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The New International System of Units: The Role of the Committee on Data for Science and Technology (CODATA)
Abstract
The mission of the Committee on Data for Science and Technology (CODATA) of the International Council for Science is to strengthen international science for the benefit of society by promoting improved scientific and technical data management and use. One of their most visible outputs comes from the Task Group on Fundamental Constants (TGFC), which periodically performs a comprehensive least-squares adjustment of the values of the constants and produces the well-known and widely cited publication entitled “CODATA recommended values of the fundamental physical constants: year” (freely available at http://physics.nist.gov/cuu/constants). When the proposal to change the International System of Units (SI) by redefining the kilogram, ampere, kelvin, and mole in terms of fixed values of the Planck constant h, elementary charge e, Boltzmann constant k, and Avogadro constant NA, respectively, is implemented in the near future, it will be the responsibility of the TGFC to provide these values. In this presentation, the least-squares adjustment procedure will be outlined and illustrated with reference to current state-of-the-art measurements in several physical disciplines.
... The International Council of Science established CODATA for facilitating improved scientific and technical data management and use for addressing issues of scientific interest for the benefit of society. Since then it seeks to provide the best values of fundamental constants and conversion factors used in physics and chemistry to scientific and metrology communities [24] Recommended laboratories to pursue their work with a view to monitoring the stability of IPK and in due course opening the way for the new definition of the unit of mass-based upon fundamental atomic constant Considered watt balance and X-ray Crystal Density (XRCD) (that counts the number of atoms in a silicon sphere) methods as candidates that could link mass with fundamental constant: watt Balance through Planck constant and XRCD through Avogadro constant. NIST USA, NPL UK, and NRLM Japan were working towards development of watt balance and PTB Germany was working to refine the Si sphere method [28] 1999 21st CGPM Recommended in its resolution to redefine kg ...
... 1969 Formation of Task Group on FundamentalPhysical Constants (TGFC)CODATA established the TGFC in 1969 and the mandate of TGFC is ''to periodically provide the scientific and technological communities with a selfconsistent set of internationally recommended values of the basic constants and conversion factors of physics and chemistry based on all of the relevant data available at a given point in time''[24] 1975 Dr. Bryan Peter Kibble at NPL Teddington demonstrated the principle of watt balance, equating mechanical power to electrical power[25] 1988-1992 The third periodic verification Confirmed the trend of mass change of prototypes of kilogram with respect to IPK which was also observed in second periodic verification. During verification, each NPK was calibrated against the IPK with the combined uncertainty of 2.3 lg[4] 1990 Availability of electrical measurements by Josephson Voltage Standard (JVS) and Quantum Hall Resistance (QHR) standard which are based on the quantum phenomena[26,27] for determination of h using watt balance Reviewed the result of the third periodic verification of NPKs against IPK[5] ...
The redefinition of mass adopted in November 2018 and implemented from 20 May 2019, i.e. World Metrology Day, eliminated the artefact-based approach dependent upon the International Prototype of the Kilogram (IPK), in favour of realizing the kilogram in terms of the Planck constant h by fixing its value as 6.62607015 × 10−34 J s. In this paper, the authors present a general outline of the circumstances and related developments that paved the way for the new definition that replaced the IPK after a period of 130 years since it was formally sanctioned to define the kilogram in 1889. The new definition opens up fascinating developments in mass metrology which include different realization techniques, realizing the unit at values other than 1 kg, numerous sources for traceability can be envisaged etc.
As most readers are probably at least vaguely aware, it is likely that the SI system of units will be redefined in 2018. This redefinition would fundamentally change the logical structure of the SI, with one result being a substantial change in how mass is realized and disseminated within national metrology institutes (NMI's) such as the National Institute of Standards and Technology (NIST). However, we expect that the only impact on how customers see calibration services will be small step changes that NIST will document and publicize to customers in advance. In this article, we list the main areas of calibration services at NIST, describe how for most of them there will be negligible impact, discuss the impact on mass and DC electrical calibrations, and explain our best predictions as to how we expect NIST to make a seamless transition for customers in those two areas.
The METAS watt balance project was initiated slightly more than a decade ago. Over this time, the apparatus has been through an uninterrupted series of upgrades that have improved its reliability to a point where continuous series of measurements can be taken fully automatically over periods of several months. A comprehensive analysis of possible systematic errors has now been completed and a large set of data has been analysed to calculate a value for the Planck constant h. This paper describes the watt balance in detail, explains the data acquisition and analysis thoroughly and presents the uncertainty budget. The value of the Planck constant determined with our apparatus is h = 6.626 069 1(20) × 10−34 J s with a relative standard uncertainty of 0.29 × 10−6. This value differs from the 2006 CODATA adjustment by 0.024 µW W−1.
