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Proposed changes to the definition of the ampere and the kilogram and
             their influence in electrical and mass measurements


                                                                  Héctor Laiz

                           Instituto Nacional de Tecnología Industrial (INTI), Buenos Aires, Argentina, laiz@inti.gob.ar




    Abstract: The proposed redefinition of four base units
of the International System of Units (Si) has produced an                                       2.     THE KILOGRAM
exiting scientific debate. The electrical metrology
                                                                               Although the international prototype has served science
community will benefit from the reduction of the
uncertainty of fundamental measurements related to the SI.                 and technology during more than one century it has some
                                                                           inherent limitations. It can be damage, destroyed, it collects
    This presentation analyses the alternatives to the                     dirt from the ambient, and it may change its mass. Its seems
definitions and their impact on electrical and mass                        that its mass may be changing with respect to the ensemble
metrology.                                                                 of Pt-Ir standards of about the same age 50 µg per century,
                                                                           or even more [3].
Keywords: International System of Units. Fundamental
Constants.                                                                                        3.    THE AMPERE
                                                                                 The current definition of the ampere is: the ampere is
                      1.     INTRODUCTION                                  that constant current which, if maintained in two straight
                                                                           parallel conductors of infinite length, of negligible circular
    The International System of Units is a coherent system                 cross-section, and placed 1 metre apart in vacuum, would
built with base and derived units. The base units are a choice             produce between these conductors a force equal to 2 x 10–7
of seven well-defined units which by convention are                        newton per metre of length [1]. In the past, its direct
regarded as dimensionally independent: the metre, the                      realization with current balances led to uncertainties of
kilogram, the second, the ampere, the kelvin, the mole, and                about 1·10-6. An alternative way with lower uncertainties for
the candela. Derived units are those formed by combining                   the realization of the SI-ampere is by means of the voltage
base units according to the algebraic relations linking the                balance [4] and the Thomsom-Lampard capacitor [5] or the
corresponding quantities [1]. The definition of a base unit is             watt balance [6]. The advent of two quantum macroscopic
drawn up so that it is unique and provides a theoretical basis             effects, the Josephson and the Quantum Hall Effects, allows
upon which the most accurate and reproducible                              for the generation of reference voltage an resistance with
measurements can be made. The search for definitions of the                high reproducibility, although not in terms of the ampere
units based on invariant of nature is as ancient as human                  definition, but in terms of the Josephson constant, K J =2e/h
technical activities. The unit of length based on the pharaoh              and the von Klitzing constant R K =h/e2. To take full practical
elbow or based on one meridian of the earth are examples of                advantage of this two experiments in 1990 the CGPM
that dream [2]. Nowadays we search for definitions of the                  assigned by convention fixed values to K J and R K , based on
units that relay on fixed values of fundamental constants of               all available data from voltage balances, watt balances,
nature. In the definition of the metre, such a fundamental                 Thomsom-Lampard capacitors and other experiments [7].
constant is the speed of light in vacuum, c o . Another
constant is the permeability of vacuum, µ o , fixed in the
definition of the ampere. Among the seven base units the
definition of the kilogram is the one that is still based on an              4.        DRAWBACKS OF THE CURRENT SITUATION
artifact, the international prototype kept at the BIPM in                      As a consequence of the current definitions of the base
Sèvres, near Paris. Nevertheless, because of the way they are              units we face the following problems:
defined, three other base units relay on the definition of the
kilogram, namely the ampere, the mole and the candela.                            a.     The mass of the prototype of the kilogram may be
Therefore, any uncertainty in the definition of the kilogram                             changing, but its value is fixed by definition.
propagates into these units.                                                             Moreover, it is only accessible at the BIPM.
                                                                                  b.     We have a practical electrical system of units
                                                                                         “outside de SI”.

