This Is The Roundest Thing On The Planet. Why Did Anyone Bother To Make It?

There are a few ways to answer the question, “What is the roundest thing in the world?”, and which one you go for likely depends on your level of scientific knowledge and nous. For those of us not too comfortable with physics, for example, the natural response will probably be along the lines of, “What kind of a question is that? How am I meant to measure roundness ?!”

If you’re a little more comfortable with science, on the other hand, your mind may go to something like the result of dropping molten metal into water from a great height – the closest thing on Earth to letting them cool in zero gravity, and one of the earliest ways discovered to mass-produce shotgun ammo.

But if you’re a real science nerd, there’s only one answer that holds any weight at all: the silicon spheres of the International Avogadro Project.

Balls of s teel silicon

Dotted around the planet in establishments as far apart as Australia, the USA, Germany, Japan, and so on, a collection of seven highly polished, highly guarded spheres are stored. They are each a unique, almost impossibly perfect shape, created by an international conglomeration of scientists and government organizations, and they were created for a single purpose: to change the world on a fundamental level.

It sounds like the setup to some new Marvel blockbuster, but the International Avogadro Project – a collaboration of researchers from across the world that has been active since the early 1990s – is 100 percent real. It was they who commissioned the spheres, which were all created at the Commonwealth Scientific and Industrial Research Organization, or CSIRO, an Australian Government agency responsible for scientific research, to exacting detail.

So just how round is “round”? Well, put it this way: their surfaces are “so smooth that if they were blown up to the size of Earth, the distance between the tallest mountain and deepest ocean would be just 3–5 meters (about 10–15 feet),” notes the National Institute of Standards and Technology (NIST), one of the organizations involved in the International Avogadro Project.

“Devices known as optical interferometers have allowed researchers to measure the sphere’s width to nanometer precision,” it explains. “They each cost about $3.2 million and had to be handcrafted by a master lens maker.”

All of which is cool, we admit – but it somewhat raises the question…

Why ?

Ceci n'est pas un kilogramme

You know how earlier, we said this was the only answer that held any weight? Well, that’s what we in the biz like to call “foreshadowing”.

“The Avogadro project […] aims to use perfect silicon spheres to accurately determine the value of the Avogadro constant (a fundamental physical constant),” notes the Powerhouse Museum , where a prototype sphere has been held since 2016.

From there, it explains, the goal was “to redefine the kilogram in terms of the Avogadro constant.”

Now, you might be wondering why we’d need or even want to redefine the kilogram – particularly if you’re in the US and therefore haven’t even got used to the old version yet – but there’s a really good reason to do so, actually. See, back in the 18th century, when the metric system first got going, the first definitions were all based on the natural world: the meter was to be one 10-millionth of the distance between the North Pole and the equator, measured along the line that goes through Paris; the liter was to be the volume of 1/1,000 of a cubic meter of water, measured at the melting point of ice; and the kilogram would be the mass of that water in a vacuum.

Having set these definitions down, the French Academy of Sciences set about making it official. In 1799, they commissioned physical objects to illustrate the units: a platinum bar exactly one meter long, and a cylinder exactly one kilogram in weight – affectionately known as Le Grand K, or Big K.

It took a while, but these new measurements proved popular across the world, and, in 1875, the Treaty of the Meter was signed by 17 countries – even including the US – to establish the General Conference on Weights and Measures. A permanent laboratory in Sèvres, near Paris, was set up as home to the international prototype meters and kilograms, while replicas were sent out to all the signatories so as to help spread and standardize the metric good news.

There was just one problem.

While this system of exact, standard, and verifiable weights and measures was much better than its various predecessors (viz. “ whatever we feel like ; deal with it ”), it held a fatal flaw: it was entirely based on physical objects. The circumference of the Earth may have seemed like an unchanging constant of nature to the guys who set the whole thing up, but in fact it’s changing all the time – and in fact, the whole thing was screwy from the start, since the scientists tasked with working out the length actually got it wrong by 0.2 millimeters, and nobody ever corrected the final figure.

