“From Artefacts to Atoms”

“From Artefacts to Atoms”

Sur la révision du Système international d’unités (SI)

Terry Quinn

Directeur honoraire du

Bureau international des poids et mesures (BIPM)

Le Prototype international de kilogram avec ces temoins dans le coffre au BIPM ou il était placé en1889 lors de la premiere Conférence général des poids et mesures.

………

Pile de Charlemagne

A modern commercial high

precision balance (known as a mass comparator). Weighing in vacuum with provision for

introducing masses from a vacuum

travelling box.

BIPM balance a suspension flexible.Precision relative: 10^-12 pour masses de 2 kg 1988

Balance a suspension flexible:

experience au BIPM en 1988, le “5^ieme force”.

Pesées en valeur relative de 5 10^-12

The safe in the vault at the BIPM where the International Prototypes of the Kilogram and Metre rested from 1889, when they were adopted by the 1st CGPM, until 1998 when they were moved to a new modern safe in the same vault.

Photo TJQ

Richard Davis with the international prototype of the kilogram 2002

Le trottoire classique/

quantique de Sèvres

Quel est la difference entre le trottoire

classique et le trottoire quantique du point de vu de la pratique?

A K

ol s

cd

kg

m

A K

mol s

cd

kg

m

h, c, ∆ν_Cs k

∆ν_Cs N_A

e ∆ν_Cs

C ∆ν_Cs h, c, ∆ν_Cs

A partir du 20 mai 2019

Le samedi 19 mars 1791

Le Mètre et le Kilogram des Archives

1795

Photo TJQ

1

The storage and carrying case of prototype metres

Image BIPM

1889

2

1892 A A Michelson measured the new International Prototype of the Metre in terms of the wavelength of the red line of cadmium

« Dès l’origine du Comité International, il a été généralement reconnu qu’il serait

d’une importance fondamentale de déterminer les relations entre les unités métriques et quelques bases constantes physiques qu’on peut déduire de certains phénomènes naturels. »

(Comite international des poids et mesures 1891)

3 1960

Krypton 86 discharge lamp

Le mètre est la longueur du trajet parcouru dans le vide par la lumière pendant une durée de 1/299 792 458 de seconde.

This definition of the metre fixes the numerical value of the speed of light to be exactly 299 782 458 when expressed in the units metres per second

4 1983

Le mètre, symbole m, est l’unité de longueur du SI. Il est défini en prenant la valeur numérique fixée de la vitesse de la lumière dans le vide, c, égale à 299 792 458 lorsqu’elle est exprimée en m/s, la seconde étant définie en fonction de ∆ν

5 2018

c = 299 792 458 metres per second or c = 983 571 056.4 feet per second or c = 327 857 018.8 yards per second

What does it mean to fix the numerical value of the speed of light, c?

c = 299 792 458 metres per second or c = 983 571 056.4 feet per second or c = 327 857 018.8 yards per second

What does it mean to fix the numerical value of the speed of light, c?

c = 299 792 458 metres per second or c = 983 571 056.4 feet per second or c = 327 857 018.8 yards per second

What does it mean to fix the numerical value of the speed of light, c?

We need to find an equation of physics that links the speed of light to length without including any unknown constants or quantities that themselves depend on length.

Such an equation is

c = λ f

Where λ is the wavelength of a light of frequency f.

We could also of course simply measure the time taken for a light

signal to travel from one place to another but this is not practical

for short distances.

Now let us consider the Planck constant h

h = 6.626 0703 × 10

kg m

s

h = numerical value  unit h is a constant of nature.

h = 6.626 0703 × 10

kg m

s

h = numerical value  unit

h is a constant of nature

h = 6.626 0703 × 10

kg m

s

h = numerical value  unit

h is a constant of nature.

h = 6.626 0703 × 10

kg m

s

h = numerical value  unit

We have thus defined the kilogram in terms of h by fixing

its numerical value and using the metre and second already

defined.

