# NIST-4 watt balance weighs in on Planck’s constant

Universal mass: NIST’s fourth-generation watt balance

The latest version of the watt balance at the US National Institute of Standards and Technology (NIST) has made its first measurement of Planck’s constant (*h*) with an uncertainty of 34 parts per billion, demonstrating that the institute’s device – dubbed NIST-4 – is accurate enough to be used to redefine the kilogram. The data from this latest measurement values the *h* at 6.626,069,83 × 10^{–34} J s, with an uncertainty of ±22 in the last two digits.

For almost 130 years, the international definition of the kilogram has been based on a lump of platinum-iridium metal housed at the International Bureau of Weights and Measures (BIPM) in Paris. This “International Prototype of the Kilogram” – or “Le Gran K” – has been used to determine the International System of Units (SI), which governs measurements in everything from commerce to science.

But as the lump is a physical artefact, it is affected by the environment despite being housed in a secure, climate-controlled vault. Periodic inspections have shown that it has slowly been losing some of its mass due to its surface reacting chemically with the air, making the object unstable and difficult to handle. “The problem with the kilogram in Paris is that it’s so precious that people don’t want to use it,” says Stephan Schlamminger, a physicist in the Physical Measurement Laboratory (PML) at NIST in Gaithersburg, Maryland.

### Global focus

There are seven base SI units: the metre, kilogram, second, kelvin, ampere, mole and candela. Because these values must be extremely stable over long periods of time, while also being universally reproducible, most of them are based on fundamental constants of nature. The kilogram, however, is the only unit still defined by a physical artefact.

To get round this problem, metrologists want to redefine the kilogram in terms of Planck’s constant. Lying at the heart of quantum mechanics, *h* links the frequency of a photon to its energy, which in turn can be related to mass through Einstein’s equation E = mc^{2}. A watt balance – a device first proposed by physicist Brian Kibble at the UK’s National Physical Laboratory (NPL) in 1975 – does this by comparing the mass of an object with an electrical force.

Specifically, a watt balance relates mechanical power – measured in terms of the metre, the second and the kilogram – to electrical power measured in terms of the volt and the ohm. Because electric power can be measured precisely in terms of *h* – by applying two quantum-mechanical effects known as the Josephson effect and the quantum Hall effect – the watt balance connects this universal constant to mass.

### New generation

The fourth-generation NIST-4 watt balance measures the weight of a test mass by determining the electromagnetic force needed to balance it. The force is created by sending an electrical current through a moveable coil of wire suspended in a magnetic field provided by a large permanent electromagnet. The coil becomes an electromagnet with a field strength proportional to the amount of current it conducts. When the coil’s field interacts with the surrounding magnetic field, an upward force is exerted on the coil, the magnitude of which is controlled by adjusting the current.

NIST’s first measurement with NIST-4 is found to be consistent with watt-balance measurements from other countries. However, the amount of uncertainty in the measurement is far lower than predicted, meaning that they are on track to redefine the kilogram. This measurement was essentially a dry run, according to Schlamminger, who adds that he and his colleagues “were hoping to achieve an uncertainty of within 200 parts per billion by this point, but we got better fast”.

### All together now

For the 2018 redefinition to go forward, at least three experiments must produce values with a relative standard uncertainty of no more than 50 parts per billion, and one with no more than 20 parts per billion. The groups now have until July 2017 to publish new measurements of Planck’s constant to be taken into account for the redefinition of the kilogram.

All these values must agree within a statistical confidence level of 95%, while also agreeing with the value calculated using the alternative “Avogadro” method, which measures *h* by counting the atoms in an ultra-pure sphere of silicon. The combined results will be used to calculate a value of *h* that best fits all of the data.

Schlamminger’s team aims to get the uncertainty down to 20 parts per billion in the coming year – a goal they think they can reach by measuring more precisely how the current in the coil affects the magnetic field at the coil’s location and by reducing the measurement noise.

While redefining the kilogram is a big deal in the metrology community, it should have little impact on the outside world. “It’s the frustrating part about being a metrologist,” says Schlamminger. “If you do your job right, nobody should notice.”

The research is published in the journal *Review of Scientific Instruments*.