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Journey of Kilogram from Physical Constant to Universal Physical Constant (h) via Artefact: A Brief Review
Abstract
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.
... By the consistent efforts of several leading NMIs and metrology organizations spanning more than four decades, this became possible when new measurement methods were developed that can realize the kilogram in terms of the Planck constant with a relative uncertainty of about one part in 10 8 . Finally, on 16 November 2018, with the consensus of all the member states of CGPM, the kilogram was redefined in terms of the Planck constant [7]. ...
... The Consultative Committee for Mass and Related Quantities (CCM) has applied a fourphase program for full implementation of the revised definition of the kilogram. These four phases are described here briefly; however, details can be found in [7,[12][13][14]. ...
Until recently, the kilogram was the only SI base unit having an artifact as its primary standard. For more than four decades, there have been continuous efforts worldwide toward redefining the kilogram, the SI unit of mass, to have an artifact-independent and time-invariant definition based on a fundamental constant. Due to the effort of metrologists across the globe, on 16th November 2018, in the 26th meeting of the General Conference on Weights and Measure (CGPM), the kilogram was finally redefined based on the Planck constant. This paper gives an overview of the limitations of an artifact-based definition and the significance of the redefinition, and, its implications. The principle of the Kibble balance and its major components and their role is also discussed.
... The result obtained by equation (39) aligns remarkably with the value of the Planck constant accepted today, as given by CODATA 2017 (6.62607015 × 10 -34 ) (Bileska, 2020;Ehtesham et al., 2020;Alekseevich, 2021). Strikingly, the correspondence of 38 digits between what the Quran encodes and what CODATA 2017 established is extraordinary, highlighting fascinating parallels and a compelling correlation between the Quran and scientific knowledge. ...
There is a strong belief that Allah Almighty could reveal His existence by encoding the laws of nature and their fundamental constants in the Quran with impeccable precision. However, the mathematical frameworks and patterns embedded within the Quranic text to reveal scientific laws and constants may contain minor deviations in numerical values to empower personal exploration, accommodate diverse interpretations, and strengthen faith. This theory is based on the fact that the Quran is the word of Allah Almighty. Consequently, one would anticipate finding evidence suggesting a divine origin. Many scholars and researchers have suggested that this evidence can be found in the mathematical structure of the Quran through patterns, numerical codes, and other mathematical features within the text that are too complex to be simply attributed to human authorship. Therefore, it is believed that the Quran contains within its structure a mathematical encoding of all physical laws and constants. Verses like 20.98, which state, "He encompasses all things in knowledge," are quoted as evidence. According to this perspective, the Quran is assumed to incorporate mathematical miracles, indicating a potential correspondence between its text and the underlying order of the universe. This theory reveals many mathematical frameworks illustrating how the Quran embeds scientific knowledge. These include the identification of frequent occurrences of the golden ratio within the Quranic text and the manifestation of the golden ratio in the human body, alongside the determination of key celestial parameters such as the length of the solar year. Furthermore, this theory uncovers a numerical link between the Quran and fundamental scientific constants, notably the universal gravitational constant, the speed of light, and the Planck constant. Moreover, this theory utilizes numerical analysis to offer a compelling rationale for why the numbers 28 and 114 are used to represent the total number of Arabic letters and chapters in the Quran, respectively. Finally, this theory highlights the Quran's remarkable mathematical architecture, offering indisputable evidence of its divine composition. We behold a mathematical marvel of cosmic scale, a phenomenon defying human intelligence. Indeed, the Quran is a product of a superintelligence exceeding our comprehension.
... The result obtained by equation (39) aligns remarkably with the value of the Planck constant accepted today, as given by CODATA 2017 (6.62607015 × 10 -34 ) (Bileska, 2020;Ehtesham et al., 2020;Alekseevich, 2021). Strikingly, the correspondence of 38 digits between what the Quran encodes and what CODATA 2017 established is extraordinary, highlighting fascinating parallels and a compelling correlation between the Quran and scientific knowledge. ...