We report a new value for the universal gas constant R: (8.314 471+/-0.000 014) J mol-1K-1. The standard error of R has been reduced by a factor of 5 to 1.7 ppm. R was determined from the speed of sound in argon contained within a thick, spherical shell at the temperature of the triple point of water Tt. The volume of the shell was measured by our weighing the mercury required to fill it at Tt. The molar mass of the argon was determined relative to that of a standard with accurately known chemical and isotopic composition by use of speed-of-sound data.
This paper gives the 1998 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. Further, it describes in detail the adjustment of the values of the subset of constants on which the complete 1998 set of recommended values is based. The 1998 set replaces its immediate predecessor recommended by CODATA in 1986. The new adjustment, which takes into account all of the data available through 31 December 1998, is a significant advance over its 1986 counterpart. The standard uncertainties (i.e., estimated standard deviations) of the new recommended values are in most cases about 1/5 to 1/12 and in some cases 1/160 times the standard uncertainties of the corresponding 1986 values. Moreover, in almost all cases the absolute values of the differences between the 1998 values and the corresponding 1986 values are less than twice the standard uncertainties of the 1986 values. The new set of recommended values is available on the World Wide Web at physics.nist.gov/constants.
This paper gives the 2006 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. Further, it describes in detail the adjustment of the values of the constants, including the selection of the final set of input data based on the results of least-squares analyses. The 2006 adjustment takes into account the data considered in the 2002 adjustment as well as the data that became available between 31 December 2002, the closing date of that adjustment, and 31 December 2006, the closing date of the new adjustment. The new data have led to a significant reduction in the uncertainties of many recommended values. The 2006 set replaces the previously recommended 2002 CODATA set and may also be found on the World Wide Web at physics.nist.gov/constants.
DOI:https://doi.org/10.1103/PhysRev.93.629
DOI:https://doi.org/10.1103/PhysRev.81.162
DOI:https://doi.org/10.1103/RevModPhys.1.1
A completely new evaluation of the fundamental atomic constants by the method of least squares is presented. A number of new and highly precise experiments have been taken into account, including the measurement of: (1) the velocity of light by an exceptionally ingenious and precise method due to Hansen and Bol, (2) the absolute proton moment, (3) the ratio of magnetic moments of proton and electron, (4) the proton moment in Bohr magnetons, (5) the hyperfine structure separation of ground-state hydrogen, (6) the ratio of cyclotron to precession frequency of the proton, (7) h/mc using annihilation radiation, and (9) h/e from the x-ray high frequency limit with improved precision.The results of the critical survey of Dorsey on the velocity of light plus the more recent measurements of c are combined to obtain a weighted-mean value: c=299790.0±0.7 km/sec. The results of the experiments listed above have been combined by several writers to compute α, e/m, and F. All of the published values, including those of certain older experiments have been corrected for the new value of c and combined in a least-squares calculation. The results are presented in a complete table of the fundamental constants and are compared with the experimental values in an isometric consistency chart. Six of the experimental results: F, N, mN, α, e/m, and h/e are found to show excellent agreement with the least-squares values. In particular the new experimental value of h/e=(1.37928±0.00004)×1017 erg sec/esu which precipitated the present work agrees well with the leastsquares value, h/e=(1.379300±0.000016)×10-17 erg-sec/esu.
The implications of the new determination of e/h using the ac Josephson effect in superconductors for both quantum electrodynamics (QED) and our knowledge of the fundamental physical constants are analyzed in detail. The implications for QED are investigated by first deriving a value of the fine structure constant α from experimental input data which do not require the use of QED theory for their analysis. These include the Josephson-effect value of e/h, the Faraday constant, the gyromagnetic ratio of the proton, the magnetic moment of the proton in units of the nuclear magneton, the ratio of the ampere as maintained by the United States National Bureau of Standards to the absolute ampere, and certain accurately known auxiliary constants. This is done by critically reevaluating all of the experimental data presently available on these quantities and applying the standard techniques of a least squares adjustment, including tests for imcompatibility. The value of α so obtained is then used to evaluate the theoretical expressions for the Lamb shift and fine structure splitting in hydrogen, deuterium, and ionized helium, the hyperfine splitting in hydrogen, muonium, and positronium, and the anomalous magnetic moment of the electron and muon. These theoretical values are compared with critically reexamined experimental values, thus providing a test of QED in which a priori information from QED itself is not essential. The consequences of the new measurement of e/h for our present knowledge of the fundamental physical constants are demonstrated by deriving new "best" values for the fundamental constants from a critically selected subset of all the available data. In addition to providing a consistent set of constants, this analysis focuses attention on areas in which there remain important questions which require clarification. The experimental and theoretical work necessary for the resolution of these questions is discussed, with emphasis on ways in which the study of quantum phase coherence effects in low temperature superfluid systems can make significant contributions.
