The Kilogram That Couldn't Lose Weight

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In a vault on the outskirts of Paris, there's a small metal cylinder about the size of a golf ball. It's made of platinum and iridium, ninety per cent of one and ten per cent of the other, and it's roughly as tall as it is wide: about thirty-nine millimetres each way.

It sits under not one, not two, but three glass bell jars, nested one inside the other.

For more than a century, that cylinder wasn't just a kilogram. It was the kilogram. Officially, it's called the International Prototype of the Kilogram. And for 130 years, every kilogram on Earth was, in the end, measured against it.

A chain of copies

The cylinder was one of three made in London in 1879. In 1889, an international conference ratified it as the kilogram.

From that point on, it was the top of a family tree. The prototype has six sister copies, kept in the same vault. There are working copies too. And countries around the world have their own national prototypes. National laboratories calibrated their own one-kilogram standards against the original, or against one of its authorised copies. Then those standards were used to check others, and so on down the chain, until eventually you get to the scales in your kitchen or at the shop.

So the mass of every bag of flour you've ever bought traced back, step by careful step, to one small cylinder under three glass jars.

The problem

The trouble with using an object as your definition is that objects change.

Comparing the prototype with its copies was a slow and painstaking job, so it didn't happen often. There were only three formal verifications, in 1889, 1948 and 1989. And when the masses were compared, they had drifted apart.

The amounts are almost absurdly small. Compared with its copies, it looks as though the prototype may have lost something like fifty micrograms of mass over the last century, possibly significantly more. A microgram is a millionth of a gram. Fifty micrograms is roughly the mass of a fingerprint.

That's tiny. But it's not nothing, and for the most precise kinds of measurement, it matters.

The cylinder that couldn't change

Here's where it gets genuinely strange. Notice that phrase: "may have lost something like fifty micrograms". Lost it compared to what?

Because, by definition, it couldn't.

Until 2019, the kilogram simply was the mass of that cylinder. So the prototype could never be heavier or lighter than one kilogram. Its error, officially, was exactly zero. If a few atoms rubbed off it, the cylinder didn't become lighter than a kilogram. The kilogram itself got lighter. Everywhere. For everyone.

That's the paradox. You can see that the prototype and its copies are drifting apart. But you can't tell which one is actually changing, because there's nothing more fundamental to compare them with. It's like having two clocks that disagree, and no way of finding out the real time. In fact, measured against anything unchanging in nature, the prototype's mass over fifty or a hundred years couldn't be pinned down more precisely than about a thousand micrograms.

Tying the kilogram to nature

The solution was to stop relying on an object altogether, and tie the kilogram to something that can't wear away, get dusty or lose atoms: a constant of nature.

The constant chosen is called the Planck constant. It's one of the fundamental numbers of physics: a fixed feature of nature, not of any object. Since 2019, the kilogram has been defined by fixing the Planck constant to an exact value. The official definition fixes that number, and defines the kilogram from it, using the metre and the second.

That's all very well on paper. But how do you turn a number into an actual weight?

Weighing with electricity

One answer is an instrument called a Kibble balance.

Like any set of scales, it balances one force against another. On one side, a test mass sits on a pan, and gravity pulls it down. On the other side, instead of a pile of counterweights, there's a coil of wire sitting in a magnetic field. Run an electric current through the coil, and it gets pushed upwards. Adjust the current until the upward push exactly balances the weight, and record it.

Then comes a second step. The mass is taken off and the current switched off, and the coil is moved through the magnetic field at a steady speed, like a little generator. That produces a voltage, which is measured too.

Put the two steps together and the awkward, hard-to-measure details, like the exact strength of the magnet, cancel out. What's left links the mass on the pan to electrical measurements. And those electrical measurements can be made using quantum effects that are tied to the Planck constant.

So once the Planck constant is fixed, a Kibble balance can measure an unknown mass against it. No golf-ball-sized cylinder required.

The last of the objects

The kilogram wasn't the first unit to make this journey. It was the last.

The metre had already moved away from physical objects. In 1960 it was redefined using light from krypton atoms, and in 1983 that was replaced with a definition based on the second and the speed of light. The second itself was redefined in 1967 using caesium atoms, rather than the rotation of the Earth.

But until 2019, the kilogram was still the one unit that depended on a physical object. In November 2018, nations voted to base the kilogram on the Planck constant, and on 20 May 2019 the new definitions came into effect. Now all seven of the base units of the international system are defined by constants rather than by things.

So what changed?

In everyday life? Nothing at all.

The new definition was carefully set up so that it didn't change the size of any unit. That way, every existing measurement still carries on exactly as before. Your bathroom scales didn't notice. A kilo of apples is still a kilo of apples.

And the cylinder is still there, under its three glass jars. It's just no longer in charge.

Permanence

There's a quiet lesson in the story of the kilogram. A standard of measurement is only as good as its permanence. For more than a century, the world's mass rested on a piece of metal, carefully protected and rarely touched, and still slowly drifting.

Nature, it turns out, is more permanent than metal.