There is a strong belief that Allah Almighty could reveal His existence by encoding the laws of nature and their fundamental constants in the Quran with impeccable precision. However, the mathematical frameworks and patterns embedded within the Quranic text to reveal scientific laws and constants may contain minor deviations in numerical values to empower personal exploration, accommodate diverse interpretations, and strengthen faith. This theory is based on the fact that the Quran is the word of Allah Almighty. Consequently, one would anticipate finding evidence suggesting a divine origin. Many scholars and researchers have suggested that this evidence can be found in the mathematical structure of the Quran through patterns, numerical codes, and other mathematical features within the text that are too complex to be simply attributed to human authorship. Therefore, it is believed that the Quran contains within its structure a mathematical encoding of all physical laws and constants. Verses like 20.98, which state, "He encompasses all things in knowledge," are quoted as evidence. According to this perspective, the Quran is assumed to incorporate mathematical miracles, indicating a potential correspondence between its text and the underlying order of the universe. This theory reveals many mathematical frameworks illustrating how the Quran embeds scientific knowledge. These include the identification of frequent occurrences of the golden ratio within the Quranic text and the manifestation of the golden ratio in the human body, alongside the determination of key celestial parameters such as the length of the solar year. Furthermore, this theory uncovers a numerical link between the Quran and fundamental scientific constants, notably the universal gravitational constant, the speed of light, and the Planck constant. Moreover, this theory utilizes numerical analysis to offer a compelling rationale for why the numbers 28 and 114 are used to represent the total number of Arabic letters and chapters in the Quran, respectively. Finally, this theory highlights the Quran's remarkable mathematical architecture, offering indisputable evidence of its divine composition. We behold a mathematical marvel of cosmic scale, a phenomenon defying human intelligence. Indeed, the Quranis a product of a super intelligence exceeding our comprehension.
... On the contrary, with the help of PB, pressure can be measured in the range from few kPa to GPa range with precision and accuracy. Thus, PBs are mainly used as primary measurement standards for high-pressure measurement & calibration at various National Metrological Laboratories and at industries as a Reference Pressure Standard [1][2][3][4][5][6][7][8]. ...
Precise and accurate pressure measurements play a prominent role in several scientific applications. The pressure balances (PBs) are used as a primary standard for pressure measurements which requires utmost accuracy. In the case of calibration and characterization of these PBs, the method of cross-floating is an internationally accepted practice used for the comparison of 2 PBs for determining their metrological parameters, i.e. effective areas, distortion coefficient and zero pressure area etc. The present paper describes the work which has been carried out to develop a cross-floating pressure balance calibration system for an organization engaged in R&D activities and providing calibration services to the process industries. The study also describes some of the newly designed, developed, upgraded and fabricated components and devices for a cross-floating system in hydrostatic pressure range up to 150 MPa. The whole system consists of an upgraded hydraulic screw pump, newly designed, developed and fabricated oil reservoir, cross-float valve, use of two commercially available needle valves in combination with a pressure balance supplied by the customer with associated pressure fittings and connector in the pressure transmitting circuit. The characterization of the pressure balance was also done using the newly developed components/parts and instruments at 12 calibration points in the high pressure range (7–140) MPa and 11 calibration points in the low pressure range (0.2–7) MPa. The development process was started in the year 2018 and completed in the month of November 2020. The combined relative measurement uncertainty (at coverage factor, k = 2) associated in high pressure range is found to be 59.3 × 10−6 and 42.3 × 10−6 with associated pressure and effective area, respectively. Similarly, in low pressure range the combined relative measurement uncertainty (k = 2) is found to be 62.2 × 10−6 and 47.3 × 10−6 with associated pressure and effective area, respectively. The results obtained are found in excellent agreement with the values of uncertainty and the effective area reported by the manufacturer. This newly developed system will help the customer in providing in-house traceability to their own instruments as well services to the industries.