VIII Semetro. João Pessoa, PB, Brazil, June 17 – 19, 2009
c.        The uncertainty given to many fundamental                                   REFERENCES
                constants of nature is rather high, due to de null   [1]    BIPM, “The international System of Units 8th
                uncertainty given to the mass of the international          edition”(Sevres, France: Bureau International des Poids et
                prototype [8].                                              Measures) www.bipm.org, 2006.
    The improvement in the accuracy on some fundamental              [2]    Valdés J, “Features and Future of the International System
experiments, mainly the watt balance, stimulated the CIPM                   of Units,” Advances in Imaging and Electron Physics vol
                                                                            138, ed P Hawkes (New York: Academic) pp 251-320,
to ask its Consultative Committees to study the possibility of
                                                                            2003.
having a fundamental constant based definition of the                [3]    Davis R, “The Si unit of mass”, Metrologia, 40 299-305,
kilogram. This decision open and exiting scientific debate                  2003.
[2, 8, 9].                                                           [4]    Funk T and Sienknecht V, Determination of the volt with
                                                                            the improved PTB voltage balance,” IEEE Trans. Instrum.
 5.        IMPACT ON ELECTRICAL MEASUREMENTS                                Meas., 40 158-161, 1991.
                                                                     [5]    Jeffery A et al, Determination of the von Klitzing constant
    Following the inquire of the CIPM, the Consultative                     and the fine-structure constant through a comparison of the
Committee for Electricity and Magnetism proposed that the                   quantized Hall resistance and the ohm derived from the
SI be changed by adopting fixed values of the elementary                    NIST calculable capacitor, Metrologia 35, No 2 (April
charge e and Planck constant h, and that this decision be                   1998) 83-96, 1998.
taken in the near future, for example in 2011, provided that         [6]    Robinson I, “Towards the Redefinition of the Kilogram:
                                                                            Measurement of Plank´s Constant Using Watt balances,”
adequate agreement is achieved among independent
                                                                            IEEE Trans. Instrum. Meas., 58 942-948, 2009.
experiments [10]. It also recommends that the ampere be              [7]    Quinn T, “News from the BIPM”, Metrologia, 26 69-74,
defined, for example, as follows: “The ampere is the                        1989.
electrical current equivalent to the flow of exactly 1/(1.602        [8]    Mills I. et al, “Redefinition of the kilograma: a decision
176 53 × 10−19)elementary charges per second.” It follows                   whose time has come,” Metrologia, 2005, 42 71-80, 2005.
that this definition fixes the elementary charge as exactly          [9]    Becker P et al, “Considerations on future definitions of the
1.602 176 53 × 10−19 A·s. This proposal would give values                   kilogram, the mole and other units,” Metrologia, 1-14,
without uncertainty to K J and R K , binging electrical units               2007.
back to the SI.                                                      [10]   CCEM, 2007. RECOMMENDATION E1: Proposed
                                                                            changes to the International System of Units (SI), ”(Sevres,
    The forthcoming change in the SI will not only deal with
                                                                            France: Bureau International des Poids et Measures)
the ampere and the kilogram but will also include the                       www.bipm.org
Kelvin, by fixing the value of the Boltzmann constant, and           [11]   Mills I. et al, “Redefinition of the kilograma, ampere,
the mole, by fixing the value of the Avogadro constant [11].                kelvin and mole: a proposed approach to implementing
                                                                            CIPM recommendation 1 (C1-2005),” Metrologia, 43 227-
                                                                            246, 2006.
           6.    IMPACT ON MASS MEASUREMETS                          [12]   OIML R111 Weights of classes E1, E2, F1, F2, M1, M1-2,
                                                                            M2, M2-3 and M3. Part 1: Metrological and technical
                                                                            requirements, International Organization of Legal
     According to the proposed changes in the definition of                 Metrology, http://www.oiml.org/publications/
the units the prototype of the kilogram should be calibrated
with a watt balance in terms of the Plank constant.
Nowadays, the best available watt balance has an
uncertainty of 4·10-8 [6]. This value is 2.5 times the
uncertainty given today by the BIPM for the calibration
kilogram standards made stainless steel. This increase in the
uncertainty will increase the uncertainty in the dissemination
of the national standards to multiples and submultiples but it
will be negligible at the level of E1 standards [12].


