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THE NEW SYSTEM OF UNITS BASED ON FUNDAMENTAL PHYSICAL CONSTANTS - THE NEXT APROACH

Explore the evolution of measurement systems, including the SI unit, quantum standards, and the progression toward defining units based on physical constants. Delve into the history, resolutions, and significance of international systems of units.

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THE NEW SYSTEM OF UNITS BASED ON FUNDAMENTAL PHYSICAL CONSTANTS - THE NEXT APROACH

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  1. THE NEW SYSTEM OF UNITS BASED ON FUNDAMENTAL PHYSICAL CONSTANTS - THE NEXT APROACH Waldemar Nawrocki Poznan University of Technology, Poznan, Poland Workshop on Precision Physics and Fundamental Physical Constants Budapest, October 13th, 2015

  2. THE NEW SYSTEM OF UNITS BASED ON FUNDAMENTAL PHYSICAL CONSTANTS - THE NEXT APROACHOutline • History of measures • System International of Units (SI) • Regularstandards and qunatumstandards • Standards depend on fundamentalphysicalconstants • Resolution of the CGPM of 2007 and 2011 • Resolution of the 25th CGPM of 2014 • Quantum metrological triangle and pyramid

  3. International Systems of Units • 1799 – The Standard of the 1 metre and of the 1 kg (Pt+Ir) in Paris. 1 m = 1/10 000 000 fraction of the meridianbetween the pole and the equator. 1 kg = mass of 1/1000 m3fraction of purewater. • 1832r. – Proposal by Carl Gauss: a system of units with 1 milimeter, 1 gram, 1 second. The base for the CGS system of units. • 1860-1870 – Proposal by Maxwell and Thomson: a coherent system of units with baseunits and derivedunits • 1875 – The MetreConvention, accepted by 17 countries(France, Russia, Turkey, England, Germany, …). Independent Poland acceptedit in 1925. Practical standards of 1 metre and 1 kg.

  4. MKSA and SI International Systems of Units • 1954 – MKSA system (metre, kilogram, second, ampere). • 1960– SI (metre, kilogram, second, ampere, kelvin and candela); 1971 - the mole as the 7thbaseunit in the SI

  5. System International (SI) • System create: • 1. The baseunits: metre, kilogram, second, ampere, kelvin, candel and mole • 2. The auxiliaryunits: the radian and the steradian • 3. The 22 deriveduntis for electrical, mechanical, magnetic, thermal, light and accousticquantities.

  6. The kilogramis the unit of mass; itisequal to the mass of the international prototype of the kilogram. The firstcandidate to be replaced by a newdefinition 2. The ampereisthatconstantcurrentwhich, ifmaintained in twostraightparallelconductors of infinitelength, of negligiblecircular cross-section, and placed 1 m apart in vacuum, wouldproducebetweentheseconductors a forceequal to 2 × 10–7 newton per metre of length. 3. The kelvin, unit of thermodynamictemperature, is the fraction 1/273.16 of the thermodynamictemperature of the triple point of water, 4. The moleis the amount of substance of a system whichcointains as many elementaryentities as thereareatoms in 0.012 kg of carbon 12. When the mole isused, elementaryentitiesmust be specified and may be atoms, moleculs, ions, electrons, otherparticles, orspecifiedgroups of suchpatrticles. System Internationaldefinitions of the kilogram, ampere, kelvin and mole

  7. 5. The metreis the length of the pathtravelled by light in vacuumduring a time interval of 1/299 792 458 of a second. 6. The secondis the duration of 9 192 631 770 periods of the radiationcorresponding to the transitionbetween the twohyperfinelevels of the ground state of the Cs 133. 7. The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. In the above 3 definitionsphysicalconstantsareknownexactly (assumption): c = 299 792 458 m/s,  = 9 192 631 770 Hz, P = 683 W/steradian System Internationaldefinitions of the metre, second and candela

  8. The 1 kg mass standard, in Central Office of Measures in Warsaw 1 kg standard Pt 90% + Ir 10% D = h = 39 mm

  9. The IPK (1 kg) changes its mass • The international prototype of the kilogram (IPK) has been used since 1889. • The results of the second (1939–1953) and third (1989–1992) periodic verifications of national prototypes of the kilogram indicate a change in mass of the IPK by 50 g in 100 years. • This means a relative change of 5 × 10–8 per 100 years. • The mass of the prototype was measured with an uncertainty of 2.3 g • The reason of this drift is unknown. NPL

  10. Voltage standards with Josephson junctions Sochocka, Nawrocki, Elektronika, vol. 42 (2001), nr 11.

  11. Quantum Hall Effect Standard at Central Office of Measures in Warsaw (the sample from NPL)

  12. 12th Resolution of the 23th General Conference on Weights and Measures - 2007 23th General Conference considered : “that, of the seven base units of the SI, only the kilogram is still defined in terms of a material artifact – the international prototype of the kilogram (2nd CGPM, 1889) and that the definitions of the ampere, mole and candela depend on the kilogram, …, that many advances, made in recent years, in experiments which relate the mass of the international prototype to the Planck constant h or the Avogadro constant NA,, initiatives to determine the value of a number of relevant fundamental constants, including work to redetermine the Boltzmann constant kB, that as a result of recent advances, there are significant implications for, and potential benefits from, redefinitions of the kilogram, the ampere, the kelvin and the mole …”.