It was for this and other reasons that, in the 20th century, people started advocating for the units to be redefined according to much more precise natural constants. The meter was defined in terms of first wavelengths of various light frequencies, and ultimately in 1983 as “the length of the path traveled by light in a vacuum in 1/299,792,458 of a second” – if you’ve ever wondered how we know the speed of light down to the exact meter per second, that’s why.

The second, in turn, was defined as “the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.” Temperature was to be set to the Boltzmann constant, a figure from thermodynamics; the mole – the unit by which we measure the amount of some substance, not the mammal – was fixed as the amount of substance of 6.02214076×10 ²³ elementary entities, aka the Avogadro constant (remember that one; it’ll be important).

But the kilogram? That was still just defined as “the mass of that lump of platinum locked up in the labs at Sèvres”.

Now, this was inconvenient, but it wasn’t until 1989 that people realized just how problematic it really was. “When [the prototype kilogram] was first created, 40 identical replicas were also made,” explained Derek Muller in a 2013 video for his YouTube channel Veritasium.

“They weren't quite identical,” he added. “They had a mass which was slightly different to Big K, but those offsets were recorded.”

But by 1989, the masses of these 40 kilograms were all slightly different – they had diverged by up to 50 micrograms. “Some physical process must have actually changed the mass of the cylinders,” Muller explained, “but how that exactly works remains a matter of speculation.”

Regardless, it was a big problem. “You can't have a unit which changes its value,” he pointed out, especially when it’s one on which more than half of the seven SI units depend for their own definitions. Clearly, something needed to be done – but what?

Weight and see

In 2005, at the 94th Meeting of the International Committee for Weights and Measures, a formal recommendation was made that the kilogram should be redefined according to a universal constant. The best bet, the committee decided, would be to use the Planck constant.

But other scientists had alternative ideas. “Since the Avogadro constant's current definition depends on a substance's mass, scientists reasoned that they could exploit this relationship by working backwards,” NIST explains. “First, though, they needed to define [the constant] with greater precision – with a relative uncertainty of just 20 parts per billion – in order for a new kilogram definition based on the Avogadro constant to compete in accuracy and reliability with the current standard.”

Basically, the plan was to construct some object out of an exactly known amount of some very precisely known stuff, and then define the kilogram according to that. It may sound like you’re going to run into the same problem as before – that you’re defining a unit based on a physical object – but in fact, it’s far more clever than that.

How to make a kilogram

The silicon spheres provide much more than Big K ever could. “Even if the silicon spheres were lost or damaged, it would have no effect on the definition of the kilogram,” Muller explained, “because it would be defined not by a physical object but by a concept.”

That said, if your definition of an international standard base unit depends on counting the number of atoms in an object, you have to be really, really exact in your accounting – and that’s why the spheres need to be so round.

“The sphere was chosen as the ideal shape because it has no corners or edges (to minimize chipping and wear),” explains Powerhouse, “and because – provided a sufficiently perfect sphere can be manufactured – the volume can be calculated from a single measured parameter (the diameter).”

Meanwhile, it continues, “ silicon was chosen over other elements […] as there already exist mature processes for the production and manipulation of ultra-high purity silicon from the electronics industry.” It’s also convenient, for a given value of “convenient”: the mass of a silicon-28 isotope is known, and the spatial parameters of its crystal lattice are regular, both of which help in the calculation of the number of atoms in the sphere.

Creating the spheres was a long and worldwide process: researchers must “grow” silicon ingots; another team will then abrade, smooth, and shape them into spheres accurate to the atomic level. And you might think it was all a waste of time – after all, the definition ultimately chosen was, indeed, the one based on the Planck constant .

But “though measurement scientists chose the Planck constant as the basis for redefinition, other constants of nature can also be used,” points out NIST, “if for no other reason than to provide a check that the Planck constant definition is correct.”

And hey: if nothing else, at least they got some real shiny balls out of it. And that’s no bad thing, surely.