arnold leitner revision of the si. 46 th ciml meeting 11 – 14 october 2011, prague, czech republik...

Arnold LeitnerRevision of the SI

Revision of the SI 46th CIML Meeting11 – 14 October 2011, Prague, Czech Republik

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Why change the SI?

• The kilogram is still defined in terms of a material artefact (IPK)

• This artefact cannot be absolutely stable – drift?• Changes in mass also influence electrical units,

mole, candela.• The CGPM recommended 1999 to refine

experiments linking the units of mass to fundamental constants – view to a redifinition

• The CIPM is proposing to the CGPM 2011 a future revision of the SI


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The third periodic verification of national prototypes of the kilogram (1988-1992)G. Girard, http://www.bipm.org/utils/common/pdf/3eVerificationkg-EN.pdf

Change in mass Δm of the six official copies and of prototype No. 25 with respect to the mass of the international prototype IPK

IPK

Courtesy of the BIPM

http://www.bipm.org/utils/common/pdf/3eVerificationkg-EN.pdf


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Proposed revision of the SI

• Draft Resolution A for the 24th CGPM, 17 – 21 October 2011http://www.bipm.org/utils/common/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf

to take note of the intention to redefine four of the SI base units

• Draft Revision of Chapter 2 of the SI Brochurehttp://www.bipm.org/utils/common/pdf/si_brochure_draft_ch2.pdf

http://www.bipm.org/utils/common/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf

http://www.bipm.org/utils/common/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf

http://www.bipm.org/utils/common/pdf/si_brochure_draft_ch2.pdf

http://www.bipm.org/utils/common/pdf/si_brochure_draft_ch2.pdf


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What changes are proposed?

• It is the intention of the CIPM to express the definitions of all seven base units of the SI in a uniform manner using the "explicit-constant formulation", in which "the unit is defined indirectly by specifying explicitly an exact value for a well-recognized fundamental constant"


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National kilogram prototype no 49 of Austria

How to redefine the kilogram?

Fundamental constant ?


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The BIPM watt balance

http://www.bipm.org/en/scientific/elec/watt_balance/wb_bipm.html

Courtesy of the BIPM

U I = m g v

f1 f2 h ~ m g v

Electrical power

Mechanical power




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The Avogadro project

Counting atoms in a silicon sphere

NA = n Vsph MSi / msph

NA = (c Me α 2)/(2R∞ h)


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Reference constants used to define the base units

current SI new SI

second s Δν(133Cs)hfs Δν(133Cs)hfs Cs hyperfine splitting

metre m c c speed of light in vacuum

kilogram kg m(IPK) h Planck constant

ampere A μ0 e elementary charge

kelvin K TTPW k Boltzmann constant

mole mol M(12C) NA Avogadro constant

candela cd Kcd Kcd luminous efficacy of a540 THz source


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One statement to define the new SIThe International System of Units, the SI, will be the system of units in

which:• the ground state hyperfine splitting frequency of the caesium 133

atom Δν(133Cs)hfs is exactly 9 192 631 770 hertz,• the speed of light in vacuum c is exactly 299 792 458 metre per

second,• the Planck constant h is exactly 6.626 06… ×10-34 joule second,• the elementary charge e is exactly 1.602 17… ×10-19 coulomb,• the Boltzmann constant k is exactly 1.380 6… ×10-23 joule per

kelvin,• the Avogadro constant NA is exactly 6.022 14… ×1023 reciprocal

mole,• the luminous efficacy Kcd of monochromatic radiation of frequency

540 ×1012 Hz is exactly 683 lumen per watt,where … represent one or more additional digits to be added to thenumerical values of h, e, k, and NA.


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Present definition of the kilogram

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.

It follows that the mass of the international prototype of the kilogram is always 1 kilogramexactly, m(K) = 1 kg.

Recommended new definition

The kilogram, kg, is the unit of mass; its magnitude is set by fixing the numerical value of the Planck constant to be equal to exactly

6.626 06… 10−34 when it is expressed in the unit s−1 m2 kg, which is equal to J s.

Thus we have the exact relation h = 6.626 06…10−34 J s. The value of the Planckconstant is a constant of nature, which may be expressed as the product of a number andthe unit joule second, where J s = s-1 m2 kg. The effect of this definition, together with thosefor the second and the metre, is to allow the unit of mass to be defined in terms offrequency, through two of the most fundamental equations of physics, namely E = mc2 andE = hν, which relate energy E to mass m and frequency ν and which together lead to the relation m = (h / c2) ν.


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Present definition of the ampereThe 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.

It follows that the magnetic constant µ0, also known as the permeability of freespace, is 4 π 10-7 H/m exactly.

Recommended new definitionThe ampere, A, is the unit of electric current; its magnitude is set by fixing the numerical value of the elementary charge to be equal to exactly 1.602 17… 10−19 when it is expressed in the unit s A, which is equal to C.

