Transcript Folie 1

Revision of the SI
Arnold Leitner
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
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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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
IPK
international
prototype IPK
Courtesy of the BIPM
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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Proposed revision of the SI
• Draft Resolution A for the 24th CGPM,
17 – 21 October 2011
http://www.bipm.org/utils/common/pdf/24_CGPM_Convo
cation_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 Brochure
http://www.bipm.org/utils/common/pdf/si_brochure_draft
_ch2.pdf
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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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"
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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How to redefine
the kilogram?
Fundamental
constant ?
National kilogram prototype
no 49 of Austria
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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The BIPM watt
balance
http://www.bipm.org/en/scientific/el
ec/watt_balance/wb_bipm.html
Electrical
power
Mechanical
power
UI = mgv
f1 f2 h ~ m g v
Courtesy of the BIPM
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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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)
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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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
Kcd
Kcd
luminous efficacy of a
540 THz source
candela cd
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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One statement to define the new SI
The 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 the
numerical values of h, e, k, and NA.
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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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 kilogram
exactly, 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 Planck
constant is a constant of nature, which may be expressed as the product of a number and
the unit joule second, where J s = s-1 m2 kg. The effect of this definition, together with those
for the second and the metre, is to allow the unit of mass to be defined in terms of
frequency, through two of the most fundamental equations of physics, namely E = mc2 and
E = hν, which relate energy E to mass m and frequency ν and which together lead to the
relation m = (h / c2) ν.
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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Present definition of the ampere
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.
It follows that the magnetic constant µ0, also known as the permeability of free
space, is 4 π  10-7 H/m exactly.
Recommended new definition
The 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 is
that the ampere is the electric current corresponding to the flow of 1/(1.602 17…  10-19 )
elementary charges per second.
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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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.
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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Present definition of the mole
1. 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 definition
The 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.
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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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 radiation
corresponding to the transition between the two hyperfine levels of the ground state of the
caesium 133 atom.
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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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 that
the metre is the length of path travelled by light in vacuum during the time interval of
1/299 792 458 of a second.
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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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 a
radiant intensity in that direction of 1/683 W/sr.
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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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: ?
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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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 ?
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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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.
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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Thank you four your attention!
[email protected]
www.bev.gv.at
www.metrologie.at
Revision of the SI
46th CIML Meeting
11 – 14 October 2011, Prague, Czech Republik
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