Report of the CCU to the 23rd CGPM November 2007 from the President of the CCU, Professor Ian Mills - two main activiti

1. Report of the CCU to the 23rd CGPM November 2007 from the President of the CCU, Professor Ian Mills - two main activities in the last four years: (i) preparing the new 8th edition of the SI Brochure (ii) revising the definitions of some of the base units imm Sep 07

2. The SI Brochure 8th edition published May 2006 180 pages (90 French, 90 English). Available from the BIPM for 20 € per copy, or free as a pdf file on the BIPM website. imm Sep 07

3. The Concise Summary of the SI Four A4 pages, available in French and English. This may be purchased in packs of 50 for 1 euro per copy, or free to download from the BIPM website. imm Sep 07

4. Should we be considering improved definitions for some of the base units of the SI ? The CCU has discussed the possibility of revised definitions many times over the past 12 years. Our advice concerning possible redefinitions concerns the kilogram, ampere, kelvin and mole. imm Sep 07

6. Desirable qualities for the definition of a base unit • We should chose reference standards that we believe to be stable under translation in space and time, on an astronomical scale, i.e. that are related to an invariant of nature • We must be able to realise the definition as accurately as the best practical measurements require • It is desirable to choose simple definitions, both to comprehend and to realise, using apparatus that is neither too expensive nor too complex. However it is the nature of modern science that this may be difficult to achieve, and it is not an essential requirement. • We should chose definitions that may be experimentally realised by anyone, anywhere, at anytime. imm Sep 07

7. Base quantities and base units: the current SI Quantity symbol time t length x mass m electric i current thermodynamic T temperature amount n of substance luminous L intensity Base unit symbol second s metre m kilogram kg ampere A kelvin K mole mol candela cd Presentdefinition fixes(hfs Cs), hyperfine splitting of caesium atom fixes c0, speed of light in vacuum fixes m(K ), the mass of the international prototype fixes 0, the magnetic const fixes TTPW, temperature of the triple point of water fixes M(12C), the molar mass of carbon 12. fixes L(source), luminous efficacy of specified source imm Sep 07

8. Base quantities and base units for the 21stCthe new SI Quantity symbol time t length x mass m electric i current thermodynamic T temperature amount n of substance luminous L intensity Proposed new definition: fixes(hfs Cs), hyperfine splitting of caesium atom fixes c0, speed of light fixes h, the Planck constant fixes e, the elementary charge fixes kB, Boltzmann constant fixes NA, the Avogadro constant fixes L(source), luminous efficacy of specified source Base unit symbol second s metre m kilogram kg ampere A kelvin K mole mol candela cd imm Sep 07

9. Redefining the kilogram • First alternative: • The kilogram, unit of mass, is the mass of exactly • 5.01845166 ×1025 free carbon 12 atoms at rest • and in their ground state • - this fixes the value of the mass of a carbon atom, and the Avogadro constant NA if the current definition of the mole is retained. • This definition would be realized by any experiment that might be used today to measure the mass of an atom, or the value of the Avogadro constant, such as the XRCD Si crystal density experiment, or the watt balance experiment combined with the relation between h and NA. imm Sep 07

10. Redefining the kilogram Second alternative: The kilogram, unit of mass, is such that the value of the Planck constant is 6.626 0693 ×10–34 kg m2 s–1 - this fixes the value of the Planck constant h. Since the metre and the second are already defined, and since the value of h is a universal constant, fixing the numerical value of h defines the kilogram. This definition would be realized by any experiment that may be used at present to determine the value of h, such as the watt balance, or the silicon crystal density experiment to measure NA combined with the relation between h and NA. imm Sep 07

11. Which definition should we choose ? • The CCU, and advice from other CCs, are essentially unanimous in preferring a new definition of the kilogram chosen to fix the value of the Planck constant h, • because h is the fundamental constant of quantum mechanics, just as c is the fundamental constant of relativity theory, and theoretical physics would be well served by having exactly defined values for the two constants h and c, • because if we also redefine the ampere to fix e, then both 2e/h and h/e2 will have precisely defined values, with advantages for electrical metrology. imm Sep 07

12. Realising the kilogram The realisation of the definition of the kilogram would be achieved by maintaining a number of kilogram prototypes which would be used as secondary standards, in exactly the same way as is done today. However these would be calibrated at intervals against the definition in terms of the Planck constant h,using a watt balance, or any other experiment that could be used today to measure the value of h. This procedure would replace the calibration of secondary standard prototypes against the international prototype K, as is done today. Initially it is likely that the international prototype would be calibrated against the Planck constant using a watt balance, so that it could continue to be used as a reference standard. However any laboratory equipped with a watt balance could maintain their own reference standard of mass. imm Sep 07

13. The Planck constant h and the Avogadro constant NA are related through the equation All of the constants in this equation are known with a relative standard uncertainty of less than 10–9, except for h and NA. The best XRCD estimate of NA (Fujii, 2005) is NA = 6.022 135 3 (18) mol–1withur = 3.0 × 10–7 and the best Watt balance estimate of h (Ed Williams et al., 2007) is h = 6.626 068 96 (33) J s withur = 5.0 × 10–8 Sadly, these values are inconsistent by a factor of 8.4 × 10–7 (Mohr and Taylor, to be published, 2007). However experiments at present underway suggest that both the XRCD result and the Watt balance result will be significantly improved in the next few years, so that this discrepancy is likely to be resolved. imm Sep 07

