The kilogram has the dubious distinction of being the only SI unit still based on a physical object; specifically, a metal cylinder kept in a vault in France. Plans are well underway to redefine the kilogram in mathematical terms instead, and to that end a team at the National Institute of Standards and Technology (NIST) has submitted a precise new calculation of a key formula.

Since 1879, the kilogram has been defined as the exact mass of the International Prototype of the Kilogram (IPK), a small cylinder made of platinum and iridium. But there are a few problems with defining a base unit in terms of a physical artefact: the IPK gathers contaminants that make it slightly heavier over time, so it needs to be regularly treated. To complicate matters, there are 40 copies around the world and they're all getting "dirty" at different rates, meaning their masses are slowly drifting out of sync.

That's obviously not something you want in a base unit that's supposed to be universal. And the discrepancies don't just affect the kilogram itself: other units such as the pound, ton or milligram are defined in terms of their relationship to the kilo, as are non-mass units like the ampere (for electric current) or the candela (luminous intensity).

A better option is to develop a new definition based on a mathematical foundation that can be calculated anywhere, and the Planck constant fits the bill. This formula allows researchers to find mass in relation to electromagnetic energy, so by finding as precise a value for it as possible, the kilogram can be redefined in terms of the official definition of the meter and the second.

NIST's new value for the Planck constant is 6.626069934 x 10^{-34} kg∙m^{2}/s, with an uncertainty of 13 parts per billion. If that number makes your eyes glaze over, the important part is the end: 13 parts per billion is incredibly precise.

To measure the Planck constant, the researchers used a Kibble balance, a device that suspends a 1-kg weight with electromagnetic forces. They can calculate the constant according to the amount of electromagnetic energy it takes to balance the mass.

The team says the more precise figure comes courtesy of having 16 months' worth of measurements to draw from, as well as adjustments they'd made in how the electromagnetic field was created and measured.

These experiments join several other projects that were attempting to find the most precise value of the Planck constant, and while everyone's answers were different, they have low enough levels of uncertainty to make a case for redefining the kilogram in terms of the Planck constant.

"There needed to be three experiments with uncertainties below 50 parts per billion, and one below 20 parts per billion," says Stephan Schlamminger, lead researcher on the project. "But we have three below 20 parts per billion."

All of these measurements have been submitted for consideration by an international body, which will review them to determine the official value of Planck's constant. The official definition of a kilogram – along with the other units that depend on it – is set to be changed in November next year.

The NIST results were published in the journal *Metrologia*.

Source: NIST