TECHNOLOGUE

# Weighing the Kilogram

Proposals to redefine this unit of mass and a related measurement, the mole, may be overlooking a clearer, simpler solution.

Standards of measurement date back to James Clerk Maxwell, nearly one and a half centuries ago. Such standards guarantee uniformity and clarity for comparisons, an especially necessary ability owing to the global nature of the marketplace, technology, and research. Today, in the International System of Units (SI) there are seven base units that define physical quantities. These units include the second, meter, ampere, kelvin, and candela. But the final two have proven particularly problematic over the years: the kilogram (for the physical quantity “mass”), and the mole (for the physical quantity “amount of substance”—the name comes from “gram molecular weight”). Although it is widely accepted that the former needs a modification, there has been slow movement to do so.

Extreme precision in the measurement of all units is more than a semantic point. Improvements in measurement technology, combined with the fundamental properties of nature that can be revealed by nearly infinitesimally small changes in magnitudes, means that more and more precise standards are needed to extract knowledge from experimental determinations or from comparison with theories. The list of Nobel Prize winners is replete with recognition of major discoveries based on precision of the highest degree. Base units, upon which measurements are structured, not surprisingly have been undergoing modernization. But the kilogram and the mole have not been at the top of the list more because of controversy than lack of motivation.

The kilogram, and by extension the mole, are the only base units still tied to a physical object. For now, the 125-year-old kilogram definition is still anchored to a metal artifact: a platinum-iridium alloy cylinder that is kept under lock and key in a suburb of Paris. The mass of this standard kilogram seems to be changing at about the millionth of a percent level over about a century. The cause of this change is uncertain, but likely relates to periodic cleaning and calibration measurements. Small as it may seem, that change is enough to lend urgency to the campaign to redefine the kilogram.

To that end, a symposium on “The Kilogram and the Mole,” sponsored by the president of the American Chemical Society, was held in San Francisco in 2010. There are now a number of formal proposals to redefine the kilogram, but I aim to demonstrate that some of the major options championed are grossly inappropriate. In 2011, Michael Kühne, then the director of the International Bureau of Weights and Measures (BIPM) spoke to the *New York Times* about the kilogram, saying that “the reason it hasn’t been redefined before now is that nobody has come up with something better.” I think that the BIPM has actually come up with something worse. This is the bureau’s proposed new definition:

The kilogram, kg, is the SI unit of mass; its magnitude is set by fixing the numerical value of the Planck constant to be equal to exactly 6.626069…×10^{-34}when it is expressed in the unit s^{-1}m^{2}kg, which is equal to J s.

I would like to decode that definition, but even its proponents agree that is not a trivial task. What it comes down to is that a device called a watt-balance can be used to realize the connection between Planck’s constant, *h,* the quantum of action in quantum mechanics, and the kilogram, based on an equation relating electrical and mechanical power that involves both that constant and the velocity of a mass moving under the influence of gravity. Making matters murkier, the suggestion has arisen to further constrain this definition in order to avoid the possibility that Planck’s constant might vary as the universe evolves. To the above would be added the qualifying phrase for the Planck constant “being constant in terrestrial space and in the current era time frame.”

Closely related to the kilogram issue is the one involving the mole. Up to now, the mole has been stipulated to be the number of atoms in exactly 12 grams of carbon-12. (*See “An Exact Value for Avogadro’s Number,” March–April 2007.*) Because it is defined in terms of grams, the mole is inextricably entangled with the kilogram. Under the new BIPM proposal, therefore, as the kilogram definition changes the mass of carbon-12 will also change, probably multiple times. Yet most recently, revisions in official atomic mass data by the International Union of Pure and Applied Chemistry still refer to the mass scale’s foothold as embodied in carbon-12 having an atomic mass of exactly 12.

Proponents of the new SI definitions, such as the BIPM, have sought to bring the kilogram and mole in line with the other five standard units, make the complete set of fundamental physical quantities invariant and not based on artifacts. In other words, they aim to rationalize the entire international system of standard units. Quoting Ian Mills, president of the BIPM’s Consultative Committee on Units: “The objective of the proposed changes is to adopt definitions referenced to constants of nature, taken in the widest sense, so that the definitions may be based on what are believed to be true invariants.”

Prominent are the phrases “constants of nature” and “true invariants.” The clearest examples of success here are the meter and the second, which are now infinitely precise and permanently defined in terms of integers. For instance, the meter is defined as the length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second. This part of the SI scheme has universal support, which is essential if it is to be extended to the remaining physical quantities. The widely accepted criteria for SI units include the following, according to Mills: the possibility of realization anywhere and at any time, at least in principle; based on commonly accepted laws in physics; and conceptually clear and easy to understand.

These are sensible and laudable goals. But the criteria and the objectives put forward by Mills seriously call into question the wisdom, if not the legitimacy, of the BIPM’s very own proposed changes.

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