From Metal to Math
It may surprise you to learn that within the past couple years it was discovered that the kilogram isn’t quite what it used to be. When the International Bureau of Weights and Measures in Paris measured the reference unit for the kilogram, they discovered it lost approximately 50 millionths of a gram. In this article, George discusses the background of this story, and reports on efforts last year by scientific teams—in more than a dozen countries—to redefine the kilogram.
The International System of Units (SI) also known as the metric system relies on precise definitions of several physical measurements, such as the mass. I have addressed some aspects and the relationship of mass and weight in detail in my article Measuring Acceleration in Circuit Cellar 332, March 2018) .
As the reference, the International Prototype of the Kilogram, IPK, also known as “le Grand K,” was created in 1889 from a block of Platinum and since then has been kept in Paris under three glass bell jars . Exact replicas have been constructed and located around the world to be used in defining mass of everything. Including countries, such as the United States, where an imperial and customary systems of units are in commercial use.
In 2018—at the International Bureau of Weights and Measures in Paris—when le Grand K was checked by the alpha metrologists and the results compared with the measurements of some of its sister replicas it was, to great surprise, discovered that it lost approximately 50 millionths of a gram. In fact, all the replicas drifted, microscopically, in one direction or another.
This may not be a big deal in commercial use, but such discrepancies add up quickly to unacceptable errors when used in nano or astronomical measurements. Consequently, the International Committee for Weights and Measures came to the conclusion that the kilogram—just as well as all the other International System Units—should be defined on immutable natural constants rather than a physical object—a chunk of Platinum in our case.
But here came a challenge. The mass, one kilogram in our case, can be defied in nature by Planck’s constant (h), which is a proportional value describing the ratio between the energy in one quantum of electromagnetic radiation—in other words, a photon—and the frequency of its associated electromagnetic wave. However, for the Planck’s constant “h” to be useful for the definition of the mass of one kilogram, the International Committee for Weights and Measures stipulated that three separate test measurements of the mass must be performed and the results agree within an infinitesimal level of uncertainty. That was a very tall order.
A British inventor named Bryan Kibble proposed a design known today as the Kibble balance—also known as the Kibble Scale or Watt balance (Figure 1). However, the principle is not new. As early as the 1920s, scientists measured mass (weight) using the so-called ampere balance—the precursor of the Kibble balance. The principle of the operation lies in suspending the mass to be measured in a magnetic field created by an electric coil. Knowing the voltage across the coil and the precisely measured current, the mass became proportional to the power consumed by coil in Watts. For the better accuracy required, power would be integrated over some time, making the mass proportional to the consumed energy. As a result, the determined mass could be expressed in purely electrical terms—that is, by purely mathematically determined SI units.
While the theory is enticing, the scale’s accuracy depends on its ability to define the Planck’s constant with sufficient precision. That drove the decision to define the constant in terms of power multiplied by time. Nevertheless, until recently, the best results provided the uncertainty of about 70 parts per billion (ppb). This was not acceptable to the International Committee for Weights and Measures as accurate enough, so the search continued.
Scientific teams in more than a dozen countries set off to refine the measurement results. Among them, proudly, a small team of Canadian scientists at the National Research Council (NRC) in Ottawa. With the constant improvement of the Kibble scale hardware as well as factoring in error causing influences, such as the fluctuating gravitational pull caused by the motion of the moon, the presence of a few molecules of water on the surface as well as some minor earthquake tremors on the other side of the world, the NRC team succeeded in bringing the mass precision down to nine parts per billion.
In cooperation with the U.S. National Institute of Standards and the German National Metrology Institute, the International Committee for Weights and Measures voted to accept the new definition of the kilogram with the official adoption scheduled for May 20, 2019. So, what does it mean for regular folks like you and I? The good news is that the new standard is expected to last us for a long time. But, more than that, those of us watching our weight can sleep better knowing that as of May 20, 2019 we’ll weigh a little bit less. Infinitesimally less, to be correct, but every little bit counts.
Editor’s Note: This article was written by George before he passed away, over a year ago. As a wrap-up to this story we’ve included a sidebar below with a news item “Science Says Goodbye to the Original Kilogram,” posted on Laboratory News on May 20, 2019. A link to the original story is available here.
This is a news item posted on Laboratory News on May 20, 2019:
As of World Metrology Day [today] (Monday, May 20), redefined standards of the International System of Measurement (SI) means a kilogram is now expressed in terms of fundamental constants that can be observed in the natural world, rather than a physical object.
The changes, voted on by global representatives last November (2018), will ensure the kilogram remains stable and will enable more accurate mass measurements in the future.
Dr Ian Robinson at the National Physical Laboratory, said: “There will be no change to the mass scale currently used in trade and industry, but by using a universal constant of nature to ensure the long term stability of the kilogram, we are both reunifying the SI and setting the stage for robust, reliable science that could pave the way for new ideas and inventions.”
The definition of kilogram will now be based on the Planck constant, a constant observed in the natural world that is inherently stable. It uses the Kibble Balance, a physical instrument that measures mass using electromagnetic and quantum techniques.
Since 1889, the kilogram has been defined by the International Prototype of the Kilogram (IPK), a metal block made of an alloy of 90% platinum and 10% iridium, contained within glass bells in a vault in Saint-Cloud, France.
Different countries have used their own prototype kilograms that were calibrated back to the IPK, to ensure mass measurements were consistent around the world.
However, the IPK can gain mass over time due to adsorption of atmospheric contamination onto its surface. Changes in the IPK’s mass over time can be deduced by comparing it to official copies, but this process is rarely undertaken and does not have the accuracy of the new standard.
Dr Richard Brown, Head of Metrology at the National Physical Laboratory, said: “The revised SI future proofs our measurement system so that we are ready for all future technological and scientific advances such as 5G networks, quantum technologies and other innovations that we are yet to imagine.”
As well as the kilogram, the Ampere will now be defined using the elementary charge (e), a fixed value; the Kelvin will be defined using the Boltzmann constant (kB); while the mole will be based on the Avogadro constant (NA).
References: George Novacek, Circuit Cellar March 2018, Issue 332, Measuring Acceleration
 Design Engineering www.design-engineering.com Volume 64, No. 6
 https://www.nist.gov/image/nist4wattbalancejpg Public Domain
 Science Says Goodbye to the Original Kilogram
Laboratory News, May 20, 2019
PUBLISHED IN CIRCUIT CELLAR MAGAZINE • MARCH 2020 #356 – Get a PDF of the issue