... Presently, NPL UK demonstrated single-mode two-measurement phase Kibble balance. The new concept opens up interesting advances in mass metrology, including various realization methods, realizing the unit (other than 1 kg) and traceability sources [11]. ...
The presented paper discusses the summary of the special issue consisting of 13 peer-reviewed papers regarding Redefinition of SI Units and Its Implications. The papers discuss state-of-the-art reviews and progress made as of now and ongoing progress regarding the redefinition of SI units at different National Metrology Institutes (NMIs) and academic/research institutes across the globe. Different methodologies adopted while investigating redefinition of SI units have been discussed and summarized by the researchers, which will serve as a pivotal point in guiding the researchers in upcoming time.
Dr. Bryan Kibble invented the watt balance in 1975 to improve the realization of the unit for electrical current, the ampere. With the discovery of the Quantum Hall effect in 1980 by Dr. Klaus von Klitzing and in conjunction with the previously predicted Josephson effect, this mechanical apparatus could be used to measure the Planck constant h. Following a proposal by Quinn, Mills, Williams, Taylor, and Mohr, the Kibble balance can be used to realize the unit of mass, the kilogram, by fixing the numerical value of Planck's constant. In 2017, the watt balance was renamed to the Kibble balance to honor the inventor, who passed in 2016. This article explains the Kibble balance, its role in the redefinition of the unit of mass, and attempts an outlook of the future.
On November 16, 2018, the 26th General Conference on Weights and Measures voted unanimously to revise the International System of Units from a system built on seven base units to one built on seven defining constants and will officially become effective on May 20, 2019, or World Metrology Day. More specifically, the unit of mass, the kilogram, will be realized via a fixed value of the Planck constant h and a Kibble balance (KB) serves as one method of achieving this. Over the past few decades, national metrology institutes around the world have developed KBs, the majority aimed at realizing the unit of mass at the 1-kg level with uncertainties on the order of a few parts in 10⁸. However, upon fixing the Planck constant, mass can be directly realized at any level, deeming the kilogram only a historically unique benchmark. At the National Institute of Standards and Technology, a tabletop-sized Kibble balance (KIBB-g1) designed to operate at the gram-level range with uncertainties on the order of a few parts in 10⁶ is currently under development.
On 16 November 2018 a revision of the International System of Units (the SI) was agreed by the General Conference on Weights and Measures. The definitions of the base units were presented in a new format that highlighted the link between each unit and a defined value of an associated constant. The physical concepts underlying the definitions of the kilogram, the ampere, the kelvin and the mole have been changed. The new definition of the kilogram is of particular importance because it eliminated the last definition referring to an artefact. In this way, the new definitions use the rules of nature to create the rules of measurement and tie measurements at the atomic and quantum scales to those at the macroscopic level. The new definitions do not prescribe particular realization methods and hence will allow the development of new and more accurate measurement techniques.
The definition of the kilogram in the International System of Units (SI) is expected to be revised in 2018. The present definition of the kilogram, the mass of the International Prototype of the Kilogram (IPK), adopted in 1889, would then be replaced by a definition based on a fixed numerical value of the Planck constant. The Consultative Committee for Mass and Related Quantities has requested that, as one of the essential steps before the redefinition, a comparison of kilogram realizations based on future realization methods, Kibble9 balances and x-ray crystal density (XRCD) experiments, be organized.
This comparison was carried out during 2016 in the form of a ‘Pilot Study’. One aim of the study was to determine the uniformity of mass dissemination after the redefinition by comparing mass calibrations based on different future realization experiments. Another aim was to test the continuity of the mass unit across the redefinition by comparing mass calibrations based on Kibble balances and XRCD experiments with those based on the IPK.
This paper describes the organization of the comparison and presents its results.