Thus we have the exact relation e = 1.602 17… 10-19 C. The effect of this definition isthat the ampere is the electric current corresponding to the flow of 1/(1.602 17… 10-19 )elementary charges per second.


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Present definition of the kelvin

The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

It follows that the thermodynamic temperature of the triple point of water is exactly 273.16 kelvin Ttpw = 273.16 K.

Recommended new definition

The kelvin, K, is the unit of thermodynamic temperature; its magnitude is set by fixing the numerical value of the Boltzmann constant to be equal to exactly 1.380 6… 10−23 when it is expressed in the unit s-2 m2 kg K-1, which is equal to J K-1.

Thus we have the exact relation k = 1.380 65… 10-23 J/K. The effect of this definition is That the kelvin is equal to the change of thermodynamic temperature that results in a change of thermal energy kT by 1.380 65… 10-23 J/K.


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Present definition of the mole1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12.

2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

It follows that the molar mass of carbon 12 is exactly 12 grams per mole. M(12C) = 12 g/mol.

Recommended new definitionThe mole, mol, is the unit of amount of substance of a specified elementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles; its magnitude is set by fixing the numerical value of the Avogadro constant to be equal to exactly 6.022 14… 1023 when it is expressed in the unit mol-1.

Thus we have the exact relation NA = 6.022 14… 1023 mol-1. The effect of this definition is that the mole

is the amount of substance of a system that contains 6.022 14… 1023 specified elementary entities.


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Present definition of the second

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 caesium 133 atom.

It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly

9 192 631 770 Hz.

Recommended new definition (reformulation)

The second, s, is the unit of time; its magnitude is set by fixing the numerical value of the ground state hyperfine splitting frequency of the caesium 133 atom, at rest and at a temperature of 0 K, to be equal to exactly 9 192 631 770 when it is expressed in the unit s-1, which is equal to Hz.

Thus we have the exact relation Δν(133Cs)hfs = 9 192 631 770 Hz. The effect of this definition is that the second is the duration of 9 192 631 770 periods of the radiationcorresponding to the transition between the two hyperfine levels of the ground state of thecaesium 133 atom.


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Present definition of the metre

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.

It follows that the speed of the light in vacuum c is 299 792 458 m/s exactly.

Recommended new definition (reformulation)The metre, m, is the unit of length; its magnitude is set by fixing the numerical value of the speed of light in vacuum to be equal to exactly

299 792 458 when it is expressed in the unit m s-1. Thus we have the exact relation c = 299 792 458 m/s. The effect of this definition is thatthe metre is the length of path travelled by light in vacuum during the time interval of1/299 792 458 of a second.


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Present definition of the candela

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.

It follows that the candela is the luminous intensity, in a given direction, of a source of monochromatic radiation with a frequency of 540 1012 Hz that has a radiant intensity of 1/683 W/sr.

Recommended new definition (reformulation)

The candela, cd, is the unit of luminous intensity in a given direction; its magnitude is set by fixing the numerical value of the luminous efficacy of monochromatic radiation of frequency 540 1012 Hz to be equal to exactly 683 when it is expressed in the unit s3 m-2 kg-1 cd sr, or cd sr W-1, which is equal to lm W-1.

Thus we have the exact relation Kcd = 683 lm/W for monochromatic radiation of frequency ν = 540 × 1012 Hz. The effect of this definition is that the candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 ×1012 Hz and that has aradiant intensity in that direction of 1/683 W/sr.


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Recommendation of CCM (G1 - 2010)

• At least three independent experiments, with u≤5∙10-8 (at least one with u≤2∙10-8)Consistency at the 95 % level of confidence

• Target uncertainty in the realization of the kilogram u≤2∙10-8

• Prepare a mise en pratique• status: 2 results u≤5∙10-8 (NIST 2007, Avogadro

2011), but discrepancy: 17 ∙10-8 • Timeline: ?


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Recommendation of CCT (T2 – 2010)

• a relative standard uncertainty of the value of k of order one part in 106 be obtained, based on measurements applying different methods of primary thermometry

• at least two fundamentally different methods such as acoustic gas thermometry and dielectric constant gas thermometry, corroborated by other measurements such as Johnson noise thermometry, total radiation thermometry or Doppler broadening thermometry

• Timeline: 2 years ?


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What is a mise en pratique?

• A mise en pratique for the definition of a unit is a set of instructions that allows the definition to be realized in practice at the highest level.

• A “pool of artefacts” developed at the BIPM will play an important role in the mise en pratique of the future definition of the kilogram for the dissemination of the unit of mass.

• The new definition has to be considered together with the mise en pratique when studying the impact on legal metrology.


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Thank you four your attention!

[email protected]

www.bev.gv.at

www.metrologie.at

mailto:[email protected]

http://www.bev.gv.at/

http://www.metrologie.at/

arnold leitner revision of the si. 46 th ciml meeting 11 – 14 october 2011, prague, czech republik...

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