SI Base Units Research Articles

Optimum choice of fundamental physical constants with fixed values for redefinition of SI units

The advantages and disadvantages of the procedure of fixing the values of fundamental physical constants (FPC) for redefining the basic SI units are examined. The case in which a fixed value of the Avogadro constant is used simultaneously for new definitions of the unit of mass and the unit of the amount of matter is discussed in detail. A criterion is proposed for choosing the optimum set of FPC with fixed values for redefining basic SI units. A set of FPC compatible with this criterion is considered.

Principles for constructing notation in unit systems and their application to the SI

The SI is the world’s premier scientific instrument and, like all instruments, must be updated as science and technology advance. The CIPM is planning to redefine four SI base units in terms of invariants of nature and has already dubbed this revision the ‘New SI’. This title will confuse most SI users, who are impacted only by the structure and notation of the SI, and neither of these has changed. A truly ‘New SI’, to be practical in the information age, would have at minimum an unambiguous, and preferably a machine- and user-friendly, notation. These and other principles for constructing a notation are proposed, and the SI historical and current notations are examined against these. Several levels of remediation are suggested.

IUPAC-IUGS common definition and convention on the use of the year as a derived unit of time (IUPAC Recommendations 2011)

The units of time (both absolute time and duration) most practical to use when dealing with very long times, for example, in nuclear chemistry and earth and planetary sciences, are multiples of the year, or annus (a). Its proposed definition in terms of the SI base unit for time, the second (s), for the epoch 2000.0 is 1 a = 3.1556925445 × 107 s. Adoption of this definition, and abandonment of the use of distinct units for time differences, will bring the earth and planetary sciences into compliance with quantity calculus for SI and non-SI units of time.

Volume determination of the Avogadro spheres of highly enriched 28Si with a spherical Fizeau interferometer

Within the scope of the efforts concerning the redefinition of the SI base unit ‘kilogram’ the final results of the international research project aiming at the redetermination of the Avogadro constant are ready to be announced. Among other quantities the volume of two spheres which are made of a highly enriched 28Si single crystal had to be determined. For this purpose a special Fizeau interferometer for the measurement of the spheres' diameters has been developed at PTB. This paper reports the final results of the volumes, the uncertainties and also the latest findings regarding systematic corrections including the effects of surface layers on the pure silicon core. The results are confirmed by density comparison measurements.

IUPAC-IUGS common definition and convention on the use of the year as a derived unit of time

The units of time (both absolute time and duration) most practical to use when dealing with very long times, e.g. in Nuclear Chemistry and Earth and Planetary Sciences, are multiples of the year, or annus (a). Its proposed definition in terms of the SI base unit for time, the second (s), for the epoch 2000.0 is 1 a = 3.155 692 5445 x 10 7 s. Adoption of this definition, and abandonment of the use of distinct units for time differences, will bring the Earth and Planetary Sciences into compliance with quantity calculus for SI and non-SI units of time.

Reproposition of numerosity as the SI base quantity whose unit is the mole

‘Amount of substance’ was introduced in the end of the 1950s as the physical quantity whose unit of measurement is the mole. Fundamental problems associated with this physical quantity have caused a never-ending discussion that continues to this day. One of the reasons for this is the fact that the expression ‘amount of substance’ is not a good choice, due to its generality and inclusion of the word ‘substance’. Considering that samples of matter commonly handled by chemists are extremely numerous in entities and that the quality of being numerous or many is referred to as numerosity (a concept related to numerical cognition), this concept is reproposed as a replacement for amount of substance. Then, taking into account ongoing discussions toward a redefinition of the mole, the following definition is proposed for this SI base unit: “the mole is the numerosity of a sample of entities numbering exactly 6.022 141 794 × 1023”. The relationships between four extensive properties of matter (mass, volume, numerosity and number of entities) are detailed and the resulting intensive physical quantities (proportionality constants) are discussed. The concept numerosity is not the product of an invented synonym; furthermore, as a consequence of its generality, it can be used to express the quantity of entities in samples of matter, as well as of light, chemical reactions, etc. The acceptance that mole is the SI unit of numerosity might also solve most of the pedagogic problems associated heretofore with teaching of mole and amount of substance.

Why the invariant atomic-scale unit, entity, is essential for understanding stoichiometry without ‘Avogadro anxiety’

The Avogadro constant is generally considered to be the relevant physical invariant for stoichiometry, intimately associated with the SI base unit for the amount of a specified substance. Unfortunately, it has dimensions of reciprocal amount rather than of amount itself, and this appears to be the source of the widespread confusion permeating this subject. It would make sense, instead, to use its reciprocal—an amount consisting of a single representative entity—as the fundamental invariant for amount. Major simplifications in comprehension then result. In particular, the mole would be redefined in a straightforward way as a designated exact number of elementary entities, making stoichiometric calculations much more easily comprehended. Unfortunately, acceptance by the CIPM of recent CCU recommendations for redefining the mole and kilogram (while keeping the inexactly known carbon-12-based dalton definition) would inject even more confusion into this subject, because the proposed definitions violate a basic compatibility condition relating the mole, kilogram and dalton, stemming from the fundamental concept of the mole itself. However, there are a number of alternative mole-concept-compatible and easily comprehended definitions worthy of consideration, where, in each case, a compatible dalton must be an exact sub-multiple of the (redefined) kilogram. These alternatives should receive much wider discussion before final decisions are made in the major restructuring of the international system of units.

