Waldemar Waldemar NawrockiNawrocki11 andand YuryYury Shukrinov Shukrinov22

1 - Poznan University of Technology, Poznan, Poland1 - Poznan University of Technology, Poznan, Poland2 - Joint Institute for Nuclear Research, Dubna, Russia2 - Joint Institute for Nuclear Research, Dubna, Russia

Workshop onWorkshop 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 History of measures System International of Units (SI) System International of Units (SI) Classical standard and qunatum standardClassical standard and qunatum standard Standards depend on fundamental physical Standards depend on fundamental physical

constantsconstants Resolution of the 23th CGPM of 2007Resolution of the 23th CGPM of 2007 Resolution of the 24th CGPM of 2011Resolution of the 24th CGPM of 2011 Proposal: the joule to repalce the kelvin as a Proposal: the joule to repalce the kelvin as a

base unitbase unit Quantum metrological triangle and pyramidQuantum metrological triangle and pyramid

The International System of Units

17991799 – The Standard of the – The Standard of the 1 metre1 metre and of the and of the 1 kg1 kg (Pt+Ir) in Paris. (Pt+Ir) in Paris.

1 m = 1/10 000 000 fraction of the meridian between the pole and the equator. 1 m = 1/10 000 000 fraction of the meridian between the pole and the equator.

1 kg = mass of 1/1000 m1 kg = mass of 1/1000 m33 fraction of pure water. fraction of pure water.

11832832 r. – Proposal by Carl Gauss r. – Proposal by Carl Gauss11: a system of units with 1 milimeter, : a system of units with 1 milimeter,

1 gram, 1 second. The base for the 1 gram, 1 second. The base for the CGSCGS system of units. system of units. 1860-18701860-1870 – Proposal by Maxwell and Thomson: a coherent system – Proposal by Maxwell and Thomson: a coherent system

of units with base units and derived unitsof units with base units and derived units 1875 1875 – The Metre Convention, accepted by 17 – The Metre Convention, accepted by 17 countries countries (France, (France,

EnglandEngland, Russia, Russia, Germany, …). Independent , Germany, …). Independent Poland Poland accepted it in 1925.accepted it in 1925.

Standards of 1 metre i 1 kg. Standards of 1 metre i 1 kg. 19541954 – – MKSAMKSA system (metre, kilogram, second, amper). system (metre, kilogram, second, amper). 19601960 – – SISI (metre, kilogram, second, ampere, kelvin and candela); (metre, kilogram, second, ampere, kelvin and candela);

1971 1971 - the mole as the 7- the mole as the 7thth base unit base unit

1 – C. Gauss 1 – C. Gauss Die erdmagnetische Kraft auf ein absolutes MaßDie erdmagnetische Kraft auf ein absolutes Maß zurűckgefűhrtzurűckgefűhrt,1832.,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 molekelvin, candel and mole 2. The auxiliary units: the radian and the steradian2. 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.

m

s

m o lA

K

k g

Dr Terry Quinn,Director of BIPM (1988-2003), Sevres

System International definitions of the kilogram, ampere, kelvin and mole

1.1. The kilogram is the unit of mass; it is equal to the mass of the international prototype of the The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. kilogram. The first candidate to be replace by a new definitionThe 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 2. The ampere is that constant current which, if maintained in two straight parallel conductors of infiniteinfinite length, of length, of negligiblenegligible circular cross-section, and placed circular cross-section, and placed

1 m apart in vacuum, would produce between these conductors a force equal to 2 × 101 m apart in vacuum, would produce between these conductors a force equal to 2 × 10 –7–7 newton per newton per metre of length. metre of length.

3. The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of3. The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 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 4. The mole is the amount of substance of a system which cointains as many elementary entities as thre are atoms in 0.012 kg of carbon 12. When the mole is used, elementary entities must be specufied are atoms in 0.012 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.and may be atom, moleculs, ions, electrons, other particles, or specified groups of such patrticles.

System Internationaldefinitions of the metre, second and candela

5. The metre is the length of the path travelled by light in vacuum during5. 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.a time interval of 1/299 792 458 of a second.

6. The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition 6. 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 Cs 133.between the two hyperfine levels of the ground state of the Cs 133.