Sufficient progress towards redefining the International System of Units (SI) in terms of exact values of fundamental constants has been achieved. Exact values of the Planck constant h, elementary charge e, Boltzmann constant k, and Avogadro constant N A from the CODATA 2017 Special Adjustment of the Fundamental Constants are presented here. These values are recommended to the 26th General Conference on Weights and Measures to form the foundation of the revised SI.
The new definition of the kilogram, which is expected to be adopted by the General Conference on Weights and Measures in 2018, will bring some major changes to mass metrology. The most fundamental change will be the replacement of the present artefact-based definition with a universal definition, enabling in principle any National Metrology Institute (NMI) to realize the kilogram. The principles for the realization and dissemination of the kilogram in the revised SI are described in the mise en pratique of the definition of the
kilogram. This paper provides some additional information and explains how traceability can be obtained by NMIs that do not operate a primary experiment to realize the definition of the kilogram.
We present a summary of the Planck constant determinations using the NRC watt balance, now referred to as the NRC Kibble balance. The summary includes a reanalysis of the four determinations performed in late 2013, as well as three new determinations performed in 2016. We also present a number of improvements and modifications to the experiment resulting in lower noise and an improved uncertainty analysis. As well, we present a systematic error that had been previously unrecognized and we have quantified its correction. The seven determinations, using three different nominal masses and two different materials, are reanalysed in a manner consistent with that used by the CODATA Task Group on Fundamental Constants (TGFC) and includes a comprehensive assessment of correlations. The result is a Planck constant of 6.626 070 133(60) ×10⁻³⁴ Js and an inferred value of the Avogadro constant of 6.022 140 772(55) ×10²³ mol⁻¹. These fractional uncertainties of less than 10⁻⁸ are the smallest published to date.
The redefinition of the SI unit of mass in terms of a fixed value of the Planck constant has been made possible by the Kibble balance, previously known as the watt balance. Once the new definition has been adopted, the Kibble balance technique will permit the realisation of the mass unit over a range from milligrams to kilograms. We describe the theory underlying the Kibble balance and practical techniques required to construct such an instrument to relate a macroscopic physical mass to the Planck constant with an uncertainty, which is achievable at present, in the region of 2 parts in 10⁸. A number of Kibble balances have either been built or are under construction and we compare the principal features of these balances.
The very first definition of the kilogram was in terms of a constant of nature, although this idea could not be fully realized at the end of the 18th century. Instead the kilogram was defined by an artefact whose mass was made to approximate as closely as possible a physical constant with unit kg m⁻³ - the maximum density of distilled water at atmospheric pressure. For the next two centuries, mass comparators improved greatly as did the materials from which artefacts could be constructed. These improvements put tighter constraints on the realization of a non-artefact definition of the kilogram. However, it is now expected that the goal of redefining the kilogram in terms of fundamental constants will be achieved in 2018. We present a history of the kilogram with emphasis on continuity of this unit of mass each time it has been redefined and the stability of a unit defined by the mass of an artefact.
The redefinition of the kilogram, expected to be approved in the autumn of 2018, will replace the artefact definition of the kilogram by assigning a fixed numerical value to a fundamental constant of physics. While the concept of such a change is pleasing, the mass community as represented by the Consultative Committee for Mass and Related Quantities (CCM) was faced with a number of technical and procedural challenges that needed to be met in order to profit in any meaningful way from the proposed change. In the following, we outline these challenges and how the CCM has met and is meeting them. We focus especially on what the mass community requires of the new definition and the process by which the CCM has sought to ensure that these needs will be met.
This report presents the results of the first phase of the campaign of calibration carried out with respect to the international prototype of the kilogram (IPK) in anticipation of the redefinition of the kilogram (Extraordinary Calibrations). The definition of the kilogram was realized according to the procedure outlined in the 8th Edition of the SI Brochure. Thus the IPK and its six official copies have been cleaned and washed following the BIPM procedure.