                        7.   CONCLUSIONS


    The forthcoming change in the definition of the ampere,
the kilogram, the mole and the kelvin, will reduce the
uncertainty of measurements and fundamental constants,
related to the new SI, in many fields of science and
technology. It will increase the uncertainty of mass
measurements at the highest level, but with no impact in
legal and industrial mass measurements.
    Attention should be paid in the new definitions to keep
the SI as a widely understandable system, in which
definitions of base units reflect the concept of the related
base quantity.



VIII Semetro. João Pessoa, PB, Brazil, June 17 – 19, 2009

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Proposed changes to the definition of the ampere and the kilogram and their influence in electrical and mass measurements

  • 1. Proposed changes to the definition of the ampere and the kilogram and their influence in electrical and mass measurements Héctor Laiz Instituto Nacional de Tecnología Industrial (INTI), Buenos Aires, Argentina, laiz@inti.gob.ar Abstract: The proposed redefinition of four base units of the International System of Units (Si) has produced an 2. THE KILOGRAM exiting scientific debate. The electrical metrology Although the international prototype has served science community will benefit from the reduction of the uncertainty of fundamental measurements related to the SI. and technology during more than one century it has some inherent limitations. It can be damage, destroyed, it collects This presentation analyses the alternatives to the dirt from the ambient, and it may change its mass. Its seems definitions and their impact on electrical and mass that its mass may be changing with respect to the ensemble metrology. of Pt-Ir standards of about the same age 50 µg per century, or even more [3]. Keywords: International System of Units. Fundamental Constants. 3. THE AMPERE The current definition of the ampere is: the ampere is 1. INTRODUCTION that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular The International System of Units is a coherent system cross-section, and placed 1 metre apart in vacuum, would built with base and derived units. The base units are a choice produce between these conductors a force equal to 2 x 10–7 of seven well-defined units which by convention are newton per metre of length [1]. In the past, its direct regarded as dimensionally independent: the metre, the realization with current balances led to uncertainties of kilogram, the second, the ampere, the kelvin, the mole, and about 1·10-6. An alternative way with lower uncertainties for the candela. Derived units are those formed by combining the realization of the SI-ampere is by means of the voltage base units according to the algebraic relations linking the balance [4] and the Thomsom-Lampard capacitor [5] or the corresponding quantities [1]. The definition of a base unit is watt balance [6]. The advent of two quantum macroscopic drawn up so that it is unique and provides a theoretical basis effects, the Josephson and the Quantum Hall Effects, allows upon which the most accurate and reproducible for the generation of reference voltage an resistance with measurements can be made. The search for definitions of the high reproducibility, although not in terms of the ampere units based on invariant of nature is as ancient as human definition, but in terms of the Josephson constant, K J =2e/h technical activities. The unit of length based on the pharaoh and the von Klitzing constant R K =h/e2. To take full practical elbow or based on one meridian of the earth are examples of advantage of this two experiments in 1990 the CGPM that dream [2]. Nowadays we search for definitions of the assigned by convention fixed values to K J and R K , based on units that relay on fixed values of fundamental constants of all available data from voltage balances, watt balances, nature. In the definition of the metre, such a fundamental Thomsom-Lampard capacitors and other experiments [7]. constant is the speed of light in vacuum, c o . Another constant is the permeability of vacuum, µ o , fixed in the definition of the ampere. Among the seven base units the definition of the kilogram is the one that is still based on an 4. DRAWBACKS OF THE CURRENT SITUATION artifact, the international prototype kept at the BIPM in As a consequence of the current definitions of the base Sèvres, near Paris. Nevertheless, because of the way they are units we face the following problems: defined, three other base units relay on the definition of the kilogram, namely the ampere, the mole and the candela. a. The mass of the prototype of the kilogram may be Therefore, any uncertainty in the definition of the kilogram changing, but its value is fixed by definition. propagates into these units. Moreover, it is only accessible at the BIPM. b. We have a practical electrical system of units “outside de SI”. VIII Semetro. João Pessoa, PB, Brazil, June 17 – 19, 2009
