This paper gives the 2010 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. The 2010 adjustment takes into account the data considered in the 2006 adjustment as well as the data that became available from 1 January 2007, after the closing date of that adjustment, until 31 December 2010, the closing date of the new adjustment. 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 2010 set replaces the previously recommended 2006 CODATA set and may also be found on the World Wide Web at physics.nist.gov/constants.

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CODATA Recommended Values of the Fundamental Physical Constants: 2006

The measurement of the Planck constant, h, is entering a new phase. The CODATA 2010 recommended value is 6.626 069 57 × 10(-34) J s, but it has been a long road, and the trip is not over yet. Since its discovery as a fundamental physical constant to explain various effects in quantum theory, h has become especially important in defining standards for electrical measurements and soon, for mass determination. Measuring h in the International System of Units (SI) started as experimental attempts merely to prove its existence. Many decades passed while newer experiments measured physical effects that were the influence of h combined with other physical constants: elementary charge, e, and the Avogadro constant, N(A). As experimental techniques improved, the precision of the value of h expanded. When the Josephson and quantum Hall theories led to new electronic devices, and a hundred year old experiment, the absolute ampere, was altered into a watt balance, h not only became vital in definitions for the volt and ohm units, but suddenly it could be measured directly and even more accurately. Finally, as measurement uncertainties now approach a few parts in 10(8) from the watt balance experiments and Avogadro determinations, its importance has been linked to a proposed redefinition of a kilogram unit of mass. The path to higher accuracy in measuring the value of h was not always an example of continuous progress. Since new measurements periodically led to changes in its accepted value and the corresponding SI units, it is helpful to see why there were bumps in the road and where the different branch lines of research joined in the effort. Recalling the bumps along this road will hopefully avoid their repetition in the upcoming SI redefinition debates. This paper begins with a brief history of the methods to measure a combination of fundamental constants, thus indirectly obtaining the Planck constant. The historical path is followed in the section describing how the improved techniques and discoveries in quantum mechanics steadily reduced the uncertainty of h. The central part of this review describes the technical details of the watt balance technique, which is a combination of the mechanical and electronic measurements that now determine h as a direct result, i.e. not requiring measured values of additional fundamental constants. The first technical section describes the basics and some of the common details of many watt balance designs. Next is a review of the ongoing advances at the (currently) seven national metrology institutions where these experiments are pursued. A final summary of the recent h determinations of the last two decades shows how history keeps repeating itself; there is again a question of whether there is a shift in the newest results, albeit at uncertainties that are many orders of magnitude less than the original experiments. The conclusion is that there is room for further development to resolve these differences and find new ideas for a watt balance system with a more universal application. Since the next generation of watt balance experiments are expected to become kilogram realization standards, the historical record suggests that there is yet a need for proof that Planck constant results are finally reproducible at an acceptable uncertainty.

https://iopscience.iop.org/article/10.1088/0034-4885/76/1/016101/pdf

History and progress on accurate measurements of the Planck constant

The definitions of some units of the Systeme International are likely to be revised as early as 2011 by basing them on fixed values of fundamental constants of nature, provided experimental realizations are demonstrated with sufficiently small uncertainties. As regards the kilogram, experiments aiming at linking it to the Planck constant and the atomic mass constant are under way in several laboratories. The other units likely to be redefined are the ampere, the kelvin and the mole. We discuss the advantages and disadvantages of different alternatives for revised definitions of the kilogram and the mole. From physical considerations, metrological consequences and ease of understanding, a definition of the kilogram based on the mass of a particle, such as an atom or the electron, is favoured. One of the proposed definitions fixes the value of the Planck constant through the Compton frequency of a material, though unphysical, particle. Finally, a redefinition of the mole, the counting unit of the amount-of-substance, is proposed which fixes the Avogadro constant as a dimensionless number.

https://iopscience.iop.org/article/10.1088/0026-1394/44/1/001/pdf

Considerations on future redefinitions of the kilogram, the mole and of other units