The mass comparisons carried out during this campaign showed a very good repeatability. The pooled standard deviation of repeated weighings of the prototypes was 0.4 µg. The effect of cleaning and washing of the IPK was to remove a mass of 16.8 µg. The effect of cleaning and washing of the six official copies was found to be very similar, giving an average mass removed from the seven prototypes of 15 µg with a standard deviation of 2 µg.
The differences in mass between the IPK and the official copies have changed by an average of 1 µg since the 3rd Periodic Verification of National Prototypes of the Kilogram (1988–1992). These results do not confirm the trend for the masses of the six official copies to diverge from the mass of the IPK that was observed during the 2nd and 3rd Periodic Verifications.
All BIPM working standards and the prototypes reserved for special use have been calibrated with respect to the IPK as part of this campaign. All of them were found to have lower masses than when they were calibrated during the 3rd Periodic Verification. As a consequence, the BIPM 'as-maintained' mass unit in 2014 has been found to be offset by 35 µg with respect to the IPK. This result will be analyzed in a further publication.
The unit of mass has been realized by the International Prototype Kilogram (IPK) for over 130 years. This will change very soon. The revision of the International System of Units (SI) that will take effect on May 20, 2019 will fundamentally change the way the United States mass scale is realized by NIST at the one kilogram level and below. For example, below 50 mg, very precise measurements of capacitance gradient by the NIST Electrostatic Force Balance (EFB) will extend the lower end of the NIST mass scale to 100 micrograms or less and improve uncertainties by a factor of ten over what they are now, all while eliminating laborious work-downs from one kilogram standards. Between 100 g and one kilogram, the NIST-4 Kibble balance will realize mass from quantum-based electrical and mechanical power measurements. Mass transfer between the vacuum environment of the Kibble balance and the mass metrology performed in laboratory air pressure will be accomplished by a unique-to-NIST magnetic suspension-based mass comparator that will allow a test mass to be directly calibrated against an artifact whose mass has been determined by the Kibble balance. When considered in its entirety, the NIST mass scale under the revised SI will be easier to realize, easier to maintain, and have equal or smaller uncertainties that the mass scale that is traceable to the IPK. This presentation will illustrate how the NIST mass scale at one kilogram and below is constructed using the new instruments described above. An uncertainty budget covering the range from 1 kilogram to 100 micrograms will be given and the techniques that are used for mass dissemination in this range will be described.
Metrology plays the key role as the engine of industrial revolution and growth of any country. It promotes global competence and confidence. With the advent of better quality products through metrological advancement, our industries can compete internationally and to overcome trade barriers/constraints and finally to achieve exports targets. This translates into growth of industries through rapid industrialization, economic growth and societal upliftment. The metrology requires continued and sustained efforts to cater the stakeholders’ demands for advancements in measurement technologies, standards and measurement techniques for more and more precise, reliable, reproducible and accurate measurements with improved measurement uncertainties. In this context, the recent revolutionary changes in redefinition of SI units based on fundamental constants were unanimously voted for adoption by world community during November 16, 2018, at Versailles, France, and implemented world over from May 20, 2019—the World Metrology Day. Therefore, it was considered appropriate to compile a brief status report and apprise the readers about these historical events. The present paper touches glimpse of some of these activities and describes the implications of these changes in our daily life.
New definitions of the units for amount of substance – the mole – and for mass – the kilogram – will presumably come into force on the World Metrology Day 2019. In the revised SI, the mole will be defined by a fixed value of the Avogadro constant and the kilogram by a fixed value of the Planck constant. The X-ray-crystal-density (XRCD) method has been used for the determination of these fundamental constants by counting the number of atoms in ²⁸Si-enriched spheres. Thus, silicon spheres will – after the redefinition – be used to realize the definitions of the mole and the kilogram. This is possible by SI-traceable measurements of lattice parameter, isotopic composition, volume, and surface properties, yielding a relative standard uncertainty below 2⋅10⁻⁸. Whereas this high accuracy is only reached with isotopically enriched silicon, it is also planned to use natural silicon spheres on a slightly lower level of accuracy. The future definitions will allow also new realization methods using silicon, in particular for small mass values.