Le 26

Conférence général des poids et mesures:

décide qu’à compter du 20 mai 2019, le Système international d’unités, le SI, est le système d’unités selon lequel :

− la fréquence de la transition hyperfine de l’état fondamental de l’atome de césium 133 non perturbé, ∆ ν Cs, est égale à 9 192 631 770 Hz,

− la vitesse de la lumière dans le vide, c, est égale à 299 792 458 m/s,

− la constante de Planck, h, est égale à 6,626 070 15 × 10

J s, le − la charge élémentaire, e, est égale à 1,602 176 634 × 10

C,

− la constante de Boltzmann, k, est égale à 1,380 649 × 10

J/K,

− la constante d’Avogadro, N

, est égale à 6,022 140 76 × 10

mol

,

− l’efficacité lumineuse d’un rayonnement monochromatique de fréquence 540 × 10

Hz, K

, est égale à 683 lm/W,

L’horloge atomique

L’ampère Le kelvin

La mole Le mètre Le kilogramme

Le candela

Effet Josephson (1962)

h K e

K f n n

U 2

, )

(

J

J

 

K_J-90 = 483 597.9 Hz/V

K 2 K

H

( ) ,

e R h

i i R

R  

R_K-90 = 25 812.807 

Effet Hall quantique (1980)

The watt balance, invented in 1974 by Bryan Kibble at the NPL and now called the Kibble balance.

But we cannot directly measure either L or B with sufficient accuracy

Combining the equations from the two configurations gives

mgv = UI

Mgv = U.I = U . U’ ^/ R

(h/2e)(h/2e)/(h/e ) ²

h

(h /4e ).(e /h) ^{2 2 2}

BK

NIST watt balance Mk II

The first Lego watt (Kibble) balance, 92 rue Brancas Sèvres, July 2013 Mass traceable to the Planck

constant

The Planck constant definition of the kilogram

i-phone, also based on high science, even more difficult to understand ! Artefact definition of the kilogram, based in

simple science, easy to understand

Early telephone also based in simple science, easy to understand

based on high science, difficult to understand

From Artefacts to Atoms; here is the atom bit:

silicon spheres weighing

about 1 kg containing about 215 253 842  10

atoms

+ 35 nm

-35 nm

Atoms are really very very small.

The molar mass of silicon is 28

The Avogadro constant is about 6 x 10²³ per mole In 1 kg of silicon there are thus 2 x 10²⁵ atoms

Suppose we take the finest sand such that in 1 cubic millimeter we can put about 4000 grains (0.06 mm diameter), in 1 cubic metre there will be 4 x 10¹² grains.

Suppose we take a ribbon of this sand on the beach, 1 metre wide, 1 metre deep and 100 metres long, it will contain 4 x 10¹⁴ grains.

If this ribbon is extended over 1 km, it will contain 4 x 10¹⁷ grains.

Let us make it 10 metres deep to give 4 x 10

grains

How many kilometres of beach will be needed to reach the number of atoms in 1 kg of silicon?

The length of the beach will be very large, some five million kilometres!

For the silicon crystal density we have:

N

= n M(Si)/ρ a

Where n is the number of atoms per unit cell of silicon, M(Si) the molar mass of silicon, ρ the density of the sample of silicon and a its lattice constant so that, remembering that

N

h = [cα

/2R

][M

A

(e)]

h

= [cα

/2R

][M

A

(e)] ρ a

/ n M(Si)

The important question is how well do these two methods of arriving at a value for h agree?

The answer is just within the respective uncertainties of the experimental measurements, namely, a few parts in 10⁸.

h

= 4mgv/in

f

h

= [cα

/2R

][M

A

(e)] ρ a

/ n M(Si)

What does this demonstrate?

The most important outcome is the demonstration that the Josephson and quantum-Hall relations correctly represent macroscopic voltages and resistances – something that had not been demonstrated at this level before.

It is also demonstrates a remarkable level of consistency among the measured values of fundamental constants using a wide variety of methods based on an equally wide variety of equations of physics.

One can conclude that classical and quantum physics in these area are consistent to a few parts in 10⁸.

- La seconde, symbole s, est l’unité de temps du SI. Elle est définie en prenant la valeur

numérique fixée de la fréquence du césium, ∆ ν_Cs, la fréquence de la transition hyperfine de l’état fondamental de l’atome de césium 133 non perturbé, égale à 9 192 631 770 lorsqu’elle est exprimée en Hz, unité égale à s^–1.

-

- − Le mètre, symbole m, est l’unité de longueur du SI. Il est défini en prenant la valeur

numérique fixée de la vitesse de la lumière dans le vide, c, égale à 299 792 458 lorsqu’elle est exprimée en m/s, la seconde étant définie en fonction de ∆ ν_Cs.