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15. The CCU are unanimous in advising that any new definition of the kilogram should wait until the present inconsistency between the watt balance results for h and the silicon crystal density results for NA is resolved. imm Sep 07

16. Redefining the ampere The current definition: the ampere, unit of electric current, is such that the value of the magnetic constant 0 is exactly 4 10−7 henries per metre Possible new alternative definition: the ampere, unit of electric current, is such that the value of the elementary charge e (charge on a proton) is exactly 1.602176487 10−19 coulomb imm Sep 07

17. Which definition should we choose? New alternative definition: To fix e Almost all members of the CCU, and almost all reports from the other CCs, prefer the definition to fix the value of e, the charge on a proton. The reason is that if the value of h is fixed to define the kilogram and the value of e is fixed to define the ampere, then both 2e/h and h/e 2 will have exactly defined values. These are at present believed to be the theoretical expressions for the Josephson constant KJ and the von Klitzing constant RK respectively, so that electrical measurements made using the Josephson and the quantum hall effects would be brought into the SI. This would be a significant advance in electrical metrology, because at present precise electrical measurements are made using the conventional non-SI values of KJ-90 and RK-90 . imm Sep 07

18. The alternative is • to retain the current definition, • Current definition: to fix 0 • There is an argument that • fixing 0 is related to the properties of vacuum which some consider more important than the properties of an electron; • the relations KJ = 2e/h and RK = h/e2 may yet need further small corrections. • An overwhelming majority of the members of the CCU regard neither of these arguments as being convincing, and there is at present no evidence to support the second conjecture. imm Sep 07

19. Note that e and 0 are related through the fine structure constant relation: = ce20 /2h Since the relative uncertainty in  is now only 7 1010, and since the value of c is already fixed to define the metre and we are planning to fix h to define the kilogram, the consequence is that fixing e would give an uncertainty in 0 of only 7 10–10, and fixing 0 would give an uncertainty in e of only 3.510–10. Thus the difference between a definition to fix e and a definition to fix 0 is small. Almost all members of the CCU would prefer to define the ampere to fix e rather than to fix 0. imm Sep 07

20. Redefining the kelvin: Current definition: The kelvin, unit of thermodynamic temperature, is such that the value of the triple point temperature of water is exactly 273.16 kelvin. Possible new alternative definition: The kelvin, unit of thermodynamic temperature, is such that the value of the Boltzmann constant is k = 1.3806504 joules per kelvin exactly. The new definition would be in terms of the fundamental constant k rather than the properties of a particular material at a particular temperature that is difficult to realise. The CCU strongly support redefining the kelvin to fix k. imm Sep 07

21. Redefining the mole Current definition: The mole, unit of amount of substance, is such that the molar mass of carbon 12 is exactly 12 grams per mole. Possible alternative simpler definition: The mole is that amount of substance that contains exactly 6.02214179 x1023 elementary entities. The current definition fixes the value of the molar mass of carbon 12.The alternative fixes the value of the Avogadro constant NA. The CCU recommend changing to the new simpler definition. imm Sep 07

22. To summarise: • The CCU advise that we should redefine the kilogram, ampere, kelvin and mole to fix the values of the Planck constant h, the elementary charge e, the Boltzmann constant k, and the Avogadro constant NA, respectively; • These changes should await resolution of the present discrepancy between watt balance results for h and the silicon crystal density results for NA; • The changes should be made simultaneously, and should be based on the latest values of the fundamental constants to preserve continuity; • The words for each new definition should be considered carefully over the next two years, along with the mises en pratique to go with each definition. imm Sep 07

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24. Relative standard uncertainties for a selection of fundamental constants multiplied by 108 (i.e. in parts per hundred million) imm Sep 07

25. “Yet, after all, the dimensions of our earth and its time of rotation, though, relative to our present means of comparison, very permanent, are not so by physical necessity. The earth might contract by cooling, or it might be enlarged by a layer of meteorites falling on it, or its rate of revolution might slowly slacken, and yet it would continue to be as much a planet as before. But a molecule, say of hydrogen, if either its mass or its time of vibration were to be altered in the least, would no longer be a molecule of hydrogen. If, then, we wish to obtain standards of length, time and mass which shall be absolutely permanent, we must seek them not in the dimensions, or the motion, or the mass of our planet, but in the wavelength, the period of vibration, and the absolute mass of these imperishable and unalterable and perfectly similar molecules.” James Clerk Maxwell, 1870 Prague Sept 2004

26. c = 299 792 458m/s value of c = numerical value  unit The value of c is a constant of nature. 1. If we define the units independently, then we must determine the numerical value by experiment, and it will have an uncertainty. That was the situation before 1983, when both the metre and the second were independently defined. 2. If the second is independently defined in terms of the frequency of the caesium transition, and we choose to fix the numerical value of c, then the effect is to define the metre. This is the current definition of the metre, since the change in 1983. The numerical value now has zero uncertainty. imm Oct 06

27. h = 6.626 0693 × 10-34m2 kg s1 value of h = numerical value  unit The value of h is a constant of nature. 1. If we define the unit m2 kg s-1 independently, then we must determine the numerical value by experiment, and it will have an uncertainty. That is the present situation. 2. If the metre and the second are already independently defined, and we choose to fix the numerical value, then the effect is to define the kilogram. This is the proposed new definition of the kilogram. The numerical value will have zero uncertainty. Note: J s = m2 kg s–1 imm Oct 06