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.
Watt balance system is the promising equipment to determine Planck constant without accurate measurement of magnetic flux and coil length. To obtain high measurement uncertainty, uniform magnetic flux density and constant velocity control are required during the coil movement. For that KRISS watt balance system incorporates a closed-type cylindrical permanent magnet, vertical linear motor and piston guide. In this paper, the vertical actuating motor including piston guide is controlled to have constant speed and magnet assembly was fabricated to have high uniform magnetic flux density during the vertical coil movement. The velocity of moving coil was controlled within 4 × 10⁻³ (1σ) at the velocity of 2 mm s⁻¹ using a linear motor and linear encoder feedback. Using 3-vertical homodyne laser interferometer the velocity ripple of coil located inside magnet is measured within the level of 7.35 × 10⁻³ (1σ) at the same speed. A magnet assembly, which consists of two permanent magnet rings and closed yokes, was fabricated. A flux shunt was designed for the magnet for minimizing the temperature effect. The yokes were divided into three parts: top, center, and bottom yokes. By re-machining of center outer yoke, magnetic flux density uniformity was improved. The uniformity of the magnetic field was within 3.9 × 10⁻⁴ over a vertical distance of 20 mm.
In previous work at MSL, the concept of a watt balance based on twin pressure balances was proposed both for a measurement of the Planck constant and for a non-artefact realisation of the kilogram. Here, further developments of the concept are described including a novel magnet system suitable for use in a pressure balance based watt balance. The feasibility of such a watt balance achieving an accuracy (relative standard uncertainty) of about 2 parts in 10 8 is considered, focusing mainly on alignment and pressure balance performance characteristics.
This paper reports the latest advances made on
the BIPM watt balance experiment. The improved apparatus is
now fully assembled. The new, open support structure allows
convenient access to all key components of the apparatus. This,
together with the alignment mechanism will allow to improve
significantly the alignment accuracy. The magnetic circuit was
aligned to better than 10 μrad with an uncertainty of 20 μrad. A
new interferometer based on space-heterodyning techniques has
been integrated.
Since 1889 the international prototype of the kilogram has served as the definition of the unit of mass in the International System of Units (SI). It is the last material artefact to define a base unit of the SI, and it influences several other base units. This situation is no longer acceptable in a time of ever increasing measurement precision. It is therefore planned to redefine the unit of mass by fixing the numerical value of the Planck constant. At the same time three other base units, the ampere, the kelvin and the mole, will be redefined. As a first step, the kilogram redefinition requires a highly accurate determination of the Planck constant in the present SI system, with a relative uncertainty of the order of 1 part in 10(8). The most promising experiment for this purpose, and for the future realization of the kilogram, is the watt balance. It compares mechanical and electrical power and makes use of two macroscopic quantum effects, thus creating a relationship between a macroscopic mass and the Planck constant. In this paper the background for the choice of the Planck constant for the kilogram redefinition is discussed and the role of the Planck constant in physics is briefly reviewed. The operating principle of watt balance experiments is explained and the existing experiments are reviewed. An overview is given of all presently available experimental determinations of the Planck constant, and it is shown that further investigation is needed before the redefinition of the kilogram can take place.
Measurements of the Hall voltage of a two-dimensional electron gas, realized with a silicon metal-oxide-semiconductor field-effect transistor, show that the Hall resistance at particular, experimentally well-defined surface carrier concentrations has fixed values which depend only on the fine-structure constant and speed of light, and is insensitive to the geometry of the device. Preliminary data are reported.
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.
