World's Roundest Object!

Can I hold it? Only if you promise to be really, really careful.

I promise I will be so incredibly careful. I will be incredibly careful with it. I promise. So, it's slippery, be careful. Alright, are we ready? I'm about to touch a 1kg sphere of silicon-28 atoms. There are about 2.15x10^25 of them. It feels absolutely incredible. Wow, that is amazing.

Besides its creators, I am one of only a handful of people ever to hold this sphere. The raw material used to make it was worth 1 million Euros, but now that it has been so precisely sculpted -- how much is that worth? It's priceless.

... This you are looking at now is the roundest object in the world. How can you say for sure it's the roundest object? I mean, the Earth is pretty round, isn't it? If this was the Earth... If this were the Earth, then the highest mountain to the lowest valley would be... about 14m apart.

That is shocking. That is shockingly round. But why would you invest one million Euros and thousands of man-hours perfecting a pure, polished silicon sphere? Well, the answer is grave. Or rather "grave" as it would have been pronounced in the original French.

You see, the grave was the original name for the base unit of mass in the metric system, which became the Systeme International d'unités or SI units. In 1793, a commission which included notable scientist and aristocrat Antoine Lavoisier defined the base unit of mass as the weight of a cubic decimeter of water at the melting temperature of ice -- essentially just a litre of ice water.

The name grave came from the Latin gravitas, meaning weight. But it wasn't to last. It sounded too similar to the aristocratic title 'graf' -- which is the equivalent of an earl or a count. And with the French Revolution in full swing, with the rallying cry of equality for all, you couldn't exactly have one unit nobler than the others.

At this, Lavoisier lost his head, literally, not because he helped devise one of the greatest systems of measurement of all time, but because he was collecting taxes as a nobleman. So things really were grave. The new republican government believed a grave would be too big for the things they wanted to measure anyway, and so they settled on the gramme, which was just a thousandth of the grave.

But soon they realized that a gram was too small, and so they returned to the grave, but since they couldn't call it that, they invented the kilogram -- a thousand grams. And that is why out of the seven base SI units, the kilogram is the only one to have a prefix in its name.

In 1799, the kilogram definition was refined to be the mass of a litre of water at 4 degrees Celsius -- the temperature at which it is densest. But water itself is obviously not the most sensible thing to use as a mass standard. So a pure platinum cylinder was created to have the same mass as the water definition, and it was declared Kilogram of the Archives.

Now it's important to note at this point the kilogram is no longer tied to the mass of a volume of water -- the kilogram of the archives is by definition THE kilogram. Ninety years later, in 1889, the kilogram was upgraded to a platinum-iridium alloy cylinder.

Now it was much harder than the original but was otherwise basically identical. And to this day, it remains the definition of the kilogram. It is officially called the International Prototype Kilogram, though it's affectionately known as Le Grand K -- or Big K.

Oh, and it's about this big... It is the only thing in the entire universe with a mass of exactly one kilogram because it IS the kilogram. It is also the only SI unit that is still defined by a physical object. It sits under three bell jars, next to six sister kilograms, in a climate-controlled vault locked by three independently controlled keys, in the basement of the International Bureau of Weights and Measures on the outskirts of Paris.

Now if you were able to break into the vault and tamper with Big K, you would be changing the definition of the kilogram, a definition on which many of our measurements rely, and so you would throw the world into chaos! Well, no, not actually-- but how would anyone ever know if the mass of Big K changed?

Well, when it was first created, 40 identical replicas were also made. Well, they weren't quite identical - they had a mass which was slightly different from Big K, but those offsets were recorded. Now these replicas were sent out to countries around the world to serve as their national standards.

In 1948, the kilograms were reunited for a weigh-in. And this is when the problems started. Because even though all the cylinders were made of the same alloy and stored under virtually the same conditions, their masses had diverged over time.

The mass of Big K wasn't even the same as the six sister cylinders stored with it. And to make matters worse, when they were brought together again forty years later, their masses had further diverged, up to about 50 micrograms - that's about the weight of a fingerprint. But fingerprints were not the culprits since the kilograms were carefully washed before their weigh-ins.