DOI:https://doi.org/10.1103/RevModPhys.20.82
Experimental data bearing on the precision determination of the numerical values of the fundamental physical constants are reviewed, with particular emphasis being placed on the identification and isolation of discrepancies and inconsistencies. The purpose of the analysis is to present a consistent set of values of the fundamental constants and to present a careful and complete description of the steps taken to reach this end. The Introduction discusses the significance of such an analysis and indicates the general method of approach. The indispensability of local unit systems and conversion factors connecting them, in order to avoid a sacrifice of precision peculiar to different metrological techniques, is emphasized. The point is stressed that conversion constants introduce the danger of ignoring error-statistical correlations between physically measured quantities, and the effects of such correlations on the assignment of errors is discussed. All available sources of experimental information relative to the necessary input data are presented, and changes in definitions of units since our last review are discussed. After the available stochastic input data have been reviewed and the less reliable items eliminated, the third section examines the remainder for mutual compatibility by means of an analysis of variance in which special criteria for recognizing the incompatibility of a datum are developed, using the analogy of the energy of internal strain introduced in overdetermined mechanical structures. Tables of least-squares adjusted values of fundamental constants and conversion factors of physics and chemistry based on the 1963 adjustment are given. Research pertinent to the constants which has been completed or published subsequent to the 1963 "recommended" adjustment is discussed, and the effect of these on our knowledge of the numerical values of the fundamental constants is presented.
Using a moving coil watt balance, electric power measured in terms of the Josephson and quantum Hall effects is compared with mechanical power measured in terms of the meter, kilogram, and second. We find the Planck constant h\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}6.62606891(58)\ifmmode\times\else\texttimes\fi{}{10}^{-{}34}\mathrm{J}\mathrm{s}. The quoted standard uncertainty (1 standard deviation estimate) corresponds to (8.7\ifmmode\times\else\texttimes\fi{}{10}^{-{}8})h. Comparing this measurement to an earlier measurement places an upper limit of 2\ifmmode\times\else\texttimes\fi{}{10}^{-{}8}/\mathrm{yr} on the drift rate of the SI unit of mass, the kilogram.
This paper is a summary of the 1973 least-squares adjustment of the fundamental physical constants carried out by the authors under the auspices of the CODATA Task Group on Fundamental Constants. The salient features of both the input data used and its detailed analysis by least-squares are given. Also included is the resulting set of best values of the constants which is to be recommended for international adoption by CODATA, a comparison of several of these values with those resulting from recent past adjustments, and a discussion of current problem areas in the fundamental constants field requiring additional research.
Some of the more interesting conclusions of a 1955 survey of atomic constants were the following. (1) Most familiar experiments described in general physics courses now carry negligible weight. (2) Probable errors in values of the constants are of the order of 10 ppm. (3) Use of x-ray “h/e experiments” has been a source of error in previous evaluations; theoretical interpretation of these results involves considerable uncertainty. (4) Electrochemical values of the Faraday are now in fair agreement, but their mean differs significantly from the value obtained by electromagnetic experiments. (5) There is still some evidence for variation of the velocity of light with frequency; however, the negative case appears stronger and is further strengthened by newer data.
Recent developments are discussed and the authors' analysis compared with the 1955 study of Cohen, DuMond, Layton, and Rollett. Recommended values for principal constants are given. These include a correction for an error in the Karplus and Kroll calculation of the anomalous moment of the electron, but do not reflect any experimental data reported since 1955.
One of the early projects established by CODATA was intended to provide
a recommended set of the fundamental physical constants, which are so
important to the analysis and interpretation of experimental data in
many scientific disciplines. The first "Recommended Consistent Values of
the Fundamental Physical Constants" appeared in 1973 and was
subsequently adopted by most international and national bodies in their
own recommendations. This process has contributed to improved
compatibility of scientific and technical data in all fields of science.