In view of the proposed redefinition of the kilogram, in 2005, 2007 and 2010 the CCM adopted recommendations and conditions to be met before the redefinition is implemented. Some of these conditions concern the uncertainty by which the kilogram will be realized after the redefinition. This uncertainty has become a point of discussion in other committees, because the needs for this value were not sufficiently transparent. Here, examples of the realization of the new kilogram with different uncertainties, along with the experimental results available from the Avogadro and watt balance experiments, the uncertainties of mass determinations and their propagation with reasonable assumptions are presented, in order to compare possible realization uncertainties with the requirements in practice. It turned out that the CCM conditions are reasonable, if major changes in the dissemination chain of the kilogram are to be avoided.
We describe a measurement, accurate to a part in a million, of the gyromagnetic ratio of the proton in water, γ'p, by the strong field method. The magnetic induction of a magnet is measured by weighing the force exerted on a rectangular current-carrying coil which has its lower end in the pole-gap. Simultaneously the precession frequency of protons in a water sample in this field is obtained by a conventional nuclear magnetic resonance technique. γ'p is then the ratio of the precession frequency to the magnetic flux density.
The significance of the measurement lies not only in the use of the result to calibrate magnetic fields in SI units for other accurate measurements of atomic constants, but also in the realization of the SI definition of the ampere which follows from combining the result with the measurement of γ́p by the weak-field technique.
Our result is γ'p = 2.6751701(27) × 10⁸ s⁻¹TB169⁻¹ for a spherical water sample at 20°C, where the standard error in the last two digits is in parenthesis.
The kilogram, the base unit of mass in the International System of Units (SI), is defined as the mass m(K) of the international prototype of the kilogram. Clearly, this definition has the effect of fixing the value of m(K)
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 m(K), 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 m(K) of the international prototype a quantity whose value would have to be determined by experiment. However, by assigning a conventional value to m(K), 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.
Kilogrammes prototypes
- A Bonhoure
values of h, e, k, and NA for the revision of the SI
- DB Newell
- F Cabiati
- J Fischer
- K Fujii
- SG Karshenboim
- HS Margolis
- E de Mirandes
- PJ Mohr
- F Nez
- K Pachucki
- TJ Quinn
- CODATA The
The Units for Mass, Voltage, Resistance, and Current in the SI
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S. Schlamminger, P. Abbott, Z. Kubarych, D. Jarrett and R.
Elmquist, The Units for Mass, Voltage, Resistance, and Current
in the SI, IEEE Instrum. Meas. Mag., 22(2019) 9-16.
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A Brief History of Metrology: Past, Present, and Future
- J.-P Fanton
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Future, Int. J. Metrol. Qual. Eng., 10(2019) 5. https://doi.org/
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The CODATA 2017 Values of h, e, k, and NA for the Revision of the SI
- D B Newell
- F Cabiati
- J Fischer
- K Fujii
- S G Karshenboim
- H S Margolis
- E De Mirandes
- P J Mohr
- F Nez
- K Pachucki
- T J Quinn
- DB Newell
D. B. Newell, F. Cabiati, J. Fischer, K. Fujii, S. G. Karshenboim,
H. S. Margolis, E. de Mirandes, P. J. Mohr, F. Nez, K. Pachucki
and T. J. Quinn, The CODATA 2017 Values of h, e, k, and N A
for the Revision of the SI, Metrologia, 55(2018) L13-L16.
https://doi.org/10.1088/1681-7575/aa950a.
Measurement of the Planck constant at the National Institute of Standards and Technology from 2015 to 2017
- D Haddad
- F Seifert
- LS Chao
- A Possolo
- DB Newell
- JR Pratt
- CJ Williams
- S Schlamminger
A Determination of the Planck Constant Using the LNE Kibble Balance in Air
- M Thomas
- D Ziane
- P Pinot
- R Karcher
- A Imanaliev
- F P Santos
- S Merlet
- F Piquemal
- P Espel
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P. Dos Santos, S. Merlet, F. Piquemal and P. Espel, A Determination of the Planck Constant Using the LNE Kibble Balance
in Air, Metrologia, 54(2017) 468-480. https://doi.org/10.1088/
1681-7575/aa78822
Foundation for the Redefinition of the Kilogram
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