  • 2. c. The uncertainty given to many fundamental REFERENCES constants of nature is rather high, due to de null [1] BIPM, “The international System of Units 8th uncertainty given to the mass of the international edition”(Sevres, France: Bureau International des Poids et prototype [8]. Measures) www.bipm.org, 2006. The improvement in the accuracy on some fundamental [2] Valdés J, “Features and Future of the International System experiments, mainly the watt balance, stimulated the CIPM of Units,” Advances in Imaging and Electron Physics vol 138, ed P Hawkes (New York: Academic) pp 251-320, to ask its Consultative Committees to study the possibility of 2003. having a fundamental constant based definition of the [3] Davis R, “The Si unit of mass”, Metrologia, 40 299-305, kilogram. This decision open and exiting scientific debate 2003. [2, 8, 9]. [4] Funk T and Sienknecht V, Determination of the volt with the improved PTB voltage balance,” IEEE Trans. Instrum. 5. IMPACT ON ELECTRICAL MEASUREMENTS Meas., 40 158-161, 1991. [5] Jeffery A et al, Determination of the von Klitzing constant Following the inquire of the CIPM, the Consultative and the fine-structure constant through a comparison of the Committee for Electricity and Magnetism proposed that the quantized Hall resistance and the ohm derived from the SI be changed by adopting fixed values of the elementary NIST calculable capacitor, Metrologia 35, No 2 (April charge e and Planck constant h, and that this decision be 1998) 83-96, 1998. taken in the near future, for example in 2011, provided that [6] Robinson I, “Towards the Redefinition of the Kilogram: Measurement of Plank´s Constant Using Watt balances,” adequate agreement is achieved among independent IEEE Trans. Instrum. Meas., 58 942-948, 2009. experiments [10]. It also recommends that the ampere be [7] Quinn T, “News from the BIPM”, Metrologia, 26 69-74, defined, for example, as follows: “The ampere is the 1989. electrical current equivalent to the flow of exactly 1/(1.602 [8] Mills I. et al, “Redefinition of the kilograma: a decision 176 53 × 10−19)elementary charges per second.” It follows whose time has come,” Metrologia, 2005, 42 71-80, 2005. that this definition fixes the elementary charge as exactly [9] Becker P et al, “Considerations on future definitions of the 1.602 176 53 × 10−19 A·s. This proposal would give values kilogram, the mole and other units,” Metrologia, 1-14, without uncertainty to K J and R K , binging electrical units 2007. back to the SI. [10] CCEM, 2007. RECOMMENDATION E1: Proposed changes to the International System of Units (SI), ”(Sevres, The forthcoming change in the SI will not only deal with France: Bureau International des Poids et Measures) the ampere and the kilogram but will also include the www.bipm.org Kelvin, by fixing the value of the Boltzmann constant, and [11] Mills I. et al, “Redefinition of the kilograma, ampere, the mole, by fixing the value of the Avogadro constant [11]. kelvin and mole: a proposed approach to implementing CIPM recommendation 1 (C1-2005),” Metrologia, 43 227- 246, 2006. 6. IMPACT ON MASS MEASUREMETS [12] OIML R111 Weights of classes E1, E2, F1, F2, M1, M1-2, M2, M2-3 and M3. Part 1: Metrological and technical requirements, International Organization of Legal According to the proposed changes in the definition of Metrology, http://www.oiml.org/publications/ the units the prototype of the kilogram should be calibrated with a watt balance in terms of the Plank constant. Nowadays, the best available watt balance has an uncertainty of 4·10-8 [6]. This value is 2.5 times the uncertainty given today by the BIPM for the calibration kilogram standards made stainless steel. This increase in the uncertainty will increase the uncertainty in the dissemination of the national standards to multiples and submultiples but it will be negligible at the level of E1 standards [12]. 7. CONCLUSIONS The forthcoming change in the definition of the ampere, the kilogram, the mole and the kelvin, will reduce the uncertainty of measurements and fundamental constants, related to the new SI, in many fields of science and technology. It will increase the uncertainty of mass measurements at the highest level, but with no impact in legal and industrial mass measurements. Attention should be paid in the new definitions to keep the SI as a widely understandable system, in which definitions of base units reflect the concept of the related base quantity. VIII Semetro. João Pessoa, PB, Brazil, June 17 – 19, 2009