7. 7. The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 of frequency 540 10101212 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. 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 In the above 3 definitions physical constants are known exactlyexactly (assumption):): cc = 299 792 458 m/s = 299 792 458 m/s = 9 192 631 770 Hz= 9 192 631 770 HzPP = 683 W/steradian = 683 W/steradian

The 1 kg mass standard, in Central Office of Measures in Warsaw

1 kg standardPt 90% + Ir 10%D = h = 39 mm

NPL

Voltage standards with Josephson junctions

+127 nV

Generator75.1GHz Komputer

Magistrala IEEE-488

19000 złącz Josephsona

UwzwzorcewtórneZenera

fale 75 GHz

Generatormikrofalowy

Tłumik

4,2 K

VC

Częstośc iomierz

Ato

mow

y w

zorz

ecc

zęst

otli

woś

ci

U

U

I

Sochocka, Nawrocki, Elektronika, vol. 42 (2001), nr 11.

Quantum Hall Effect Standard at Central Office of Measures in Warsaw

(the sample from NPL)

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 ofrecent advances, there are significant implications for, and potential benefitsfrom, redefinitions of the kilogram, the ampere, the kelvin and the mole …”.

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 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 ...”.

www.bipm.org/en/convention/cgpm

Units and Fundamental Physical Constants

Different New Definitions of the 1 kg1.1. The kilogram is the mass of a body whose Compton frequency is 1.356392The kilogram is the mass of a body whose Compton frequency is 1.356392XXXXXX… × 10… × 105050

hertz exactlyhertz exactly. . ((frequency of cosmic ray ~ frequency of cosmic ray ~ 10102424 Hz) Hz)

2.2. The kilogram is the mass of a body whose de Broglie-Compton frequency is equal to exactly The kilogram is the mass of a body whose de Broglie-Compton frequency is equal to exactly [(299 792 458[(299 792 45822/(6.626 0693) × 10/(6.626 0693) × 10–34–34)) [ [hertz hertz ]]..

3.3. The kilogram is the mass of a body whose equivalent energy is equal to that of a number of The kilogram is the mass of a body whose equivalent energy is equal to that of a number of photons whose frequencies sum to exactlyphotons whose frequencies sum to exactly

[(299 792 458[(299 792 45822/(66 260 693)] × 10/(66 260 693)] × 104141 hertz. hertz.

1.1. The kilogram, unit of mass, is such that the Planck constant is exactly The kilogram, unit of mass, is such that the Planck constant is exactly h h = 6.626 0693 × = 6.626 0693 × 1010–34–34 Js Js..

2.2. The kilogram is (6.022 1415 × 10The kilogram is (6.022 1415 × 102323/0.012) times the rest mass of the /0.012) times the rest mass of the 1212C atom in the ground C atom in the ground state. state.

3.3. The kilogram is (6.022 1415 × 10The kilogram is (6.022 1415 × 102323/0.012) times the rest mass of a particle whose creation /0.012) times the rest mass of a particle whose creation energy equals that of a photon whose frequency is: energy equals that of a photon whose frequency is:

[0.012/(6.022 1415 × 10[0.012/(6.022 1415 × 102323) × 299 792 458) × 299 792 45822/66 260 693 × 10/66 260 693 × 10–34–34)) [ [hertzhertz].].

7. 7. The kilogram is 1.097 769 24 × 10The kilogram is 1.097 769 24 × 103030 times the rest mass of the electron times the rest mass of the electron..

The Si sphere – the possible standard of the 1 kilogram

Silicon sphere Silicon sphere at the PTB, at the PTB, BraunschweigBraunschweig

DD = 90 mm = 90 mm diameter controlled in diameter controlled in 16 000 directions16 000 directions 2 mln Euro2 mln Euro

New definitions of ampere, kelvin and mole

1.1. The ampere is the electrical current equivalent to the flow of The ampere is the electrical current equivalent to the flow of exactly 1/(1.602 176 53 × 10exactly 1/(1.602 176 53 × 10-19-19) elementary charges per ) elementary charges per secondsecond..

2. 2. The kelvin is the change of thermodynamic temperature The kelvin is the change of thermodynamic temperature T T that that results in a change of thermal energy results in a change of thermal energy kT kT by exactly by exactly

1.380 6488 × 101.380 6488 × 10–23 –23 joule, where joule, where kk is the Boltzmann constant. is the Boltzmann constant.

3. 3. The mole is the unit of amount of substance. It is equal to The mole is the unit of amount of substance. It is equal to

6.022 1415 × 106.022 1415 × 102323 mol mol-1-1 specified identical entities. The entities specified identical entities. The entities may be atoms, ions, molecules or other particles.may be atoms, ions, molecules or other particles.

