The International System of Units:
A shift to fundamental constants
Alan Steele
NCSLI 2011
Facebook Metrology
Outline
• A bit about the SI and the Convention of the Metre
– Base Units in the International System
– Thinking about the metric system
– The General Conference on Weights and Measures
• Proposed
p
Changes
g to the SI
– Fundamental constants
– New definitions for kg, A, K, mol
– New wording for s, m, cd
• The time line for change – it’s not this year!
International System of Units
• SI units must be:
– stable, invariant, self-consistent
– independent of other parameters
– transferable at the lowest uncertainty
– realizable at the lowest uncertaintyy
SI & Fundamental Constants
•
SI units must be:
– stable, invariant, self-consistent
– independent of other parameters,
– transferable at the lowest uncertainty
– realizable at the lowest uncertainty
• Fundamental constants are:
– stable, invariant, self-consistent
– independent of other parameters,
parameters
– universally transferable
– determinations are sometimes limited by SI units
SI : Proposed Change
In essence
essence, the change involves exactly fixing the values of
7 constants that set the scale of the units themselves:
c – speed of light
Δν – ground state hyperfine splitting frequency of 133Cs
h – Planck constant
E = hυ
e – the elementary charge charge on an electron
k – Boltzmann constant
E = kT
NA – Avogadro constant
number of entities in a mole
Kcd – luminous efficacy of 540 × 1012 Hz radiation
Think about Speed
• With definitions for units of length (metre) and time
interval (second), we can derive a unit for speed:
v = d / t (in metre per second)
Speed Of Light
• With a definition for the unit of time interval (second)
and a fixed value for a fundamental constant such as
the speed of light (metre / second), we can define the
unit of length (metre):
d=c*s
• Th
The metre
t is
i the
th length
l
th off the
th path
th travelled
t
ll d b
by lilight
ht iin
vacuum during a time interval of 1/299 792 458 of a
second.
second
Not Quite the Speed Of Light
• If we used a different fixed value for the fundamental
constant we would alter the size of the unit of length:
d' = c' * s
• The newMetre is the length of the path travelled by
light in vacuum during a time interval of 1/300 000 000
off a second.
d It is
i slightly
li htl shorter
h t than
th the
th SI metre
t but
b t
the new speed of light is easier to remember!
Visit the BIPM Website...
...get the SI Brochure
...and read about the “New SI”
Metre Convention (1875)
• The International Bureau shall operate under the
exclusive direction and supervision of an International
Committee for Weights and Measures, itself placed
under the authority of a General Conference on
Weights and Measures, consisting of the delegates of
all the contracting Governments
Governments.
General Conference
• The mission of the CGPM is to discuss and instigate
measures necessary for the propagation and
improvement of the metric system as well as to
approve new fundamental metrological
determinations that might have been made in the
interval between its meetings
• Votes at a General Conference are made by
Member States, each State has the right to one vote.
Convocation of CGPM
• The General Conference on Weights and Measures is
convoked for its 24th meeting for Monday 17 October
2011 in Paris.
