Scattered across facilities in Australia, the United States, Germany, Japan, and elsewhere is a collection of seven meticulously polished and heavily guarded spheres. These are the International Avogadro Project's silicon spheres. They were made at Australia's Commonwealth Scientific and Industrial Research Organization (CSIRO) with extreme precision and are considered the roundest objects in the world.

Their surfaces are so smooth that if magnified to the size of Earth, the distance between the tallest mountain and the deepest ocean would be just 3-5 meters, according to the US National Institute of Standards and Technology (NIST), one of the organizations participating in the International Avogadro Project. Optical interferometers have helped researchers measure the sphere's width with nanometer accuracy. Each sphere costs about $3.2 million and is handcrafted by skilled lens makers.

So what is the purpose of these spheres? The International Avogadro Project aims to use perfect silicon spheres to determine the exact value of the Avogadro constant (a fundamental physical constant), according to the Powerhouse Museum, which has housed a prototype sphere since 2016. Specifically, the goal is to redefine the kilogram based on the Avogadro constant.

Back in the 18th century, when the metric system was born, the first definitions were based on the natural world. The meter is one-tenth of a millionth of the distance between the North Pole and the equator, measured in a straight line through Paris. The liter is the volume of 1/1,000 of a cubic meter of water, measured at the melting point of ice. The kilogram is the mass of that amount of water in a vacuum.

After coming up with these definitions, the French Academy of Sciences began to formalize them. In 1799, they used physical objects to illustrate the units of measure, including a one-kilogram cylinder called Le Grand K, or Big K.

Over time, these measurements became popular around the world. But a serious problem was that they were based entirely on physical objects. The circumference of the Earth seemed to be an immutable constant to those who established this system, but in fact it was constantly changing. In fact, the system was also flawed from the beginning because the scientists in charge of calculating the length had miscalculated by 0.2 mm and no one had ever corrected the final figure.

For this and other reasons, in the 20th century, people began to advocate redefining units according to more precise natural constants. Among them, the mole - the unit used to measure the amount of substance - was defined as the amount of substance of 6.02214076 x 1023 fundamental entities, also known as Avogadro's constant.

In 2005, at the 94th meeting of the International Committee for Weights and Measures, experts recommended that the kilogram be redefined in terms of a universal constant. The committee decided that the best option was to use Planck's constant.

But some scientists had other ideas. Since the current definition of Avogadro's constant depends on the mass of a substance, they thought it might be possible to exploit this relationship in the opposite way. But first, they needed to define the constant with greater precision - the relative error would be just 20 parts per billion - so that a new definition of the kilogram based on Avogadro's constant could compete in accuracy and reliability with the current standard.

Basically, the plan was to make an object from a precise amount of a known substance, and then define the kilogram accordingly. These objects are silicon spheres, which have several advantages over the Big K. Losing or damaging the silicon spheres does not affect the definition of the kilogram, because the kilogram is defined not by physical objects but by concepts.

When the definition of an international standard base unit depends on counting the number of atoms in an object, calculations must be extremely precise. That is why the spheres are round. "The sphere was chosen as the ideal shape because it has no corners or edges (to avoid chipping or wear), and if a sphere were made perfectly, it would be possible to calculate the volume from a single parameter (the diameter)," the Powerhouse Museum explains.

Meanwhile, silicon was chosen because processes for producing and manipulating ultra-high-purity silicon were already well established. Silicon also offers scientists a number of advantages: The mass of the silicon-28 isotope is known, and the spatial parameters of the crystal lattice are standardized, allowing for calculations of the number of atoms in the sphere.

Although the International Committee for Weights and Measures has chosen the Planck constant as the basis for redefining the kilogram, other natural constants can also be used, at least to help check the accuracy of the Planck definition, according to NIST.

Thu Thảo (IFL Science)