-

- − Le kilogramme, symbole kg, est l’unité de masse du SI. Il est défini en prenant la valeur numérique fixée de la constante de Planck, h, égale à 6,626 070 15 × 10^–34 lorsqu’elle est exprimée en J s, unité égale à kg m² s^–1, le mètre et la seconde étant définis en fonction de c et ∆ ν_Cs.

-

- − L’ampère, symbole A, est l’unité de courant électrique du SI. Il est défini en prenant la

valeur numérique fixée de la charge élémentaire, e, égale à 1,602 176 634 × 10^–19 lorsqu’elle est exprimée en C, unité égale à A s, la seconde étant définie en fonction de ∆ ν_Cs.

Les nouveaux definitions d’unités de base du SI:

− Le kelvin, symbole K, est l’unité de température thermodynamique du SI. Il est défini en prenant la valeur numérique fixée de la constante de Boltzmann, k, égale à 1,380 649 × 10^{– 23} lorsqu’elle est exprimée en J K^–1, unité égale à kg m2 s^–2 K^–1, le kilogramme, le mètre et la seconde étant définis en fonction de h, c et ∆ ν_Cs .

− La mole, symbole mol, est l’unité de quantité de matière du SI. Une mole contient exactement 6,022 140 76 × 10²³ entités élémentaires. Ce nombre, appelé « nombre d’Avogadro »,

correspond à la valeur numérique fixée de la constante d’Avogadro, N_A, lorsqu’elle est exprimée en mol^–1. La quantité de matière, symbole n, d’un système est une représentation du nombre d’entités élémentaires spécifiées. Une entité élémentaire peut être un atome, une molécule, un ion, un électron, ou toute autre particule ou groupement spécifié de particules.

− La candela, symbole cd, est l’unité du SI d’intensité lumineuse dans une direction donnée. Elle est définie en prenant la valeur numérique fixée de l’efficacité lumineuse d’un rayonnement monochromatique de fréquence 540 × 10¹² Hz, K_cd, égale à 683 lorsqu’elle est exprimée en

lm W^–1, unité égale à cd sr W^–1, ou cd sr kg^–1 m^–2 s³, le kilogramme, le mètre et la seconde étant définis en fonction de h, c et ∆ ν_Cs

Air France Concorde over the Atlantic at Mach 2.03 and 18 km altitude on 7 March 1999 en route for New York (photo TJQ)

Le Mètre et le Kilogram des Archives

Photo TJQ

Relative standard

deviation about the mean:

5 ppm!

Taken from Base du Système métrique by J-B Delambre

Photo TJQ

The Toise of Peru

made in about 1736 it became the official unit of length in France in 1766 and became officially the toise of the Acadèmie.

Photo TJQ

The Pavillon de Breteuil in 1875 damaged in the Franco-Prussian war of 1870

La Convention du mètre 1875

Article premier

Les Hautes Parties contractants s’engagent à fonder et

entretenir à frais commun, un Bureau international des poids et mesures, scientifiques et permanent, dont le siège est à Paris.

Image BIPM

Details of thermal- expansion comparator

The primary barometer installed in one of the front rooms of the

Observatoire, used for the hydrogen gas thermometry in the 1880s. It served as the BIPM

primary barometer until the 1960s

Travaux et Mémoires Vol III, 1884.

Image BIPM

The safe in the vault at the BIPM where the International Prototypes of the Kilogram and Metre rested from 1889, when they were adopted by the 1st CGPM, until 1998 when they were moved to a new modern safe in the same vault.

Photo TJQ

Richard Davis taking the international prototype of the kilogram from its safe 2002

The Pavillon de Breteuil in the 1920s

Image BIPM

The site and buildings of the BIPM in 2002

Located at: 48^o 49’ 46” N, 2^o 13’ 13” E The Pavillon de Breteuil

1672 modified in 1743

The Petit Pavillon 1672 modified in the

1920s

Nouveau Pavillon 1988 Offices and library

Pavillon du Mail 2001 (meeting room and mechanical workshop) Laser building 1984

(now time laboratory) Observatoire 1878 The original laboratories

Observatoire

extension 1929 Ionizing radiation building 1964, now also chemistry

The International Committee for Weights and Measures on the steps of the Grand Salle, Pavillon de Breteuil, 1894

The International Committee for Weights and Measures on the steps of the Grand Salle, Pavillon de Breteuil, 1994

The CIPM Mutual

Recognition Arrangement (CIPM MRA) was signed in October 1999 by

Directors of 38 NMIs and one International

Organization. It is now signed by the Directors of 98 NMIs, 4 International Organizations and 152 secondary metrology institutes.

