How much does a kilogram weigh?


The International Prototype Kilogram is under all of those bell jars

This is a picture of the international prototype kilogram, or IPK. It is exactly, and always, a kilogram. It’s a big lump of metal which the world has agreed is how much a kilogram weighs. It was made in 1879, and it is still beautifully, perfectly, and exactly the same as it was then.

Er, more or less. And that is the problem.

Now, the thing is, technically the IPK can never be anything other than exactly one kilogram. But everyone can’t use the one physical object, so every 50 years some copies are compared to the IPK, and the copies go out into the world. So by comparing all of these to each other we’ve learned that no matter how carefully you store something like the IPK, you can never stop it getting a tiny bit heavier over time. The air *itself* deposits a measurable amount of mass onto the IPK every year, which means it has to be cleaned (very, very carefully); its actual mass is never totally static. It can’t be.

Now the differences in mass here are very small – the IPK gains maybe a millionth of a gram a year. But it’s a measurable amount, and it starts to make a difference when you’re doing experiments that make measurements on that scale. So The International Bureau of Weights and Measures (or BIPM, to use the French acronym) are making a move to define the kilogram in relation to a fundamental constant of nature.

This isn’t a new idea – they did it in the 80s with the metre. There used to be an International Prototype Metre, but one metre is now defined as being the distance light covers in 1/299,792,458 of a second while travelling through a vacuum. That is the sort of thing a lab can replicate without having to go into a vault in France, and isn’t a value which is going to change (assuming that the speed of light doesn’t change over time, mind you. But there’s no reason to think that will happen. It is the kind of thought that festers in the back of the mind of the BIPM, though…)

So what’s the plan for the kilogram? Which constant of nature is it going to be defined in relation to? Well, the best candidate at the moment seems to be the Planck constant. This is a number which turns up all over the place when you look at quantum physics; it was originally described as the number that relates the energy of a photon to its frequency, but it’s since popped up all over the place.

But how can we use a number that describes the relationship between a wave’s energy and its frequency to define mass? Well, as it turns out, it is perfectly sensible to describe matter as a wave. I’ll let the weirdness of that sink in for a moment, in case you’ve not come across that before. Physical matter is not a thing which just sits there, but a wobbling wave.

Follow me on this one:

So if matter is a wave, the we can talk about the frequency of this matter-wave

Then with this frequency, through the Planck constant, we can talk about the energy of this matter-wave

And Einstein told us that energy and mass are the same thing.

So if we know what the Planck constant is, precisely, we can then define the kilogram in relation to it.

Phew. Of course, if the IPK is no longer needed, then it will become a very expensive collectible. And so a very interesting thing to try and steal


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