1. Arnold Leitner Revision of the SI

2. 46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 2 Why change the SI? The kilogram is still defined in terms of a material artefact (IPK) This artefact cannot be absolutely stable – drift? Changes in mass also influence electrical units, mole, candela. The CGPM recommended 1999 to refine experiments linking the units of mass to fundamental constants – view to a redifinition The CIPM is proposing to the CGPM 2011 a future revision of the SI

3. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 3 The third periodic verification of national prototypes of the kilogram (1988-1992) G. Girard, http://www.bipm.org/utils/common/pdf/3eVerificationkg-EN.pdfhttp://www.bipm.org/utils/common/pdf/3eVerificationkg-EN.pdf Change in mass Δm of the six official copies and of prototype No. 25 with respect to the mass of the international prototype IPK  IPK Courtesy of the BIPM

4. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 4 Proposed revision of the SI Draft Resolution A for the 24 th CGPM, 17 – 21 October 2011 http://www.bipm.org/utils/common/pdf/24_CGPM_Convo cation_Draft_Resolution_A.pdf to take note of the intention to redefine four of the SI base units http://www.bipm.org/utils/common/pdf/24_CGPM_Convo cation_Draft_Resolution_A.pdf Draft Revision of Chapter 2 of the SI Brochure http://www.bipm.org/utils/common/pdf/si_brochure_draft _ch2.pdf http://www.bipm.org/utils/common/pdf/si_brochure_draft _ch2.pdf

5. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 5 What changes are proposed? It is the intention of the CIPM to express the definitions of all seven base units of the SI in a uniform manner using the "explicit-constant formulation", in which "the unit is defined indirectly by specifying explicitly an exact value for a well-recognized fundamental constant"

6. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 6 National kilogram prototype no 49 of Austria How to redefine the kilogram? Fundamental constant ?

7. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 7 The BIPM watt balance http://www.bipm.org/en/scientific/el ec/watt_balance/wb_bipm.html Courtesy of the BIPM U I = m g v f 1 f 2 h ~ m g v Electrical power Mechanical power

8. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 8 The Avogadro project Counting atoms in a silicon sphere N A = n V sph M Si / m sph N A = (c M e α 2 )/(2R ∞ h)

9. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 9 Reference constants used to define the base units current SI new SI second s Δν( 133 Cs) hfs Δν( 133 Cs) hfs Cs hyperfine splitting metre m ccspeed of light in vacuum kilogram kgm( IPK )hPlanck constant ampere Aμ 0 eelementary charge kelvin KT TPW kBoltzmann constant mole molM( 12 C)N A Avogadro constant candela cdK cd K cd luminous efficacy of a 540 THz source

10. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 10 One statement to define the new SI The International System of Units, the SI, will be the system of units in which: the ground state hyperfine splitting frequency of the caesium 133 atom Δν( 133 Cs) hfs is exactly 9 192 631 770 hertz, the speed of light in vacuum c is exactly 299 792 458 metre per second, the Planck constant h is exactly 6.626 06… ×10 -34 joule second, the elementary charge e is exactly 1.602 17… ×10 -19 coulomb, the Boltzmann constant k is exactly 1.380 6… ×10 -23 joule per kelvin, the Avogadro constant N A is exactly 6.022 14… ×10 23 reciprocal mole, the luminous efficacy K cd of monochromatic radiation of frequency 540 ×10 12 Hz is exactly 683 lumen per watt, where … represent one or more additional digits to be added to the numerical values of h, e, k, and N A.

11. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 11 Present definition of the kilogram The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. It follows that the mass of the international prototype of the kilogram is always 1 kilogram exactly, m(K) = 1 kg. Recommended new definition The kilogram, kg, is the unit of mass; its magnitude is set by fixing the numerical value of the Planck constant to be equal to exactly 6.626 06…  10 −34 when it is expressed in the unit s −1 m 2 kg, which is equal to J s. Thus we have the exact relation h = 6.626 06…  10 −34 J s. The value of the Planck constant is a constant of nature, which may be expressed as the product of a number and the unit joule second, where J s = s -1 m 2 kg. The effect of this definition, together with those for the second and the metre, is to allow the unit of mass to be defined in terms of frequency, through two of the most fundamental equations of physics, namely E = mc 2 and E = hν, which relate energy E to mass m and frequency ν and which together lead to the relation m = (h / c 2 ) ν.

12. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 12 Present definition of the ampere The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2  10 –7 newton per metre of length. It follows that the magnetic constant µ 0, also known as the permeability of free space, is 4 π  10 -7 H/m exactly. Recommended new definition The ampere, A, is the unit of electric current; its magnitude is set by fixing the numerical value of the elementary charge to be equal to exactly 1.602 17…  10 −19 when it is expressed in the unit s A, which is equal to C. Thus we have the exact relation e = 1.602 17…  10 -19 C. The effect of this definition is that the ampere is the electric current corresponding to the flow of 1/(1.602 17…  10 -19 ) elementary charges per second.

13. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 13 Present definition of the kelvin The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. It follows that the thermodynamic temperature of the triple point of water is exactly 273.16 kelvin T tpw = 273.16 K. Recommended new definition The kelvin, K, is the unit of thermodynamic temperature; its magnitude is set by fixing the numerical value of the Boltzmann constant to be equal to exactly 1.380 6…  10 −23 when it is expressed in the unit s -2 m 2 kg K -1, which is equal to J K -1. Thus we have the exact relation k = 1.380 65…  10 -23 J/K. The effect of this definition is That the kelvin is equal to the change of thermodynamic temperature that results in a change of thermal energy kT by 1.380 65…  10 -23 J/K.

14. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 14 Present definition of the mole 1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. 2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. It follows that the molar mass of carbon 12 is exactly 12 grams per mole. M( 12 C) = 12 g/mol. Recommended new definition The mole, mol, is the unit of amount of substance of a specified elementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles; its magnitude is set by fixing the numerical value of the Avogadro constant to be equal to exactly 6.022 14…  10 23 when it is expressed in the unit mol -1. Thus we have the exact relation N A = 6.022 14…  10 23 mol -1. The effect of this definition is that the mole is the amount of substance of a system that contains 6.022 14…  10 23 specified elementary entities.

15. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 15 Present definition of the second The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly 9 192 631 770 Hz. Recommended new definition (reformulation) The second, s, is the unit of time; its magnitude is set by fixing the numerical value of the ground state hyperfine splitting frequency of the caesium 133 atom, at rest and at a temperature of 0 K, to be equal to exactly 9 192 631 770 when it is expressed in the unit s -1, which is equal to Hz. Thus we have the exact relation Δν( 133 Cs) hfs = 9 192 631 770 Hz. The effect of this definition is that the second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

16. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 16 Present definition of the metre The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. It follows that the speed of the light in vacuum c is 299 792 458 m/s exactly. Recommended new definition (reformulation) The metre, m, is the unit of length; its magnitude is set by fixing the numerical value of the speed of light in vacuum to be equal to exactly 299 792 458 when it is expressed in the unit m s -1. Thus we have the exact relation c = 299 792 458 m/s. The effect of this definition is that the metre is the length of path travelled by light in vacuum during the time interval of 1/299 792 458 of a second.

17. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 17 Present definition of the candela The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540  10 12 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. It follows that the candela is the luminous intensity, in a given direction, of a source of monochromatic radiation with a frequency of 540  10 12 Hz that has a radiant intensity of 1/683 W/sr. Recommended new definition (reformulation) The candela, cd, is the unit of luminous intensity in a given direction; its magnitude is set by fixing the numerical value of the luminous efficacy of monochromatic radiation of frequency 540  10 12 Hz to be equal to exactly 683 when it is expressed in the unit s 3 m -2 kg -1 cd sr, or cd sr W -1, which is equal to lm W -1. Thus we have the exact relation K cd = 683 lm/W for monochromatic radiation of frequency ν = 540 × 10 12 Hz. The effect of this definition is that the candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 ×10 12 Hz and that has a radiant intensity in that direction of 1/683 W/sr.

18. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 18 Recommendation of CCM (G1 - 2010) At least three independent experiments, with u≤5∙10 -8 (at least one with u≤2∙10 -8 ) Consistency at the 95 % level of confidence Target uncertainty in the realization of the kilogram u≤2∙10 -8 Prepare a mise en pratique status: 2 results u≤5∙10 -8 (NIST 2007, Avogadro 2011), but discrepancy: 17 ∙10 -8 Timeline: ?

19. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 19 Recommendation of CCT (T2 – 2010) a relative standard uncertainty of the value of k of order one part in 10 6 be obtained, based on measurements applying different methods of primary thermometry at least two fundamentally different methods such as acoustic gas thermometry and dielectric constant gas thermometry, corroborated by other measurements such as Johnson noise thermometry, total radiation thermometry or Doppler broadening thermometry Timeline: 2 years ?

20. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 20 What is a mise en pratique? A mise en pratique for the definition of a unit is a set of instructions that allows the definition to be realized in practice at the highest level. A “pool of artefacts” developed at the BIPM will play an important role in the mise en pratique of the future definition of the kilogram for the dissemination of the unit of mass. The new definition has to be considered together with the mise en pratique when studying the impact on legal metrology.

21. Revision of the SI46 th CIML Meeting 11 – 14 October 2011, Prague, Czech Republik 21 Thank you four your attention! arnold.leitner@bev.gv.at www.bev.gv.at www.metrologie.at