DIY: How to measure Planck's constant using LEGO

The kilogram is about to be redefined using Planck’s constant and you can now measure this constant yourself with a little ‘do-it-yourself’ effort and some LEGO.

The International System of Units (Le Système International d'Unités or SI units) is based on seven building blocks which can measure length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity - or in other words, the metre, kilogram, second, ampere, kelvin, mole and candela. All other ‘coherent SI units’ can be derived from these base units plus a set of decimal-based multipliers.

In the olden days, artefacts were used to define the root units. However, over time, these unit definitions have been modified as the technology of measurement progresses and the precision of measurements improves. The meter was first defined as 1/10 000 000 of the meridian through Paris between the North Pole and the equator but the first prototype was short by 0.2 mm because researchers miscalculated the flattening of the earth due to its rotation. Still this length became the standard. In 1889, a new international prototype was made of an alloy of platinum with 10% iridium, to within 0.0001, that was to be measured at the melting point of ice. In 1927, the meter was more precisely defined as the distance, at 0°, between the axes of the two central lines marked on the bar of platinum-iridium. This bar being subject to standard atmospheric pressure and supported on two cylinders of at least one centimetre diameter, symmetrically placed in the same horizontal plane at a distance of 571 mm from each other.

This definition was replaced in 1960 using a definition based on a wavelength of krypton-86 radiation. This definition was adopted in order to reduce the uncertainty with which the meter may be realised. In turn, to further reduce the uncertainty, in 1983 this latter definition was replaced by the following definition: The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

Meanwhile, the second was originally defined as 1/86 400 of a day … It is now 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 cesium 133 atom.

Currently the kilogram is the only SI base unit that relies on a specific physical artefact (a chunk of metal sitting in a vault in France), the international prototype of the kilogram, for its definition.

But this definition is on its way out - physicists are about to change the definition of mass so that it depends on Planck’s constant rather than on the mass of the lump of metal in Paris.

Redefining the kilogram using Planck’s constant

Planck’s constant describes the relationship between the energy and frequency of an electromagnetic wave in an equation known as the Planck-Einstein relation: E = hv (where E is energy, v is frequency and h is Planck’s constant).

It is one of the five constants of nature (the speed of light, the Planck constant, an elementary charge, the Boltzmann constant and the Avogadro number) that the SI system of measurements requires to have exact values.

So now there is the imperative to know Planck’s constant with a high degree of accuracy.

Planck’s constant comes in because of an historical idiosyncrasy in the way power units have been defined. Since 1990, almost all electrical measurements have been calibrated using a system of units in which Planck’s constant, along with various other constants, are defined rather than measured.

By contrast, mechanical power relies on ordinary SI units, which rely on a measured value of Planck’s constant. By comparing electrical power in conventional units to mechanical power in SI units, h can be determined.

Watt balance

One kind of device that can be used to measure mass based on Planck’s constant or taken the other way, to find a value for Planck's constant based on a known mass, is called a watt balance. It does its work by balancing the force exerted by gravity with the force of current in a coil - the mass of an object can be calculated by comparing the mechanical power to the electrical power in the device.

CAD model of the LEGO watt balance. The balance pivots about the T-block at the centre. Two PVC endcaps with copper windings hang from universal joints off either side of the balance beam. Coil A is on the left and Coil B is on the right. A 10 gram mass sits on the Coil A mass pan and each coil is concentric to its own magnet system. Two lasers are used to calibrate and measure the linear velocity of each coil. Credit: arXiv:1412.1699 [physics.ins-det]

This device is simple in principle. The idea is to balance the force on a mass due to gravity with the force generated by a current-carrying coil in a magnetic field. The mass can then be calculated in a straightforward way by comparing the mechanical power to the electrical power involved in the experiment (the machine gets its name because electrical and mechanical power are both measured in watts).

The experiment involves measurements of only the voltage and current through the coil as well as the velocity of the mass as it moves through the coil. It also requires an accurate value for g, the acceleration due to gravity, which can be easily read off a website operated by the National Oceanic and Atmospheric Administration by entering any location on the planet.

Build your own watt balance using LEGO

Scientists at NIST and other places have built elaborate and expensive watt balances, but in a new effort, they wanted to find a way to create one that anyone could build. They found a way to do this using LEGO blocks. They actually built three, one of which they chose to outline in detail, describing not only how it works, but the parts used so that others could build one too.

Image of three similar versions of the LEGO watt balance. The acrylic cases are backlit with blue LEDs and serve the purpose of blocking out disturbances from air currents. Two hinged doors on the front panel allow for small masses to be placed and removed from the mass pans. All the electronics are mounted below the wooden base board. Four adjustable feet are used for levelling the balance. Credit: arXiv:1412.1699 [physics.ins-det]

Their design, they say, would require a would-be constructor to lay down just $634 for all the parts, which include 2 sub-mW lasers, photodiode, controllers, etc. They note that some industrious sorts would likely be able to reduce costs using other less expensive parts they source themselves.

They’ve also written a paper (A LEGO watt balance: An apparatus to demonstrate the definition of mass based on the new SI - http://arxiv.org/abs/1412.1699) in which they describe their device and how it was built, should readers wish to construct one of their own.

So if you’re searching for the perfect present for the physicist who has everything or fancy a little LEGO fun for yourself, how about creating a LEGO kit for measuring one of the universe’s fundamental constants?