Le Grand K was fun while it lasted, but constants of nature are forever. Today representatives from more than 50 countries voted at the General Conference on Weights and Measures in Versailles, France, to adopt a revised International System of Units (SI). Though most observers are focused on the dethroning of the international prototype of the kilogram in Paris as a standard bearer, the implemented changes are far more sweeping: The foundation of the SI system has shifted from the kilogram and other base units, several of which had arbitrary or abstract definitions, to explicitly designated constants. When the new system takes effect on 20 May 2019, every SI unit—not only the kilogram but also the volt, the newton, the weber, and more—will be derived by some combination of seven invariants of nature.
“We go from a foundation of definitions of base units to exact values of defining constants,” says David Newell, a physicist at NIST in Gaithersburg, Maryland, and cochair of the Committee on Data for Science and Technology (CODATA). Newell previewed the next-generation SI in a July 2014 feature article in Physics Today.
The newly approved changes, the most radical since the SI was established in 1960, required a suite of innovative measurements to reduce the uncertainty in the values of the constants that now underlie the system. Though the general public and even most researchers won’t be affected, the change offers increased precision for scientists making measurements at extreme scales. It could also lead to improved processes for pharmaceutical companies and other manufacturers.
For decades metrologists have been working toward a system of weights and measures based on nature’s invariants. The SI unit of time, the second, was tied to the oscillations of a cesium transition in 1967; the meter was based on the wavelength of an emission line of krypton and then, in 1983, on the speed of light. Yet binding the kilogram to a fundamental constant with an uncertainty on par with that of the mass of a platinum–iridium block always seemed a difficult task. In 2005, when five leaders in the field published a paper in Metrologia arguing that the time had come to redefine the kilogram, “it caused a big uproar,” Newell says. But it also got people thinking about what a revised SI system with a new kilogram might look like. The community soon coalesced around a system based on seven constants, with the Planck constant, h, as the foundation for defining the kilogram. The value of h is expressed in J s, or kg m2 s–1.
Three of the constants that form the basis of the revised SI were already precisely known or defined: the speed of light in a vacuum, c; the hyperfine transition frequency of cesium-133, ∆νCs; and the most arbitrarily determined of the seven, the luminous efficacy of monochromatic radiation of frequency 540 THz, Kcd. The challenge became making sufficiently precise measurements of the elementary charge, e; Boltzmann’s constant, k; the Avogadro constant, NA; and h.
Things didn’t go smoothly at first. To accept the new kilogram definition, a governing committee required that the value of h be confirmed by at least three experiments, using at least two different methods, with a relative uncertainty of no more than 50 ppb. Researchers at NIST used a watt balance, also known as a Kibble balance, which counteracts the weight of a test mass with the force produced by current run through a wire in a magnetic field. Meanwhile, the international Avogadro Project analyzed nearly perfect spheres of silicon-28 to come up with a value of NA, which is inversely proportional to h. The calculated values of h weren’t consistent with each other. A watt-balance measurement at the UK’s National Physical Laboratory was supposed to resolve the discrepancy, but NPL abruptly canceled the experiment. Fortunately, Canada’s National Research Council swooped in, bought NPL’s watt balance, and performed a measurement in 2012 that provided some clarity. An improved measurement at NIST two years later brought all three values of h into agreement.
Since then, researchers have homed in on h and the other constants. The latest update published by CODATA, which provides recommended values for constants and conversion factors, incorporates data on h from four watt-balance and four silicon-sphere measurements to achieve a relative uncertainty of 10 ppb. The highest uncertainty is that of k, at an acceptable 0.37 ppm, which is a nearly fivefold improvement from two decades ago.
| Foundational SI constants | |
|---|---|
| ∆νCs | 9 192 531 770 Hz |
| c | 299 792 458 m s–1 |
| h | 6.626 070 15 × 10–34 J Hz–1 |
| e | 1.602 176 634 × 10–19 C |
| k | 1.380 649 × 10–23 J K–1 |
| NA | 6.022 140 76 × 1023 mol–1 |
| Kcd | 683 lm W–1 |
Now, after today’s vote, those seven constants will be set at exact values—their presumed uncertainties will be zero. Constants directly related to the seven—for example, Josephson’s constant, which is equal to 2e/h—will also be presumed to have zero uncertainty. The uncertainties of some other constants, such as the electron rest mass, will decrease since they are tied to both the SI foundational constants and other constants (see the article by Peter Mohr and Barry Taylor, Physics Today, March 2001, page 29). Meanwhile, several constants that are central to the lame-duck SI, including the triple point of water, the molar mass of carbon-12, and the famous kilogram prototype in Paris, will gain uncertainties.
The kilogram and three other arbitrarily defined SI base units will get redefined through the newly set constants. The ampere will be defined as 1/(1.602 176 634 × 10–19) elementary charges per second (essentially, the numerical value of 1/e, expressed in C/s), the kelvin will be a change in thermal energy of k joules, and the mole will be the amount of substance that contains NA elementary entities.
Beyond those redefinitions, the kilogram, second, meter, ampere, mole, kelvin, and candela will essentially lose their special status. Though those units will continue to be referred to as base units, the so-called SI derived units will also be directly tied to the foundational constants (see the chart below). That change is especially important for electrical measurements. Since 1990 researchers have relied on definitions of the Josephson and von Klitzing constants that are separate from the SI, which based its electrical measurements on the ampere—the current carried by two arbitrarily spaced wires that generate an arbitrary amount of force. Now those values will be based on h and e.
The worth of the revised SI to those outside metrology lies in the role of the seven constants in special relativity, quantum mechanics, and other theories. Researchers can now measure mass at the kilogram scale via a watt balance, but they can also do so at much smaller scales via frequency measurements of atomic recoil; both methods center on the value of the now exactly set h. “You’re using the same constants in different laws of physics to inherently scale to the level you need,” Newell says. And by getting rid of Le Grand K, there will no longer be any fudge factor in converting between mass and energy—say, between, kilograms and electron volts. Precision measurements should become more precise.
Newell also expects the changes to reverberate through industry. Companies could precisely realize measurements on the factory floor rather than coming to NIST or other institutes for calibration with a standard. Newell says he’s trying to sell companies on manufacturing calibration devices that take NIST out of the equation, such as for measuring the power of lasers used in welding or etching. Says Newell: “It’s our job to put ourselves out of business.”
Editor’s note, 21 November: The article has been updated to correct some connections between units and constants. The definition of the ampere was fixed, and the chart was changed to correct the constants that determine the coulomb, radian, and steradian.