CODATA presents here a revised version of these recommendations which
takes into account the significant advances in metrology that have
occurred since the 1973 analysis. "The 1986 adjustment of the
fundamental physical constants" represents a 5-year effort involving
experts from the major metrological laboratories of the world. It is
hoped that this recommended data set will receive the acceptance of the
scientific community which was achieved by its predecessor.
DOI:https://doi.org/10.1103/RevModPhys.25.691
If at a given epoch one wishes a consistent system of values of the
fundamental constants of physics and chemistry, that is to say a system
consistent with all the accepted laws interrelating these quantities and
as consistent as possible with all the reliable precision data then
available, it is emphasized in this paper that one cannot treat the
problem in a piecemeal way, one constant at a time, but one is forced to
adopt a unified approach involving a complete analysis and synthesis of
all the data simultaneously. The least-squares adjustment of 1955 by
Cohen, DuMond, Layton, and Rollett is briefly reviewed as an example. A
wealth of new data has been accumulated since the 1955 adjustment and a
list of 26 examples of such new determinations, either completed or in
process, is presented, described, and discussed. When the results of
certain of these redeterminations, now well advanced, have become
definitely available it is felt that a new least-squares adjustment will
be in order. The desirability of such periodic reassessments as well as
their unavoidable shortcomings are discussed. A graphic record of past
performance shows that the “best values” so obtained tend
satisfactorily to stabilize within ever narrower error ranges which at
each epoch are satisfactorily close to (usually in factinside) the error
ranges of prior adjustments.
Mechanical and electrical power in SI units have been equated by measurements made on a coil part of which is in a strong magnetic field. The force due to a current I flowing in the coil, is weighed by opposing it with a mass M subject to the earth's gravitational acceleration g. This is combined with a separate measurement in which a voltage V is generated in the coil when it is moved vertically with velocity u through the relationship IV = M g u.
If the current produces a voltage V across a resistor whose value R is known in SI units, then V = (M g u R)1/2. Hence the voltage V and the current I are known in SI units and can be used to express the value of the NPL working standards in SI units. The working standard of voltage has hitherto been maintained in terms of a Josephson effect apparatus by ascribing the value 483 594 GHz/volt (maintained) to the Josephson constant KJ presumed equal to 2e/h. The measurements reported here suggest a different value of KJ 483 597,903 ± 0,035 ought to be used, based on the premise that the SI value of the quantum Hall resistance is RK = 25 812,8092 ± 0,0014 Ω.
If one presumed also that RK = h/e² exactly, the values of elementary charge e and the Planck constant, h, which may be deduced from these measurements are e = 1,602 176 35 ± 0,000 000 14 × 10⁻¹⁹ C, h = 6,626 068 21 ± 0,000 000 90 × 10⁻³⁴ J s, which may be compared with the values recommended by the CODATA Task Group on Fundamental Constants which are e = 1,602 177 33 ± 0,000 000 14 × 10⁻¹⁹ C, h = 6,626 075 5 ± 0,000 004 0 × 10⁻³⁴ J s.
This paper concerns an international research project aimed at determining the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The counting procedure was based on the measurement of the molar volume and the volume of an atom in two 1 kg crystal spheres. The novelty was the use of isotope dilution mass spectrometry as a new and very accurate method for the determination of the molar mass of enriched silicon. Because of an unexpected metallic contamination of the sphere surfaces, the relative measurement uncertainty, 3 × 10−8 NA, is larger by a factor 1.5 than that targeted. The measured value of the Avogadro constant, NA = 6.022 140 82(18) × 1023 mol−1, is the most accurate input datum for the kilogram redefinition and differs by 16 × 10−8 NA from the CODATA 2006 adjusted value. This value is midway between the NIST and NPL watt-balance values.
The volt has been determined to high accuracy using a liquid electrometer. The representation of the volt maintained by the Josephson effect using the value of 2 e/h = 483.594 THz/V recommended by the Consultative Committee on Electricity of the International Committee of Weights and Measures in 1972 has been measured to be smaller than the SI volt by (8.09 ± 0.27) ppm. This implies that the SI value of 2 e/h is (483.59791 ± 0.00013) THz/V. Full experimental details are given.