Terahertz Frequency Metrology Based on Frequency Comb

Two techniques for terahertz (THz) frequency metrology based on frequency comb, namely, a THz-comb-referenced spectrum analyzer and a continuously tunable, single-frequency continuous-wave (CW)-THz generator, are reviewed. Since the frequency comb enables to coherently link the frequency among microwave, optical, and THz regions, it is possible to establish the THz frequency metrology traceable to time of the SI base units. Using a THz-comb-referenced spectrum analyzer based on a stable THz comb generated in a photoconductive antenna for THz detection, the absolute frequency of CW test sources in the sub-THz and THz regions was determined at a precision of 10-11. Furthermore, a continuously tunable, single-frequency CW-THz generator was demonstrated around 120 GHz by photomixing of an accurately tunable CW laser and a tightly fixed CW laser in the optical frequency region, phase locked to two independent optical combs. The combination of the CW-THz generator with the THz-comb-referenced spectrum analyzer will open the door for establishment of frequency metrology in the THz region.

Establishment of traceability in the measurement of the mechanical properties of materials

Many important mechanical properties of materials including tensile strength are procedure dependent. This means that test results are traceable to standard test procedures rather than SI base units. However, most of the test procedures described in the current international standards such as ISO and ASTM are not suitable to be adopted as a primary standard procedure since they were developed to be used at industrial sites as well as testing laboratories. The Working Group on Hardness under CCM is working to develop a primary standard procedure to establish traceability for hardness measurement through key comparison among NMIs. These kinds of activities are necessary for other properties such as tensile strength, impact strength, creep and fatigue for the establishment of a traceability system. KRISS has been trying to establish a traceability chain in the measurement of materials' mechanical properties through international round-robin tests, the development of certified reference materials and uncertainty evaluation. In this paper, the activities of KRISS for establishing traceability and those of related ISO technical committees are described.

The Quantum SI - Towards the New Systems of Units

The possibility or even necessity of revising definit ions of some of the base units of the present SI has been discussed over the past 15 years. The last General C onference of Weights and Measures (2007) recommended to redefine the kilogram, the ampere, the kelvin, and th e mole using fixed values of the fundamental constants by the time of the next General Conference in 2011. This paper is a review of proposals of new definitions of units of mentioned quantities and arguments voting for part icular variants of definitions. Most relevant papers for this review have been published by Me trologia, the international journal appointed at the BIPM, an d many other useful pieces of information are available on www pages of the BIPM. The author notes that not only new definitions have been discussed but as well as the se t of the base units of the SI. It means a replacement of the ampere by the volt or the kelvin by the joule. Decisions concerning new definitions are not made and the discussions are still open. Ke ywords: SI system, base units, quantum standards.

Fundamental metrology in the future: Measuring the single quantum

Great progress has been made over the past 50 years in replacing artefact definitions of the SI base units by those based on fundamental constants. However it is important to recognise that the development of the SI is not ‘complete’ once the base units are all defined in this way. New physics and technologies can always be expected to emerge and these will require developments and modifications to the SI. At the present time a dominant trend seems to be that measurements are changing from dealing with average properties of ensembles to metrology on single entities. This is already apparent for single atoms, ions or photon detection and measurement but can be expected to extend into the technologically important areas of single spins, single THz photons and even phonons in the future. Another significant development may be expected towards measurement of quite different physical quantities from those currently required, such as spin current, decoherence time etc. The paper addresses some of these issues, as well as the influence of quantum mechanics on precise measurement, which will also increase as metrology addresses both single entities and the nano scale.

The atomic-scale unit, entity: key to a direct and easily understood definition of the SI base unit for amount of substance

The atomic-scale unit, entity (ent), is defined as the number-specific amount of substance, n/N, the amount of substance of a single entity. This unit is an invariant physical quantity (the reciprocal of the Avogadro constant) that serves as the basis for redefining the SI base unit for amount of substance in a direct and easily understood manner. It is argued here that the kilomole should be the base unit in order to avoid factors of 10−3 or 103 appearing in relationships involving both mass and amount of substance expressed in base units. Since, in a compatible formulation, the amount-specific number of entities, N/n (= NA), is equal to Mu/Da, exactly, where Mu = kg kmol−1 = g mol−1 = Da ent−1, exactly, then NA = (kg/Da) kmol−1 = (g/Da) mol−1 = 1 ent−1, exactly. The kilomole can thus be defined very simply as: , exactly, where , the exact kilomole-to-entity amount ratio, is identical to the kilogram-to-dalton mass ratio: . The Avogadro constant, , does not appear explicitly in the defining equation, its reciprocal having been replaced by one entity. Like the dalton, the entity would be categorized as a unit in use with SI.