Among the priority tasks in the further development of the International System of Units is the redefinition of the kilogram based on fundamental constants. One of the strategies pursued today is to relate mass to Planck's constant h using the equivalence between mechanical and electrical energies. In this paper, possible experimental approaches in this direction are described. The approach which promises to reach the required uncertainty at the earliest is the concept of the moving-coil watt balance. The status of the different watt balance experiments is reviewed in detail.

https://iopscience.iop.org/article/10.1088/0026-1394/40/6/007/pdf

Tracing Planck's constant to the kilogram by electromechanical methods

The kilogram is the only base unit of the Systeme International d’unites (SI) still defined by a material artefact. Regarding the past evolution of the SI and the poor knowledge of the stability of the international prototype, its definition is not satisfactory. In the long term, it would be better to move to a definition based either on atomic properties or on fundamental constants. Among the various researches in progress in metrology laboratories, one of the most promising ways seems to be the watt balance. Its principle consists in comparing a mechanical power to an electromagnetic power. This comparison results from a measurement performed in two steps: a static measurement during which the Laplace force acting on a coil driven by a DC current and subjected to an induction field is compared to the weight of a standard mass, and a dynamic measurement where the induced voltage at the terminals of the same coil is determined when it is moved in the same field at a known velocity. The measurement of electrical quantities in terms of the Josephson and the quantum Hall effects then allows the mass unit be linked to the Planck constant. Although the principle of the experiment remains simple and direct, obtaining sufficiently low uncertainty ( 10-8) implies that devices relevant of various fields of physics must be implemented at their best level. In this paper, a review of the present developments at international level is presented.

Determination of the Planck constant by means of a watt balance

A method for efficiently and accurately measuring mass under conditions of weightlessness is proposed using the law of conservation of momentum. In this method, the velocities of two different uniform motion states of an object and the reference mass are measured highly accurately using an optical interferometer. For the preparatory experiments on earth, an instrument, with which linear motion of constant velocity is realized using pneumatic linear bearings, is developed. The combined standard uncertainty in mass measurements from 4 to 18 kg by a single collision is estimated to be about u c = 0.012 kg, which corresponds to 0.07% (7 x 10 -4 ) of the maximum value of 18 kg. For a mass-measurement instrument employed under microgravity conditions, a design for the instrument and a measurement procedure are proposed.

Balance for Measuring Mass Under Microgravity Conditions

The current status of our superconducting magnetic levitation experiment for determining the magnetic flux quantum is described. The flux-up system has been improved significantly by using a Josephson voltage standard. Studies are also in progress to improve the mechanical measurement relevant to the floating body with the goal of reducing the uncertainty to less than 1 ppm. >

Absolute determination of the magnetic flux quantum using superconducting magnetic levitation

A method for measuring the impact force in crash testing is developed. In this method, a mass is made to collide with the object being tested and the instantaneous value of the impact force is measured as the inertial force acting on the mass. To realize linear motion with a sufficiently small friction acting on the mass, a pneumatic linear bearing is used, and the velocity and acceleration of the mass, the moving part of the bearing, are measured using an optical interferometer. The relative combined standard uncertainty in determining the impact force in a three point bending test is estimated to be 0.5x10 -2 (0.5 %) of the maximum value of the impact force.

A method for determining the impact force in crash testing

The superconducting magnetic levitation system for absolute determination of magnetic flux quantum /spl Phi//sub 0/, which is aimed at the future replacement of the kilogram unit of mass, has been developed at the National Research Laboratory of Metrology (NRLM) with a small floating body of approximately 25 g mass. The consistency of the relation between potential energy of the floating body and the electromagnetic energy of the superconducting magnetic levitation system has been evaluated with 1 ppm order resolution. In this paper, the results of the evaluation as well as the improvements made in the apparatus in recent years at NRLM are described.

Yukinobu Miki

Papers

Balance for Measuring Mass Under Microgravity Conditions

Absolute determination of the magnetic flux quantum using superconducting magnetic levitation

A method for determining the impact force in crash testing

A method for determining the impact force in crash testing

Evaluation of equilibrium trajectory of superconducting magnetic levitation system for the future kg unit of mass