  13. Resolution of the 23th General Conference on Weights and Measures - 2007 Following the above arguments, the 23th General Conference (CGPM) recommended in the 12th resolution: “pursue the relevant experiments so that the International Committee can come to a view on whether it may be possible to redefine the kilogram, the ampere, the kelvin, and the mole using fixed values of the fundamental constants at the time of the 24th General Conference (2011), should, together with the International Committeeand appropriate working groups, work on practical ways of realizing any new definition …., and consider the most appropriate way of explaining the new definitions to users ...”. www.bipm.org/en/convention/cgpm

  14. Units and Fundamental Physical Constants Physical constants – more candidates than necessary

  15. Fundamental physical constants from CODATA 2014 How does the h change? Table on the building of the Nicolaus Copernicus University,Toruń, Poland „The symbol X in this draft represents one or more additional digits to be added to the numerical values of h, e, k and NA using values based on the most recent CODATA adjustment” – Resolution of 24th CGPM

  16. Different New Definitions of the 1 kg • The kilogram is the mass of a body whose Compton frequency is 1.356392XXX… × 1050 hertz exactly. (frequency of cosmicray ~ 1024Hz) • The kilogram is the mass of a body whose de Broglie-Compton frequency is equal to exactly [(299 792 4582/(6.626 0693) × 10–34) [hertz ]. • The kilogram is the mass of a body whose equivalent energy is equal to that of a number of photons whose frequencies sum to exactly [(299 792 4582/(66 260 693)] × 1041 hertz. • The kilogram, unit of mass, is such that the Planck constant is exactly h = 6.626 0693 × 10–34Js. • The kilogram is (6.022 1415 × 1023/0.012) times the rest mass of the 12C atom in the ground state. • The kilogram is (6.022 1415 × 1023/0.012) times the rest mass of a particle whose creation energy equals that of a photon whose frequency is: [0.012/(6.022 1415 × 1023) × 299 792 4582/66 260 693 × 10–34) [hertz]. 7. The kilogram is 1.097 769 24 × 1030 times the rest mass of the electron.

  17. The Si sphere – the possible standard of the 1 kilogram • Siliconsphereat the PTB, Braunschweig • D = 90 mm • diametercontrolled in 16 000 directions • 2 mln Euro

  18. X-ray crystal density technique (XRCD): “counting” atoms 8 atoms per unit cell result in 2005: ur = 3 x 10-7 repeated with isotopically pure 28Si (99.995 %) result in 2011: ur = 3 x 10-8 Target for 2014: 2 x 10-8 2015: 1.5 x 10-8 measurands: • volume • mass • lattice constant • mean molar mass • crystal imperfections • surface layers 86

  19. New definitions of ampere, kelvin and mole • The ampere is the electrical current equivalent to the flow of exactly 1/(1.602 176 53 × 10-19) elementary charges per second. 2. The kelvin is the change of thermodynamic temperature T that results in a change of thermal energy kTby exactly 1.380 6488 × 10–23 joule, where k is the Boltzmann constant. 3. The mole is the unit of amount of substance. It is equal to 6.022 1415 × 1023 mol-1 specified identical entities. The entities may be atoms, ions, molecules or other particles.

  20. Resolution of the 24th General Conference on Weights and Measures - 2011 The 24th General Conference (17-21 October 2011) considered: “that, although the work (to redefine four base units of the SI) has progressed well, not all the requirements set out by the 23th General Conference in 2007 have been satisfied and so the International Committee for Weights and Measures isnot yet ready to make a final proposal.” The definitions of the metre, kilogram, second, ampere, kelvin, mole and candela will be abrogared (will be canceled). The 24th General Conference „invites CODATA to continue provide adjusted values of the fundamental physical constants based on all relevant information …” The first attempt to adopt a new measurement system - failed! www.bipm.org/en/convention/cgpm

  21. Requirements for the redefinition of the kg In 2010, Consultative Committee for Mass made the following recommendations (confirmed in February 2013): ● Conditions before redefining the kilogram: • 1. at least 3 independent results (watt balance and XRCD) with ur < 5 x 10-8 • 2. at least 1 result with ur≤ 2 x 10-8 • 3. results consistent ● Traceability to the IPK of BIPM working standards and of mass standards used to determine h needs to be re-established (“Extraordinary Calibrations”) ● a mise-en-pratique for the definition of the kilogram is well under way.

