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 13 th, 2015

THE NEW SYSTEM OF UNITS BASED ON FUNDAMENTAL PHYSICAL CONSTANTS - THE NEXT APROACH Outline  History of measures  System International of Units (SI)  Regular standards and qunatum standards  Standards depend on fundamental physical constants  Resolution of the CGPM of 2007 and 2011  Resolution of the 25th CGPM of 2014  Quantum metrological triangle and pyramid

International Systems of Units  1799 – The Standard of the 1 metre and of the 1 kg (Pt+Ir) in Paris. 1 m = 1/ fraction of the meridian between the pole and the equator. 1 m = 1/ fraction of the meridian between the pole and the equator. 1 kg = mass of 1/1000 m 3 fraction of pure water. 1 kg = mass of 1/1000 m 3 fraction of pure water r. – Proposal by Carl Gauss: a system of units with 1 milimeter, 1832 r. – Proposal by Carl Gauss: a system of units with 1 milimeter, 1 gram, 1 second. The base for the CGS system of units. 1 gram, 1 second. The base for the CGS system of units.  – Proposal by Maxwell and Thomson: a coherent system of units with base units and derived units  1875 – The Metre Convention, accepted by 17 countries (France, Russia, Turkey, England, Germany, …). Independent Poland accepted it in Practical standards of 1 metre and 1 kg. Practical standards of 1 metre and 1 kg.

MKSA and SI International Systems of Units  1954 – MKSA system (metre, kilogram, second, ampere).  1960 – SI (metre, kilogram, second, ampere, kelvin and candela); the mole as the 7 th base unit in the SI the mole as the 7 th base unit in the SI

System International (SI) System create: System create: 1. The base units: metre, kilogram, second, ampere, 1. The base units: metre, kilogram, second, ampere, kelvin, candel and mole kelvin, candel and mole 2. The auxiliary units: the radian and the steradian 2. The auxiliary units: the radian and the steradian 3. The 22 derived untis for electrical, mechanical, 3. The 22 derived untis for electrical, mechanical, magnetic, thermal, light and accoustic quantities. magnetic, thermal, light and accoustic quantities.

System International definitions of the kilogram, ampere, kelvin and mole 1. The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. The first candidate to be replaced by a new definition 2. 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. 3. The kelvin, unit of thermodynamic temperature, is the fraction 1/ of the thermodynamic temperature of the triple point of water, the thermodynamic temperature of the triple point of water, 4. The mole is the amount of substance of a system which cointains as many elementary entities as there are atoms in kg of carbon 12. When the mole is used, elementary entities must be specified and may be atoms, moleculs, ions, electrons, other particles, or specified groups of such patrticles.

System International definitions of the metre, second and candela 5. The metre is the length of the path travelled by light in vacuum during a time interval of 1/ of a second. a time interval of 1/ of a second. 6. The second is the duration of periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the Cs The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540  hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. In the above 3 definitions physical constants are known exactly): In the above 3 definitions physical constants are known exactly (assumption): c = m/s, = Hz, P = 683 W/steradian c = m/s, = Hz, P = 683 W/steradian

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

The IPK (1 kg) changes its mass NPL The international prototype of the kilogram (IPK) has been used since 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.

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

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

12 th Resolution of the 23 th General Conference on Weights and Measures th General Conference c onsidered : “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 (2 nd 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 N A,, initiatives to determine the value of a number of relevant fundamental constants, including work to redetermine the Boltzmann constant k B, 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 …”.

Resolution of the 23 th General Conference on Weights and Measures Following the above arguments, the 23 th General Conference (CGPM) recommended in the 12 th 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 24 th General Conference (2011), should, together with the International Committee and 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...”.

