Andy Pye looks at how the fundamental constants that govern the laws of nature are being determined with progressively increasing accuracy.
Fundamental constants describe a variety of physical properties in the world around us. Planck’s constant, for example, governs the relationship between energy and frequency. The fine-structure constant explains the strength of electromagnetic interaction between charged particles. Fundamental constants such as these underlie the development of much of today’s technology, from atomic clocks to GPS systems.
An international community of physicists and metrologists convened at the Workshop on the Determination of the Fundamental Constants to share their research into an array of fundamental constants. The workshop took place in February 2015 at the Hotel Frankenbach, Eltville, Germany.
To make the system more consistent and accessible, the international metrology community plans to redefine all SI units in terms of fundamental constants by 2018. Better definitions of these fundamental constants will aid in efforts to redefine several standard scientific units, including the kilogram and the Kelvin. They are also linked to the International System of Units (SI), the standard measurement system used throughout the scientific community and in most countries around the world. By defining units like the metre in terms of fixed fundamental constants, such as the speed of light, they remain the same over time.
Before we can redefine an entire system of units, however, it is important to be certain that the fundamental constants upon which the definitions depend are as accurate and precise as possible. And since different measurement procedures or data collection techniques can yield slightly different results, pinning down the exact values of these constants can be a surprisingly fussy business.
“The objective of the SI is to provide the best possible standards, and the redefinition will be a step in that direction,” said Peter Mohr, a researcher at the National Institute for Standards and Technology (NIST).
Luckily, some of the values for previously-contested constants appear to be converging. For instance, the recent workshop highlighted advances in the determination of the Bolzmann constant k, which explains the relationship between temperature and particle energy. Under the new SI system, the fixed Bolzmann constant will be used to define the Kelvin, the SI unit of temperature.
Planck’s constant has also seen marked progress. “The Planck constant was problematic in the past, as there were disagreeing values obtained by different experiments. However, the values seem to be converging to a sufficiently reliable value for the redefinition of the SI to move forward,” said Mohr. Planck’s constant will eventually be fixed and used to define the kilogram.
“The new definitions will make many of the physical constants exact in the future, although they are measured now. Others, although not exact, will be more accurate,” said Mohr. “This will stabilise the values of the constants and provide accurate measurement standards.”
The 2015 workshop provided input to the latest adjustment of the official values for a number of fundamental physical constants. This adjustment is not the final one before the official SI redefinition in 2018, but it is still an important step forward. Growing consensus on the values of certain fundamental physical constants suggests that we may be almost ready to fix their values and move to a more reliable and streamlined measurement system.
However, some SI units, like the kilogram, still rely on a physical standard. The mass standard, the kilogram, is currently defined as the international prototype kilogram (IPK) which is a 135 year old platinum-iridium artefact that is held at the International Bureau of Weights and Measures (BIPM) in Sevres near Paris with about 80 ‘national prototype’ replicas distributed world-wide to metrology institutes.
Now that scientific research is carried out across the globe, relying on a single physical standard is somewhat limiting. Periodically, the replicas are compared with the original IPK for reference with the increasing realisation that the prototypes have been slowly but inexorably deviating from each other due to reasons such as micro-contamination, surface adsorption and other complex factors that are extremely difficult to counter. The standard itself is also subject to changes in mass over time. These minuscule variations, which amount to nothing more than the mass of a fingerprint over several years, have led scientists to look for other ways to quantify mass and one line of research led to the foundation of the international Avogadro Project – a long term collaboration set up in 2003 between metrology institutes in Germany, Italy, Belgium, Japan, Australia and the USA. The Project aims to redefine the kilogram in terms of a constant on the basis of atomic mass.
Researchers at the Physikalisch-Technische Bundesanstalt (PTB) have set up a complex chain of many manufacturing and analytical steps in order to – by counting the atoms in a silicon sphere – accurately determine two constants of nature: the Avogadro constant and Planck’s constant. These are the pillars of a redefinition of the kilogram.
PTB started with a crystal made of high-purity silicon-28, from which two spheres were manufactured and then analysed. “Our goal is to master the realisation of the future kilogram completely autonomously”, says project leader Horst Bettin. The complete sphere production took place at PTB and is so exact that the deviation from the ideal sphere shape is considerably less than 100nm. With the sphere interferometer it is possible to determine the average diameter of the sphere accurately down to three diameters of an atom, and a UHV reflectometer determines the thickness of oxide layers on the sphere surface down to one nanometer.
The accuracy is also based on the purity of the supplied material. In the Electrochemical Plant in Zelenogorsk, Russia, thousands of centrifuges were in operation for months in order to facilitate the more than 99.998 percent isotope purity of the silicon-28. The subsequent cleaning of the highly explosive gaseous silicon tetrafluoride (28SiF4) and its conversion to silane (28SiH4), and subsequently to polycrystalline silicon was pioneering work which took place at the Institute of Chemistry of High-Purity Substances of the Russian Academy of Sciences in Nishniy Novgorod.
From the round-bodied, cylindrical single-crystals, PTB produces crystal spheres that are rounder than anything else in the world. Each sphere is then measured individually, connecting the coarse characteristics to the fine characteristics, to produce the connection between the mass of the sphere and the mass of an atom. Thus, the researchers measure the mass and the volume of the 28Si sphere as well as the arrangement of the atoms in the crystal and the abundance of the three existing silicon isotopes, which yields the molar mass of the silicon used. Thus, they know how many moles of silicon are present in their sphere and how many atoms there are in one mole. The researchers have thus determined the Avogadro constant. And since the Avogadro constant is linked to the Planck constant via a fixed physical relation, both can be determined in one fell swoop. At this point, PTB scientists are working to an accuracy of two in every one hundred million atoms. The goal is to miscount only by one atom for every one hundred million atoms.
PTB commissioned Heason Technology to design a non-magnetic 3-axis manipulator, suitable for use in ultra-high vacuum. This is used to microposition the silicon sphere. First, it was supplied to the German Technical Consultancy firm of Dr.-Ing. Giora Baum (Precision-Motion) who provided the motion control system.
The ongoing project has returned some very promising results and many milestones have been achieved but more exhaustive work is scheduled well into the future. As surface contamination is still a concern and a barrier to obtaining the levels of measurement certainty required the PTB are analysing, amongst many other aspects, the surface properties of these high purity silicon balls using a synchrotron beam to determine its influence at the atomic level on the sphere diameter and consequent volume. The Heason 3-axis manipulator is used inside a vacuum chamber to position the sphere relative to the synchrotron radiation beam for surface spectroscopy work.
Karshenboim, Mohr and Newell. Advances in determination of fundamental constants. Journal of Physical and Chemical Reference Data, July 2015.