So some physical process must have actually changed the mass of the cylinders, but how that exactly works remains a matter of speculation. One thing is for certain, the mass of a platinum-iridium cylinder is not stable over time. And this is a big problem. You can't have a unit which changes its value.

And the fallout isn't limited to measurements of mass since of the seven base SI units, four of them depend on the mass of the kilogram, not to mention all the derived units like Newtons, Joules, Volts, and Watts. At this point, those of you in countries that have not adopted the metric system--yes, I'm speaking to you Liberia, Burma, and the US--you may be feeling rather smug that your unit of mass, the avoirdupois pound, is no longer defined by a physical object.

No, instead it is defined as precisely 0.45359237 kilograms. Sucked in. So clearly something needs to be done to eliminate the kilogram's dependence on a physical object, and this is where the silicon sphere comes in, but how exactly does that help?

Here you have a physical object, and it's beautiful, but you know it's still a physical object. You're trying to get away from that. We're trying to get away from the physical object, but what we're doing with this particular object is counting how many atoms are in there.

You can't actually count how many are in there, can you? You can't count how many are in there, but you can calculate how many are in there because this material is silicon; there's no voids or dislocations. So this is like a perfect crystal of silicon. That's right. Not only is it pure silicon, it contains only one isotope of silicon, silicon-28, and that explains why the original material was so expensive.

And why a sphere? Well, a sphere is a pretty simple object. If you know the diameter of the sphere, you can characterize the entire dimension of the object. Well, that explains why the sphere has to be the roundest object ever created, but how do you actually make something that round?

We actually start with an oversized sphere. So it was about two millimeters larger in diameter, and then we just grind it progressively finer and finer using abrasive. It's actually massaging atoms. You're down at that level of trying to control the shape of an object down at the atomic level.

But making the sphere is only half the battle; then you need to accurately measure its diameter. The diameter is actually measured via a laser. So you're actually measuring having the sphere in the center of a cavity and a laser is hitting both sides, and you're actually measuring the gap.

By knowing the diameter, you can determine its volume. And since the atom spacing in silicon is known to high precision, you can then calculate how many atoms make up the sphere. This allows you to redefine Avogadro's constant. At the moment, Avogadro's constant is defined based on the kilogram.

It is equal to the number of atoms in twelve grams of carbon 12. But using this approach, the number of silicon atoms in the sphere would be used to fix Avogadro's constant, which would then define the kilogram. So even if the silicon spheres were lost or damaged, it would have no effect on the definition of the kilogram because it would be defined not by a physical object but by a concept.

You would like to see the official definition of the kilogram say "a kilogram is the mass of 2.15x10^25 silicon-28 atoms"? Yes. Is it - is it going to happen? There's a likelihood, a high likelihood that it's going to happen.

But there is another approach to redefining the kilogram which involves fixing Planck's constant, and it's done using something called a Watt Balance. These two approaches are complimentary. Each one provides a check on the other, and if they show good agreement and are able to bring their uncertainties down to about twenty micrograms, they may redefine the kilogram as early as 2014.

And then the kilogram finally will be an unchanging unit, no longer defined by a physical object in the basement vault of some place in Paris. Now if the kilogram was originally intended to be the mass of a litre of water at its densest temperature, then how well did we do?

Well, if you look at a litre of water at nearly four degrees Celsius, it has a mass of 999.975 grams. So I guess you could look at this two ways. On the one hand, you could say the kilogram is slightly heavier than it should be, but on the other hand, 214 years ago, scientists were able to create an artifact that was correct within the margin of error of a grain of rice. Now that is truly remarkable.

Now if you want to hear more about the Watt Balance, let me know in the comments, and I will see what I can do. It does seem to be the frontrunner in terms of redefining the kilogram, so we will have to wait and see what happens.

One last thing, I should point out that it took an international collaboration of scientists to create the silicon sphere, but don't you think that the scientist who originally conceived of silicon as an element should receive some of the credit? Well, in 1787, that was none other than Antoine Lavoisier.

So he's been involved in the definition of a kilogram from start to finish or from cradle to grave.