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Beyond the Kilogram: Redefining the International System of Units

The world’s official standard for mass—a 115-year-old cylinder of metal—will likely join the meter bar as a museum piece in the near future. Will the standards for electric current, temperature, and amount of substance soon follow?

Measurement experts long have planned to replace the kilogram standard—its mass actually fluctuates slightly—with a definition based on an invariable property of nature. The next logical step in the quest for the most precise, consistent, and accessible measurements possible is to redefine several more units of the International System of Units (SI), according to a new paper by five eminent scientists from three countries.

Base Unit

Would be Linked to Possible New Definition


Planck constant the mass of a body whose energy is equal to that of a number of photons (the smallest particles of light) whose frequencies add up to a particular total
Ampere Elementary charge the electric current in the direction of the flow of a certain number of elementary charges per second
Kelvin Boltzmann constant the change of thermodynamic temperature that results in a change of thermal energy by a specific amount
Mole Avogadro constant the amount of substance that contains exactly [set value for Avogadro’s constant] specified elementary entities, such as atoms, molecules, electrons, or other particles or groups of particles

The paper, published April 6, 2006, in Metrologia,* advocates redefining not only the kilogram, but also three more base units of the SI that are not currently linked to true invariants of nature—the ampere, kelvin, and mole (used to measure electric current, thermodynamic temperature, and amount of substance, respectively). The paper suggests that all four units be redefined in terms of four different fundamental constants or atomic properties to which precise values would be assigned. A property of nature is, by definition, always the same and can in theory be measured anywhere. (See chart.)

The paper represents the collective opinions of the authors, including one from the University of Reading in the United Kingdom, who heads an influential international metrology committee, as well as three scientists from the U.S. National Institute of Standards and Technology (NIST) and the former director of Bureau International des Poids et Mesures (BIPM) near Paris.

The paper does not represent the official policy position of any of the authors’ three institutions. However, much of the paper echoes, and suggests a practical strategy for implementing, an October 2005 recommendation by the International Committee for Weights and Measures (CIPM).

If implemented, the proposed changes would affect measurements requiring extreme precision and reduce the uncertainty in values for numerous fundamental constants, not only the four constants named in the redefinitions, but also many others because of their interrelationships. Physical constants are widely used by scientists and engineers to make many types of calculations, and also are used in designing and calibrating quantum-based measurement systems.
“Our general conclusion is that the changes we propose here would be a significant improvement in the SI, which would be to the future benefit of all science and technology,” the authors state in the paper. “We believe that these changes would have the widespread support of the metrology community as well as the broader scientific community. …”

The proposed SI system would enable scientists to independently determine measurement standards without the need to refer to a particular object, the kilogram artifact, which is kept at BIPM and has been made available for comparisons on only two occasions since 1889. Further, in the new system, measurements made today could be compared to measurements made far in the future with no ambiguity. For example, the new SI system would provide the basis for precise electrical measurements, without the use of approximate values assigned to two fundamental constants related to resistance and voltage, as is necessary today. Voltmeters then could be calibrated with high accuracy in SI units, which is not possible now.

At the same time, the authors note that ripple effects from such changes in the SI system would be too small to have a negative effect on everyday commerce, industry, or the public.

The international metrology community has been moving for years toward redefining the kilogram, and last year began considering the ampere, kelvin, and mole, as recorded in the recent CIPM recommendation. The committee's action was prompted by an April 2005 paper by the same five authors,** which advocated a quicker redefinition of the kilogram than had previously been planned. The 2005 paper stimulated extensive discussions in the international metrology community, which is also the authors' hope for the new paper.

Any decisions about when and how to redefine the SI are made by an international group, the International Committee for Weights and Measures, and ratified by a General Conference on Weights and Measures, which meets every four years. The new paper suggests that the redefinitions could be ratified at the conference meeting in 2011.

* I.M. Mills, P.J. Mohr, T.J. Quinn, B. N. Taylor and E.R. Williams. Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing CIPM recommendation 1 (CI-2005), Metrologia. Available online April 6, 2006.

** I.M. Mills, P.J. Mohr, T.J. Quinn, B.N. Taylor and E.R. Williams. Redefinition of the kilogram: A decision whose time has come. Metrologia, April 2005.


The SI is founded on seven base units—the meter, kilogram, second, ampere, kelvin, mole, and candela (corresponding to the seven base quantities of length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity).

Of the seven units, only the second and the meter are directly related to true invariants of nature. The kilogram is still defined in terms of a physical artifact—a cylinder of platinum-iridium alloy about the size of a plum—and the definitions of the ampere, the mole, and the candela depend on the definition of the kilogram. The kelvin is based on the thermodynamic state of water, which is a constant, but it depends on the composition and purity of the water sample used.

