Waldemar Nawrocki 1 and Yury Shukrinov Poznan University of Technology, Poznan, Poland 2 - Joint Institute for Nuclear Research, Dubna, Russia Workshop on Workshop on Precision Physics and Fundamental Physical Constants Dubna, December 2011 ROLE OF FUNDAMENTAL PHYSICAL CONSTANTS IN THE NEW SYSTEM OF UNITS – THE QUANTUM SI

Role of fundamental physical constants in the new system of units – the quantum SI Outline  History of measures  System International of Units (SI)  Classical standard and qunatum standard  Standards depend on fundamental physical constants  Resolution of the 23th CGPM of 2007  Resolution of the 24th CGPM of 2011  Proposal: the joule to repalce the kelvin as a base unit  Quantum metrological triangle and pyramid

The International System 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 1 : a system of units with 1 milimeter, 1832 r. – Proposal by Carl Gauss 1 : 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, England, Russia, Germany, …). Independent Poland accepted it in Standards of 1 metre i 1 kg. Standards of 1 metre i 1 kg.  1954 – MKSA system (metre, kilogram, second, amper).  1960 – SI (metre, kilogram, second, ampere, kelvin and candela); the mole as the 7 th base unit the mole as the 7 th base unit 1 – C. Gauss Die erdmagnetische Kraft auf ein absolutes Maß zurűckgefűhrt, – C. Gauss Die erdmagnetische Kraft auf ein absolutes Maß zurűckgefűhrt,1832.

System International 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 acoustic quantities. magnetic, thermal, light and acoustic quantities. Dr Terry Quinn, Director of BIPM ( ), Sevres

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 replace 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. 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 thre are atoms in kg of carbon 12. When the mole is used, elementary entities must be specufied and may be atom, 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 c = m/s = Hz = 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 NPL

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 based on fixed values of the fundamental constants, prepare a mise en pratique for each of them, and consider the most appropriate way of explaining the new definitions to users...”.

Units and Fundamental Physical Constants

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

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 available and to make the results known to the International Committee through its Consultative Committee for Units since these CODATA values and uncertainties will be those for the revised SI, …”

Resolution of the 24 th General Conference, 2011, Possible New Definitions for Units The 24 th General Conference take note the International 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 International 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,  ( 133 Cs) hfs is exactly hertz, 2. the speed of light in vacuum c 0 is exactly metre per second, 3. the Planck constant h is exactly X × 10 –34 joule second, 4. the elementary charge e is exactly X × coulomb, 5. the Boltzmann constant k B is exactly X × 10 –23 joule per kelvin, 6. the Avogadro constant N A is exactly X × reciprocal mole, 7. the luminous efficacy K of monochromatic radiation of frequency 540 × hertz is exactly 683 lumen per watt. 7. the luminous efficacy K cd of monochromatic radiation of frequency 540 × hertz is exactly 683 lumen per watt.

Fundamental physical constants from CODATA 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 2010 Revised 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

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

Qunatum metrological pyramid Nawrocki W., Revising the SI: the joule to replace the Kelvin as a base unit, Metrology and Measurement Systems, vol. 13 (2006)

Joule instead of Kelvin Proposal: Proposal: Replacement the kelvin, the unit for temperature, with the joule, the unit for energy (work and heat) Replacement the kelvin, the unit for temperature, with the joule, the unit for energy (work and heat). Nawrocki W., Revising the SI: the joule to replace the Kelvin as a base unit, Metrology and Measurement Systems, vol. 13 (2006)

Arguments for the replacement: Joule instead fo Kelvin 1. Energy is perhaps the most universal of all physical quantities in nature 1. Energy is perhaps the most universal of all physical quantities in nature The total quantity of energy in the universe remains constant (1st low of thermodynamics) The total quantity of energy in the universe remains constant (1st low of thermodynamics) 2. Energy is a common object of trade on a large scale 2. Energy is a common object of trade on a large scale 3. Different forms of energy allow to compare standard of mechanical, thermal, electrical quantities to the 3. Different forms of energy allow to compare standard of mechanical, thermal, electrical quantities to the E = h f; E = mc 2 ; E = U I t; E = F l; E = k B T; E = m v 2/ 2; Q =c h m  T 3. The definition of joule according SI and for base unitsantowych 3. The definition of joule according SI and for base unitsantowych 1J = m 2 kg s -2 1J = V s  1J = m 2 kg s -2 1J = V 2 s  Measurement resolution limits according to the Heisenberg`s formulas 4. Measurement resolution limits according to the Heisenberg`s formulas  x·  p  h  E·  t  h

System of basic units - proposal

Poznań – Old Market Square Conclusion: The role of fundamental physical constants for system of units is very large