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

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 24th 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, …”

www.bipm.org/en/convention/cgpm

Resolution of the 24th General Conference, 2011, Possible New Definitions for Units

TThe 2he 244thth General Conference General Conference take note take note of intention of the International the International Committee Committee for Weights and Measures to propose a revision of the SI as follows:for Weights and Measures to propose a revision of the SI as follows:

TThe International System of Units, the SIhe International System of Units, the SI,, will be will be the system of units the system of units in whichin which::

1.1.the the ground state hyperfine splitting frequency of the caesium 133 atomground state hyperfine splitting frequency of the caesium 133 atom

((133133Cs)Cs)hfshfs is is exactly exactly 9 192 631 770 hertz,9 192 631 770 hertz,

2. the 2. the speed of light in vacuum speed of light in vacuum cc0 0 is is exactly exactly 299 792 458 metre per second, 299 792 458 metre per second,

3. the 3. the Planck constant Planck constant hh is is exactly exactly 6.626 066.626 06XX × 10 × 10–34–34 joule second, joule second,

4. the 4. the elementary charge elementary charge ee is is exactly exactly 1.602 171.602 17XX × 10 × 10-19-19 coulomb, coulomb,

5. the 5. the Boltzmann constant Boltzmann constant kkBB is is exactly exactly 1.380 61.380 6XX × 10 × 10–23–23 joule per kelvin, joule per kelvin,

6. the 6. the Avogadro constant Avogadro constant NNAA is is exactly exactly 6.022 146.022 14XX × 10 × 102323 reciprocalreciprocal mole, mole,

7. the7. the luminous efficacy luminous efficacy KKcd of monochromatic radiation of frequency 540 × 10of monochromatic radiation of frequency 540 × 101212

hertz is hertz is exactly exactly 683 lumen per watt.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 NA using values based on the most recent CODATA adjustment” – Resolution of 24th CGPM

Source CODATA 1986

CODATA 2010

Revised SIGCPM 2011

Planck constant h Js 6.626 075 5 × 10–34

6.626 069 3 × 10–34

6.626 06X × 10–34

elementary charge e C 1.602 177 33 × 10-19

1.602 176 53 × 10-19

1.602 17X× 10-19

Boltzmann constant k J/K 1.380 658 × 10–23

1.380 648 8 × 10–23

1.380 6X × 10–23

Avogadro constant NA mole 6.022 136 7 × 1023

6.022 141 5 × 1023

6.022 14X × 1023

V h e f = ( /2 )

R h e i = ( / )/

I ef e f = (2 ) or

2

Quantum metrological triangle

1. Josephson effect:1. Josephson effect: Nobel Prize for Brian D. Josephson Nobel Prize for Brian D. Josephson (1973)(1973)

2. Qunatum Hall effect (QHE)2. Qunatum Hall effect (QHE) Nobel Prize for Klaus von Klitzing Nobel Prize for Klaus von Klitzing (1985)(1985)

3. Single electron tunneling 3. Single electron tunneling Will be the Nobel Prize for Likharev and Will be the Nobel Prize for Likharev and Averin?Averin?

Likharev, Zorin, Jour. Low Temp. Physics, vol. 59 (1985)

Qunatum metrological pyramid

V h e f = ( /2 ) R h e i = ( / )/ I ef e f = (2 ) or

Q e e= 2or

E hf =

h/ e = 2

2

0

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

ProposalProposal: :

Replacement the kelvin, the unit for Replacement the kelvin, the unit for temperature, with the joule, the unit for temperature, with the joule, the unit for energy (work and heat) 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 nature1. Energy is perhaps the most universal of all physical quantities in nature

The total quantity of energy in the universe remains constant The total quantity of energy in the universe remains constant (1st low of (1st low of thermodynamics)thermodynamics)

2. Energy is a common object of trade on a large scale2. Energy is a common object of trade on a large scale

3. Different forms of energy allow to compare standard of mechanical, 3. Different forms of energy allow to compare standard of mechanical, thermal, electrical quantities to the thermal, electrical quantities to the

E = h f; E = mc2; E = U I t; E = F l; E = kBT; E = m v2/2; Q =chm T

3. The definition of joule according SI and for base unitsantowych3. The definition of joule according SI and for base unitsantowych

1J = m1J = m22 kg s kg s-2-2 1J = V1J = V2 s s -1

4. Measurement resolution limits according to the Heisenberg`s formulas4. Measurement resolution limits according to the Heisenberg`s formulas

x·p hE·t h

System of basic units - proposal

m

kgs

1 m

J mol

cd

Cs

Poznań – Old Market Square

Conclusion:The role of fundamental physical constants for system of units is very large