• Much of this talk is drawn from the Convocation
published to guide the meeting, circulated as a part of
the invitation to each of the Member States
• This includes background information and DRAFT
Resolutions on the various agenda items
The Original SI (~1880)
kg
m
N
J
W
s
K
Four base units, all independent
and all based on artefacts
g – international p
prototype
yp
kg
m – quadrant of the earth
s
– rotation of the earth
K – fixed points of water
The SI Today
Δν
kg
c
Kcd
μ
s
0
K
cd
mol
m
NA
N
A
u
m(12C)/12
J
C
V
F
Ω
W
The Electrical “SI”, As Used
• Since 1990 the Josephson and Quantum Hall effects
have been used to realize the volt and the ohm
SI Did NOT Change in 1990
• Adopting conventional values for RK-90
K 90 and KJ-90
J 90
improved electrical metrology
• Fixing the values of h and e at that time was not
possible since our knowledge was insufficient and we
would have broken the equivalence principle between
mechanical and electrical force
• Electrical metrology is routinely outside the SI and the
proposed change fixes this
CGPM Draft Resolution A
• takes note of the intention of the International Committee
for Weights and Measures to propose a revision to the SI as
follows:
• the International System of Units,
Units the SI,
SI will be the system
of units in which:
– the ground state hyperfine splitting frequency of the caesium 133 atom
Δν(133Cs)hfs
hf 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 06X × 10-34 joule second,
– the elementary charge e is exactly 1.602 17X × 10-19 coulomb,
– the Boltzmann constant k is exactly 1.380 6X × 10-23 joule per kelvin,
– the Avogadro constant NA is exactly 6.022 14X × 1023 reciprocal mole,
– the luminous efficacyy Kcd of monochromatic radiation of frequency
q
y
540 × 1012 Hz is exactly 683 lumen per watt,
Base Units: kg
• the kilogram will continue to be the unit of mass
• its magnitude will be set by fixing the numerical value
of the Planck constant to be equal to exactly
6.626 06X × 10-34 when it is expressed in the SI unit
m2 kg s-11, which is equal to J s
Base Units: A
• the ampere will continue to be the unit of electric
current
• its magnitude will be set by fixing the numerical value
of the elementary charge to be equal to exactly
19 when it is expressed in the SI unit
1.602 17X × 10-19
A s, which is equal to C,
Base Units: K
• the kelvin will continue to be the unit of
thermodynamic temperature
• its magnitude will be set by fixing the numerical value
of the Boltzmann constant to be equal to exactly
23 when it is expressed in the SI unit
1.380 6X × 10-23
m2 kg s-2 K-1, which is equal to J K-1,
Base Units: mol
• the mole will continue to be the unit of amount of
substance of a specified elementary entity
• its magnitude will be set by fixing the numerical value
of the Avogadro constant to be exactly equal to
23 when it is expressed in the SI unit
6.022 14X × 10-23
mol-1.
New Wording for Old Units
• Although there is no immediate intention to change
the definitions for the second, metre or candela the
intention is to re-write them using the new language to
enhance the understandability of the new System
Base Units: s
• the second 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 SI unit s-1, which is equal to Hz
Base Units: m
• the metre 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 SI unit m s-1
Base Units: cd
• the candela 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 SI unit m-2 kg-1 s3 cd sr, or
cd sr W-1, which is equal to lm W-1
The Proposed Change
NA
c
Δν
h
e
k
Kcd
mol
m
s
V
Ω
K
cd
dalton
~m((12C)/12
A
F
u
W
Mu
kg
1u ~ m(12C)/12 No longer Exact
an experimentally derived quantity
μ
ε
0
No llonger exact,
N
t
a derived quantity
0
No longer exact,
d i d quantity
tit
a derived
Nothing Is Free...
• To ensure a seamless transition for the four base
units involved in the proposal, we will use the best
experimental values of the fundamental constants to
make the change
• The best experimental uncertainties of the four
fundamental constants involved in the proposed
change don’t
don t just disappear forever when we fix their
values
Consequence for kilogram
• The mass of the international prototype of the
kilogram m(K) will be exactly 1 kg but with a relative
uncertainty equal to that of the recommended value of
h just before redefinition and that subsequently its
value will be determined experimentally
Consequence for Ampere
• The magnetic constant (permeability of vacuum) μ0
will be exactly 4π × 10-7 H m-1 but with a relative
uncertainty equal to that of the recommended value of
the fine-structure constant α and that subsequently its
value will be determined experimentally
Consequence for Kelvin
• The thermodynamic triple point of water TTPW will be
exactly 273.16 K but with a relative uncertainty equal
to that of the recommended value of k just before
redefinition and that subsequently its value will be
determined experimentally
Consequence for mole
• The molar mass of carbon 12 M(12C) will be exactly
0.012 kg mol-1 but with a relative uncertainty equal to
that of the recommended value of NA just before
redefinition and that subsequently its value will be
determined experimentally.
The Proposed Change
NA
c
Δν
h
e
k
Kcd
mol
m
s
V
Ω
K
cd
dalton
~m((12C)/12
A
F
u
W
Mu
kg
1u ~ m(12C)/12 No longer Exact
an experimentally derived quantity
μ
ε
0
No llonger exact,
N
t
a derived quantity
0
No longer exact,
d i d quantity
tit
a derived
When Will This Happen?
k
e
Δν
NA
c
Kcd
• When we’re sure we’re ready!
h