Recent adjustments of the atomic constants show a serious discrepancy between the adjusted value of lambda /sub g// lambda /sub s/ (the conversion factor from the Siegbahn x-ray scale to absolute units) and the accepted average of the direct experimental results by ruled grating measurements. As an attempt to resolve this discrepancy, a general survey of the atomic constants was made. Much information which is chiefly of historical interest was included. An attempt is made to reevaluate errors wherever this appeared necessary and to choose the most reliable experiments for inclusion in the present adjustment. (auth)
The errors involved in published calculations and research on the ; physical constants are considered in detail. Among the errors mentjoned are: ; reliance on authorities which actually are at fault; adopting values of constants ; independently of the value of other, often related constants; using a variety of ; values for the various auxiliary constants involved in a calculation; failure to ; reduce several measured quantities appearing in a certain formula to a common ; physical condition; the occasional use of an approximate formula, with no ; indication of the magnitude of the error introduced; the failure to state ; explicitly just what formula was used to calculate a certain quantity; lack of ; attempt to estimate the uncertainty involved in each phase of work; and the use ; of purely ad hoc and ill-advised methods of calculation. A plea is made for the ; intelligent use of the least squares method of calculation. The value of the ; electronic charge is discussed in detail since Millikan published his ; experimental results in sufficient detail to make extensive recalculations ; possible. Other topics discussed include the velocity of light, group and wave ; velocity, the Avogadro number. N, the fine structure constant and the ; representation of experimental uncertainty, and the general system of universal ; constants. (M.H.R.) Topics discussed on experimental data are a geometric ; interpretation, the criterion of least squares, standard errors and correlatron ; coefficients, the standard errors of the residues of a least squares adjustment, ; analysis of data, and output values, recommended (1955) least squares adjustment, ; The 1955 adjustment is tabulated, based on the determrnation of four primary ; unknowns BETA , e, N, and DELTA , by least-squares adjustment from seven ; independent sources of experimental input data combined with a number of ; auxiliary constants whose values are known so much more accurately than the ; aforementioned input data that they are negligible error contributors. (M.H.R.);
This paper gives the 2002 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. Further, it describes in detail the adjustment of the values of the subset of constants on which the complete 2002 set of recommended values is based. Two noteworthy additions in the 2002 adjustment are recommended values for the bound-state rms charge radii of the proton and deuteron and tests of the exactness of the Josephson and quantum-Hall-effect relations and , where and are the Josephson and von Klitzing constants, respectively, e is the elementary charge, and h is the Planck constant. The 2002 set replaces the previously recommended 1998 CODATA set. The 2002 adjustment takes into account the data considered in the 1998 adjustment as well as the data that became available between 31 December 1998, the closing date of that adjustment, and 31 December 2002, the closing date of the new adjustment. The differences between the 2002 and 1998 recommended values compared to the uncertainties of the latter are generally not unreasonable. The new CODATA set of recommended values may also be found on the World Wide Web at physics.nist.gov/constants.
A measurement using a one-electron quantum cyclotron gives the electron
magnetic moment in Bohr magnetons, g/2 = 1.001 159 652 180 73 (28) [0.28 ppt],
with an uncertainty 2.7 and 15 times smaller than for previous measurements in
2006 and 1987. The electron is used as a magnetometer to allow lineshape
statistics to accumulate, and its spontaneous emission rate determines the
correction for its interaction with a cylindrical trap cavity. The new
measurement and QED theory determine the fine structure constant, with
alpha^{-1} = 137.035 999 084 (51) [0.37 ppb], and an uncertainty 20 times
smaller than for any independent determination of alpha.
This paper summarizes the latest uncertainty improvements and data for a new result from the National Institute of Standards and Technology (NIST) electronic kilogram experiment. The result of 8 pm 36 nW/W for the ratio , as well as the Planck's constant, is comparable to the NIST 2005 value but with a lower uncertainty. Of the eight largest Type B uncertainty contributions, gravity acceleration, wheel surface, and reference mass magnetic susceptibility are considerably reduced. Humidity dependence in the recent data and limitations on the volt/velocity signal analysis are now the main limitations on the uncertainty.
We have carried out a new evaluation of the eighth-order contribution to the electron g-2 using FORTRAN codes generated by an automatic code generator gencodeN. Comparison of the "new" result with the "old" one has revealed an inconsistency in the treatment of the infrared divergences in the latter. With this error corrected we now have two independent determinations of the eighth-order term. This leads to the revised value 1 159 652 182.79 (7.71) x 10^{-12} of the electron g-2, where the uncertainty comes mostly from that of the best non-QED value of the fine structure constant alpha. The new value of alpha derived from the revised theory and the latest experiment is alpha^{-1} = 137.035 999 084 (51) [0.37 ppb], which is about 4.7 ppb smaller than the previous alpha^{-1}.
Theoria Combinationis Observationum Erroribus Minimis Obnoxiae,” in Commentationes societatis regiae scientiarum Gottingensis recentiores
- C F Gauss