agree can agree, cheaply and durably.

Seen that way, an artefact is a perfectly sensible first solution. Make one object, declare it the standard, and let everyone calibrate against copies of it. Agreement is achieved by deference to a centre: a hub, with spokes running out through national copies to working standards to the scale in a shop.

Now interrogate that arrangement, since it worked for 130 years and was still abandoned. Three weaknesses.

The first is that it cannot be checked. When the prototype was compared with its official copies over the twentieth century, they had drifted apart by some tens of micrograms. Which of them changed? The question has no answer, because the prototype is the definition. If it gains mass, the mass of everything else in the universe formally decreases, and no experiment inside the system can detect it. A standard that cannot be wrong is a standard that cannot be improved.

The second is fragility. The definition had a single point of failure sitting in one building, vulnerable to fire, theft, or a clumsy hand. Nothing could recreate it.

The third is access. To use the definition you had to send metal to Paris or to a national institute holding a copy, and every link in the chain added uncertainty. Coordination through a hub means everybody pays to reach the hub.

So ask the design question directly: what could a scattered set of laboratories agree on that would carry none of those costs? It would have to be something each of them could reach independently, without deferring to anyone; something that could not drift; and something that could be reached better as instruments improved.

Constants of nature fit exactly. And there is a move available that the metre had already demonstrated. In 1983 the speed of light stopped being something measured in metres and became a defined number, with the metre becoming whatever makes that number true. Nothing about lengths changed at that moment; what changed is that every future improvement in measurement went into realising the unit better rather than into refining a constant.

The kilogram took the same path, using the Planck constant. It is not obvious that a quantum of action has anything to do with mass, and this part repays attention. A Kibble balance weighs a mass against an electromagnetic force, and the electrical quantities involved are measured using the Josephson and quantum Hall effects, whose scales are set by the Planck constant and the elementary charge. The instrument therefore converts a mass into an electrical measurement anchored to Planck's constant. A quite different route, counting atoms in an almost perfect sphere of silicon-28, agrees.

Two details show that this was a coordination problem being solved, not a physics discovery. The fixed value was chosen so that the new kilogram matched the old one within the uncertainty of the best measurements — continuity mattered more than tidiness, which is why the number is so ugly. And several constants were fixed together in 2018, taking effect on 20 May 2019, because the units interlock and cannot be redefined piecemeal.

Three clarifications.

First, definition and realisation are now separate things, and keeping them apart is the whole trick. The definition is a sentence. Realisation is the experimental business of building something that embodies it, described in a published mise en pratique, and it may be done by different methods, improved indefinitely, and — crucially — got wrong. Errors have moved from an invisible place to a visible one.

Second, nothing weighs differently. The redefinition was engineered to be undetectable in ordinary use. Its benefits are all at the top of the chain: no drift, no single point of failure, no ceiling on future precision.

Third, this is not a claim that nature's constants are exactly these numbers. Fixing the Planck constant does not measure it; it makes it a matter of definition, in exchange for making the kilogram a matter of measurement. Something must be held fixed for the system to be a system, and the redefinition decides which thing — justified only by making agreement easier to reach and to audit. With it, the last SI base unit tied to a manufactured object retired.

• How the Kibble balance links mass to the Josephson and quantum Hall effects.
• Why the second, defined by a caesium transition, is the unit everything else leans on.
• What happens to the old prototype and its copies now that they are ordinary objects.
• The proposed optical-clock redefinition of the second, and why the pattern keeps repeating.

Every term the collection defines is gathered in the glossary.