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

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 N A using values based on the most recent CODATA adjustment” – Resolution of 24th CGPM SourceCODATA 1986 CODATA 2014Revised SI GCPM 2011 Planck constant hJs × 10 – × 10 – X × 10 –34 elementary charge eC × × X × Boltzmann constant kJ/K × 10 – × 10 – X × 10 –23 Avogadro constant N A mole × × X × 10 23

Different New Definitions of the 1 kg 1. The kilogram is the mass of a body whose Compton frequency is XXX… × hertz exactly. (frequency of cosmic ray ~ Hz) 2. The kilogram is the mass of a body whose de Broglie-Compton frequency is equal to exactly [( /( ) × 10 –34 ) [hertz ]. 3. 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 [( /( )] × hertz. [( /( )] × hertz. 1. The kilogram, unit of mass, is such that the Planck constant is exactly h = × 10 –34 Js. 2. The kilogram is ( × /0.012) times the rest mass of the 12 C atom in the ground state. 3. The kilogram is ( × /0.012) times the rest mass of a particle whose creation energy equals that of a photon whose frequency is: [0.012/( × ) × / × 10 –34 ) [hertz]. [0.012/( × ) × / × 10 –34 ) [hertz]. 7. The kilogram is × times the rest mass of the electron.

The Si sphere – the possible standard of the 1 kilogram Silicon sphere at the PTB, Braunschweig D = 90 mm diameter controlled in directions 2 mln Euro

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

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

Resolution of the 24 th General Conference on Weights and Measures The 24 th 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 23 th General Conference in 2007 have been satisfied and so the International Committee for Weights and Measures is not 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 24 th 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!

In 2010, Consultative Committee for Mass made the following recommendations (confirmed in February 2013): Requirements for the redefinition of the kg ● Conditions before redefining the kilogram: 1. at least 3 independent results (watt balance and XRCD) with u r < 5 x at least 1 result with u r ≤ 2 x 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.

The results of measurements of h k= x 10 -7

Resolution of the 24 th GCPM, 2011, Possible new definition of SI The 24 th General Conference take note the Int. Committee for Weights and Measures to propose a revision of the SI as follows: The 24 th General Conference take note of intention of the Int. Committee for Weights and Measures to 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  ( 133 Cs) hfs is exactly hertz,  second, Hz  ( 133 Cs) hfs is exactly hertz,  second, Hz 2. the speed of light in vacuum c 0 is exactly metre per second,  m 3. the Planck constant h is exactly X × 10 –34 joule second,  kg 4. the elementary charge e is exactly X × coulomb,  A 5. the Boltzmann constant k B is exactly X × 10 –23 joule per kelvin,   K 6. the Avogadro constant N A is exactly X × reciprocal mole,  mol 7. the luminous efficacy K of monochromatic radiation of frequency 7. the luminous efficacy K cd of monochromatic radiation of frequency 540 × hertz is exactly 683 lumen per watt.  cd 540 × hertz is exactly 683 lumen per watt.  cd Comment: it is no proposal for a new systems of units. It is the set of physical constants!

The recent results of measurements of h, K J, and k Milton, Davis, Fletcher, Towards a new SI: a review of progress made since 2011, Metrologia, 51 (2014)

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

On the future revision of the International System of Units Resolution th General Conf. on Weights and Measures 2014 Recalling the Resolution 12 of the 23 rd CGPM (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

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 25th meeting,

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 CIPM to 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 second attempt to adopt a new measurement system - failed! The second attempt to adopt a new measurement system - failed!

Practical realization Avogadro collaboration ( 28 Si-sphere), u r  2 x aimed at for 2014; u r  1.5 x aimed at for 2015 NIST, NRC watt balancesjoint effort to resolve the difference NRC watt balanceexpect 2.5 x in 2014 LNE watt balancefirst measurements mid 2012, objective u r close to 7.5 x in 2014 BIPM watt balancefirst measurements made, u r ≤ 5 x10 -8 planned for 2015 NIM joule balanceunder development, < in 2019 MSL watt balancefirst measurements 2014 but no published results, target 1 x 10 -8

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

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

System of basic units - proposal

Conlusions 1. It is generally accepted to base a new system of unites on fundamental physical constants 1. It is generally accepted to base a new system of unites on fundamental physical constants 2. The new system of units defined separate from definitions of particular units could be not understood widely (for common peaple) 2. The new system of units defined separate from definitions of particular units could be not understood widely (for common peaple) 3. The new standards of units can be accepted if they will be not expensive (the watt balance set-up is expensive, the Si sphere costs 2 mln Euro ) 3. The new standards of units can be accepted if they will be not expensive (the watt balance set-up is expensive, the Si sphere costs 2 mln Euro )

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