  22. The results of measurements of h k=1 1 x 10-7 89

  23. Resolution of the 24th GCPM, 2011, Possible new definition of SI The 24th General Conference takenoteof intention of the Int. Committee for Weights and Measuresto propose a revision of the SI as follows: The International System of Units, the SI,will be the system of units in which: 1. the ground state hyperfine splitting frequency of the caesium 133 atom (133Cs)hfs is exactly9 192 631 770 hertz, second, Hz 2. the speed of light in vacuum c0 is exactly299 792 458 metre per second,  m 3. the Planck constant h is exactly6.626 06X × 10–34 joule second, kg 4. the elementary charge e is exactly1.602 17X × 10-19 coulomb,  A 5. the Boltzmann constant kB is exactly1.380 6X × 10–23 joule per kelvin, K 6. the Avogadro constant NA is exactly6.022 14X × 1023reciprocal mole, mol 7. the luminous efficacy Kcdof monochromatic radiation of frequency 540 × 1012 hertz is exactly683 lumen per watt. cd Comment: itis no proposal for a newsystems of units.It is the set of physicalconstants!

  24. The recentresults of measurements of h, KJ, and k Milton, Davis, Fletcher, Towards a new SI: a review of progress made since 2011, Metrologia, 51 (2014)

  25. Discussion of a new system of units – new books • 1. Nawrocki, Introduction to Quantum Metrology, Springer 2015. • 2. Goebel, Siegner, Quantum Metrology, Wiley 2015

  26. On the future revision of the International System of Units Resolution 1. 25thGeneral Conf. on Weights and Measures 2014 Recallingthe Resolution 12 of the 23rdCGPM (2007), …. that could enable the planned revision of the SI, considering that there has been significant progress in completing the necessary work, including: • the acquisition of relevant data by the CODATA • establishment by BIPM of an ensemble of reference standards of mass • the preparation of mises‐en‐pratique for the new definitions of the kilogram, ampere, kelvin, and mole • awareness campaigns to alert user communities as well as the general public to the proposed revision of the SI, • the preparation of the 9th edition of the SI Brochure

  27. On the future revision of the International System of Units- part 2 • • establishment by the BIPM of an ensemble of reference standards of mass to facilitate the dissemination of the unit of mass in the revised SI, • • the preparation of mises‐en‐pratique for the new definitions of the kilogram, ampere, kelvin, and mole, noting that further work the CIPM, the BIPM, the NMIs and the CCs should focus on • • awareness campaigns to alert user communities as well as the general public to the proposed revision of the SI, • • the preparation of the 9th edition of the SI Brochure that presents the revised SI in a way that can be understood by a diverse readership without compromising scientific rigour, that despite this progress the data do not yet appear to be sufficiently robust for the CGPM to adopt the revised SI at its 25thmeeting,

  28. On the future revision of the International System of Units– part 3 • Encourages: • continued effort in the NMIs, the BIPM, and academic institutions to obtain data relevant to the determination of h, e, k, and NA with the requisite uncertainties, • the CIPM to continue developing a plan to provide the path via the Consultative Committees and the CCU for implementing Resolution 1 adopted by the CGPM at its 24th meeting (2011), • continued effort by the CIPMto complete all work necessary for the CGPM at its 26th meeting to adopt a resolution that would replace the current SI with the revised SI, provided the amount of data, their uncertainties, and level of consistency are deemed satisfactory. • The secondattempt to adopt a new measurement system - failed!

  29. Practical realization Avogadro collaboration (28Si-sphere), ur2 x 10-8 aimed at for 2014; ur 1.5 x 10-8 aimed at for 2015 NIST, NRC watt balances joint effort to resolve the difference NRC watt balance expect 2.5 x 10-8 in 2014 LNE watt balance first measurements mid 2012, objective ur close to 7.5 x 10-8 in 2014 BIPM watt balance firstmeasurements made, ur ≤ 5 x10-8 planned for 2015 NIM joule balance under development, < 10-7 in 2019 MSL watt balance first measurements 2014 but no published results, target 1 x 10-8

  30. Quantum metrological triangle 1. Josephsoneffect: Nobel Prize for Brian D. Josephson (1973) 2. Qunatum Hall effect (QHE) Nobel Prize for K. von Klitzing (1985) 3. Single electrontunneling Will be the Nobel Prize for Likharev and Averin? Likharev, Zorin, Jour. Low Temp. Physics, vol. 59 (1985)

  31. Qunatum metrological pyramid 1. Nawrocki, Revising the SI: the joule to replace the Kelvin as a base unit, Metrology and Measurement Systems, vol. 13 (2006) 2. Nawrocki, Introduction to Quantum Metrology, Springer, 2015

  32. System of basic units - proposal

  33. Conlusions 1. It isgenerallyaccepted to base a new system of unites on fundamentalphysicalconstants 2. The new system of unitsdefinedseparate from definitions of particularunitscould be not understoodwidely(for commonpeaple) 3. The newstandards of unitscan be acceptediftheywill be not expensive(the wattbalance set-upisexpensive, the Si spherecosts 2 mln Euro)

  34. 5th International Conference on Quantum Metrology 11 – 13 May, 2016, Poznan

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