The new Metrologia paper lays out a roadmap for implementing CIPM Recommendation 1 (CI-2005), which calls for linking the kilogram, ampere, kelvin, and mole to exactly known values of fundamental constants. As a model, consider the meter, which was once equal to the length of a metal bar that was prone to shrinking and growing slightly with changes in temperature; the meter is now defined as the distance light travels in vacuum in a prescribed time. In a similar way, the mass of the physical kilogram changes slightly depending on trace levels of dirt or on polishing; scientists plan to replace it with a definition based on a quantity of light or the mass of a certain number of specific atoms.

If the changes proposed in the paper were carried out, then six of the seven base units of the SI (the exception being the candela) would be related to fundamental constants or atomic properties, which are true invariants of nature. The proposed changes are outlined briefly below and in the accompanying chart.

The Kilogram

The paper suggests redefining the kilogram by selecting a fixed value for the Planck constant, which is widely used in physics to describe the sizes of “quanta,” or units of energy. Quanta are the building blocks of the theory of quantum mechanics, which explains the behavior of the smallest particles of matter and light.

A possible new definition might be something like: The kilogram is the mass of a body whose energy is equal to that of a number of photons (the smallest particles of light) whose frequencies add up to a particular total. The Planck constant is tied into this definition because the energy of a photon is the product of the Planck constant and its frequency, and the relation between energy and the corresponding mass follows from Einstein's famous equation E=mc2.

The new definition could, in principle, be realized using either one of the two leading approaches for redefining the kilogram. One method is the "watt balance," currently being refined by NIST and other metrology laboratories in England, Switzerland, and France. This method relies on selecting a fixed value for the Planck constant. The alternative method involves counting the number of atoms of a specific atomic mass that equal the mass of 1 kilogram. This method depends on selecting a fixed value for the Avogadro constant, which describes the number of atoms or molecules in a specified amount of a substance. The new paper suggests this constant should be the basis of a new definition of the mole instead (see below).

Although the proposed re-definition of the kilogram (using the Planck constant) would be more directly implemented using the watt balance, the alternative method could still be used if additional calculations were made using the theoretical relationship between the Planck and Avogadro constants. This relationship depends on having accurate values for a number of other fundamental constants. Researchers are working on improving both methods, which have not yet met consensus goals for precision and also produce slightly different results.

The Ampere

The ampere is used widely in electrical engineering, for example, to design electrical devices and systems. It is now defined in terms of a current that, if maintained in two straight parallel conductors of specific sizes and positions, would produce a certain amount of [magnetic] force between the conductors. The ampere is extremely difficult to realize in practice. 

The paper suggests linking the ampere to a specific value for the elementary charge, which is the electric charge carried by a single proton, a particle with a positive charge in an atomic nucleus. The ampere might be defined, for example, as the electric current in the direction of the flow of a certain number of elementary charges per second.

The Kelvin

The kelvin is used in scientific experiments to represent temperature. Conveniently, absolute zero, the point at which no more heat can be removed from an entity, is 0 K. The kelvin is now defined as a fraction of the thermodynamic temperature of the “triple point” of water (the temperature and pressure at which the gas, liquid, and solid phases coexist in a stable way). The kelvin is extremely difficult to realize, as it requires special thermometers, and attempts to define it have led to new temperature scales.

The paper suggests redefining the kelvin as the change of thermodynamic temperature that results in a change of thermal energy by a specific amount. This has the effect of fixing the value of the Boltzmann constant, which relates temperature to energy. This constant, together with the Avogadro constant, is used in, for example, studies of gases and semiconductors, and serves as a link between the everyday and microscopic worlds. This suggested definition would be easier to realize over a broad range of temperatures than the existing definition.

The Mole

Chemists often use the mole to describe sample sizes. The mole is now defined as an amount that contains as many elementary entities (such as atoms, molecules, or electrons) as there are atoms in 0.012 kilograms of a particular type of carbon.

The new paper proposes a definition that sets a specific value for Avogadro's number. This is a very large constant used in chemistry and physics, currently representing the number of atoms in 12 grams of carbon. The number is so huge (6.022… x 1023) that it would take a computer billions of years to count that high.

The new definition of the mole would be something like: the amount of substance that contains exactly [set value for the Avogadro constant] specified elementary entities, such as atoms, molecules, electrons, or other particles or groups of particles.


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Created: 4/12/06
Last updated: 4/13/06