Edwin R. Williams

Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing CIPM recommendation 1 (CI-2005)

The International System of Units (SI) is founded on seven base units, the metre, 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. At its 94th meeting in October 2005, the International Committee for Weights and Measures (CIPM) adopted a recommendation on preparative steps towards redefining the kilogram, ampere, kelvin and mole so that these units are linked to exactly known values of fundamental constants. We propose here that these four base units should be given new definitions linking them to exactly defined values of the Planck constant h, elementary charge e, Boltzmann constant k and Avogadro constant NA, respectively. This would mean that six of the seven base units of the SI would be defined in terms of true invariants of nature. In addition, not only would these four fundamental constants have exactly defined values but also the uncertainties of many of the other fundamental constants of physics would be either eliminated or appreciably reduced. In this paper we present the background and discuss the merits of these proposed changes, and we also present possible wordings for the four new definitions. We also suggest a novel way to define the entire SI explicitly using such definitions without making any distinction between base units and derived units. We list a number of key points that should be addressed when the new definitions are adopted by the General Conference on Weights and Measures (CGPM), possibly by the 24th CGPM in 2011, and we discuss the implications of these changes for other aspects of metrology.

Redefinition of the kilogram: a decision whose time has come

The kilogram, the base unit of mass in the International System of Units (SI), is defined as the mass of the international prototype of the kilogram. Clearly, this definition has the effect of fixing the value of to be one kilogram exactly. In this paper, we review the benefits that would accrue if the kilogram were redefined so as to fix the value of either the Planck constant h or the Avogadro constant NA instead of , without waiting for the experiments to determine h or NA currently underway to reach their desired relative standard uncertainty of about 10−8. A significant reduction in the uncertainties of the SI values of many other fundamental constants would result from either of these new definitions, at the expense of making the mass of the international prototype a quantity whose value would have to be determined by experiment. However, by assigning a conventional value to , the present highly precise worldwide uniformity of mass standards could still be retained. The advantages of redefining the kilogram immediately outweigh any apparent disadvantages, and we review the alternative forms that a new definition might take.

Towards an electronic kilogram: an improved measurement of the Planck constant and electron mass

The electronic kilogram project of NIST has improved the watt balance method to obtain a new determination of the Planck constant h by measuring the ratio of the SI unit of power W to the electrical realization unit W90, based on the conventional values for the Josephson constant KJ−90 and von Klitzing constant RK−90. The value h = 6.626 069 01(34) × 10−34 J s verifies the NIST result from 1998 with a lower combined relative standard uncertainty of 52 nW/W. A value for the electron mass me = 9.109 382 14(47) × 10−31 kg can also be obtained from this result. With uncertainties approaching the limit of those commercially applicable to mass calibrations at the level of 1 kg, an electronically-derived standard for the mass unit kilogram is closer to fruition.

Details of the 1998 Watt Balance Experiment Determining the Planck Constant

The National Institute of Standards and Technology (NIST) watt balance experiment completed a determination of Planck constant in 1998 with a relative standard uncertainty of 87 × 10−9 (k = 1), concurrently with an upper limit on the drift rate of the SI kilogram mass standard. A number of other fundamental physical constants with uncertainties dominated by this result are also calculated. This paper focuses on the details of the balance apparatus, the measurement and control procedures, and the reference calibrations. The alignment procedures are also described, as is a novel mutual inductance measurement procedure. The analysis summary discusses the data noise sources and estimates for the Type B uncertainty contributions to the uncertainty budget. Much of this detail, some historical progression, and a few recent findings have not been included in previous papers reporting the results of this experiment.

NBS determination of the fine-structure constant, and of the quantized Hall resistance and Josephson frequency-to-voltage quotient in SI units

Results of US National Bureau of Standards (NBS) experiments to realize the ohm and the watt, to determine the proton gyromagnetic ratio by the low-field method, to determine the time dependence of the NBS representation of the ohm using the quantum Hall effect, and to maintain the NBS representation of the volt using the Josephson effect, are appropriately combined to obtain an accurate value of the fine-structure constant and of the quantized Hall resistance in SI units, and values in SI units of the Josephson frequency-to-voltage quotient, Planck constant and elementary charge. >

Measuring the Electron's Charge and the Fine-Structure Constant by Counting Electrons on a Capacitor

The charge of the electron can be determined by simply placing a known number of electrons on one electrode of a capacitor and measuring the voltage, Vs, across the capacitor. If Vs is measured in terms of the Josephson volt and the capacitor is measured in SI units then the fine-structure constant is the quantity determined. Recent developments involving single electron tunneling, SET, have shown bow to count the electrons as well as how to make an electrometer with sufficient sensitivity to measure the charge.

A measurement of the NBS electrical watt in SI units

The National Bureau of Standards (NBS) electric watt in SI units to be: W/sub NBS//W=K/sub W/=1-(16.69+or-1.33) p.p.m. The uncertainty of 1.33 p.p.m. has the significance of a standard deviation and includes the best estimate of random and known or suspected systematic uncertainties. The mean time of the measurement is May 15, 1988. Combined with the measurement of the NBS ohm in SI units: Omega /sub NBS// Omega =K/sub Omega /=1-(1.593+or-0.022) p.p.m., this leads to a Josephson frequency/voltage quotient of E/sub J/=E/sub 0/(1+(7.94+or-0.67) p.p.m.) where E/sub 0/=483, 594 GHz/V. >

Monitoring the mass standard via the comparison of mechanical to electrical power

An ongoing absolute watt experiment that shows the promise of being able to monitor the stability of the kilogram standard to better than 0.05 p.p.m. is discussed. The theory is presented, and the latest improvements to the experimental apparatus are briefly described. >

Application of single electron tunneling: Precision capacitance ratio measurements

A metrological application is reported of the single electron tunneling (SET) phenomena: a precise measurement of the ratio of two cryogenic capacitors. The measurement used a superconducting SET electrometer as the null detector for a capacitance bridge. A 3‐ppm level of imprecision has been achieved in the measurement of the capacitance ratio from 100 to 1000 Hz. Further improvements can be made in the attempt to obtain an imprecision of 10−8 at lower frequencies, sufficient for the metrological measurement of capacitance or the fine‐structure constant using a SET pump.

A Noncontacting Magnetic Pickup Probe for Measuring the Pitch of a Precision Solenoid

The magnetic-field gradients produced by a current sequentially activating a few turns of wire of a precision solenoid are used to measure its pitch. The position of the activated portion of wire can be resolved to 0.1 ?m. Preliminary results are found to be in agreement with an earlier measurement using a contacting probe to within the uncertainty of the latter determination. This new technique reduces many of the difficulties associated with conventional pitch measuring schemes and at the same time provides a method of obtaining increased accuracy.