The atomic units, the kilogram and the other proposed changes to the SI

The close relationship between the SI units incorporating the proposed changes of Mills et al and the atomic system of units is discussed. It is shown that when the definition of the second is taken into account, a definition of the kilogram in terms of the mass of a photon of specified frequency results in a kilogram that implicitly depends on α4me and other dimensionless constants, where α is the fine structure constant and me is the electron rest mass. Thus the choice of definitions proposed by Mills et al implicitly yields a kilogram that depends either essentially on α4me or on the unified atomic mass unit, mu. Consequently, the kilogram could be regarded as implicitly retaining its present status as an independently defined SI base unit with either definition. The α-dependence of the kilogram and many other SI quantities would, of course, be affected by future changes in the definition of the second.

The IMGC/CENAM-HG6 mercury manobarometer

The Centro Nacional de Metrología (CENAM, Mexico) has established a national primary standard for barometric pressure based on a mercury column and a laser interferometer, the first in this range in Latin America. The original design of the manobarometer, the HG5, was made at the Istituto di Metrologia ‘Gustavo Colonnetti’ (CNR-IMGC, Italy) and it served to develop this new version, the IMGC/CENAM-HG6 mercury manobarometer which was constructed and assembled at CENAM. The special features of this new version and its main design characteristics are presented here, together with the differences from its predecessor. To verify its performance, an internal comparison in absolute mode (gas, N2) was carried out with a primary pressure balance, a piston-cylinder assembly with 50 mm diameter having direct traceability to SI base units and measuring range to 2.5 kPa to 175 kPa. The results of the comparison are presented and discussed.

Base units of the SI, fundamental constants and modern quantum physics

Over the past 40 years, a number of discoveries in quantum physics have completely transformed our vision of fundamental metrology. This revolution starts with the frequency stabilization of lasers using saturation spectroscopy and the redefinition of the metre by fixing the velocity of light c. Today, the trend is to redefine all SI base units from fundamental constants and we discuss strategies to achieve this goal. We first consider a kinematical frame, in which fundamental constants with a dimension, such as the speed of light c, the Planck constant h, the Boltzmann constant k(B) or the electron mass m(e) can be used to connect and redefine base units. The various interaction forces of nature are then introduced in a dynamical frame, where they are completely characterized by dimensionless coupling constants such as the fine structure constant alpha or its gravitational analogue alpha(G). This point is discussed by rewriting the Maxwell and Dirac equations with new force fields and these coupling constants. We describe and stress the importance of various quantum effects leading to the advent of this new quantum metrology. In the second part of the paper, we present the status of the seven base units and the prospects of their possible redefinitions from fundamental constants in an experimental perspective. The two parts can be read independently and they point to these same conclusions concerning the redefinitions of base units. The concept of rest mass is directly related to the Compton frequency of a body, which is precisely what is measured by the watt balance. The conversion factor between mass and frequency is the Planck constant, which could therefore be fixed in a realistic and consistent new definition of the kilogram based on its Compton frequency. We discuss also how the Boltzmann constant could be better determined and fixed to replace the present definition of the kelvin.

Quantum Standard for Units of Length, Time, Mass and Fundamental Physical Constants

Contemporary methods are considered for storage and reproduction of the dimensions of basic SI units, i.e., length, time, and mass. The main trends are discussed for improving these methods in order to reduce reproduction errors for the dimensions of units. The importance of using results of theoretical calculations for microprocess characteristics and precise values for a number of fundamental physical constants is noted.

Shedding Light on the Candela

Though the candela is one of the seven SI base units, it receives little attention from physics teachers. This paper will discuss the history of the candela, its measurement techniques (photometry), and its relation to the lumen. The luminous properties of incandescent and fluorescent lamps are compared. Of the SI base units, only the candela is linked to the peculiarities of human perception.

General principles for the definition of the base units in the SI

The objective of this paper is to provide general principles that should guide any future discussions regarding the redefinition of the SI base units. The suggestion is to use the envisaged redefinition of the unit of mass, the kilogram, as an opportunity to generally check the compliance of all base units with modern demands and the needs of economy, science and society. In order to meet these requirements it is proposed principally to separate the 'carrier' of the definition and the 'carriers' of the realization of the SI units. By providing an example of a revised SI it is shown that these considerations could add value to the International System of Units.

Reliability of values of molar mass, the factor that relates measurements expressed in two SI base units (mass and amount of substance)

Reliability of values of molar mass, the factor that relates measurements expressed in two SI base units (mass and amount of substance)

The problem of the choice of the basic si units (for discussion)

The error is indicated in ascribing the units of angular measurement, radians and steradians, to the class of dimensionless physical quantities and the possibility is also demonstrated of including the lumen and the radian as fundamental SI units.