The results of the 900 key comparisons and some 24000 calibration and measurement capabilities are on the public BIPM Key Comparison

Database (KCDB).

The Planck constant definition of the kilogram

i-phone, also based on high science, even more difficult to understand ! Artefact definition of the kilogram, based in

simple science, easy to understand

Early telephone also based in simple science, easy to understand

based on high science, difficult to understand

Photo BIPM

silicon spheres weighing about 1 kg containing about 215 253 842  10¹⁷ atoms

At the Royal Society Summer Science

Exhibition July

2013

Appendix 1. The base units of the SI

It follows from the new definition of the SI adopted above in terms of the seven defining constants, that the base units of the SI are henceforth defined as follows:

The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency _Cs, the unperturbed ground-state hyperfine splitting frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s^–1 for periodic phenomena.

The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m/s, where the second is defined in terms of the caesium frequency _Cs.

The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 040 ×10^–34 when expressed in the unit J s,

which is equal to kg m² s^–1, where the metre and the second are defined in terms of c and _Cs. The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed

numerical value of the elementary charge e to be 1.602 176 620 8 ×10^–19 when expressed in the unit C, which is equal to A s, where the second is defined in terms of _Cs.

The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380 648 52 ×10^–23 when expressed in the unit J K^–1, which is equal to kg m² s^–2 K^–1, where the kilogram, metre and second are defined in terms of h, c and _Cs.

The mole, symbol mol, is the SI 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. It is defined by taking the fixed numerical value of the Avogadro constant N_A to be 6.022 140 857 ×10²³ when expressed in the unit mol^-1.

The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 ×10¹² Hz, K_cd, to be 683 when expressed in the unit lm W^–1, which is equal to cd sr W^–1, or kg^–1 m^–2 s³ cd sr, where the kilogram, metre and second are defined in terms of h, c and _Cs.

Appendix 2. Abrogation of former definitions of the base units:

It follows from the new definition of the SI adopted above and from the new definitions of the base units that

the definition of the second in force since it was adopted by the 13th CGPM (1967/68, Resolution 1) is abrogated,

the definition of the metre in force since it was adopted by the 17th CGPM (1983, Resolution 1), is abrogated,

the definition of the kilogram in force since 1889 based upon the mass of the international prototype of the kilogram (1st CGPM, 1889, 3rd CGPM, 1901) is abrogated, …………

Appendix 3. Status of constants previously used in the former definitions:

It also follows from the new definition of the SI adopted above and from the new definitions of the base units that

•the mass of the international prototype of the kilogram m(K) remains 1 kg but with a relative uncertainty equal to that of the recommended value of h at the time this Resolution was

adopted, namely xxxx, and that in the future its value will be determined experimentally,

•that the magnetic constant (permeability of vacuum) µ₀ remains 4π ×10^–7 H m^–1 but with a relative uncertainty equal to that of the recommended value of the fine-structure constant α at the time this Resolution was adopted, namely xxxx, and that in the future its value will be determined experimentally,

•that the thermodynamic temperature of the triple point of water T_TPW remains 273.16 K but with a relative uncertainty equal to that of the recommended value of k at the time this

Resolution was adopted, namely xxxx, and that in the future its value will be determined experimentally,

The first is by means of a watt balance in which electrical power is compared with

mechanical power to give a value for h and the second is via measurements of the crystal density of silicon, which gives a value for the Avogadro constant N_A which is linked to h through the following equation:

N_Ah = [cα²/2R_][M_u A_r(e)],

where α, R_, M_u and A_r(e) are the fine structure constant (known to parts in 10¹⁰), the

Rydberg for infinite mass (parts in 10¹²), the molar mass constant (exact) and the relative atomic mass of the electron (parts in 10¹⁰) respectively.

In conformity with the law of the 18^th Germinal an 3 (7 April 1795). Presented on 4^th Messidor an 7 (22 June 1799)

(made by) F. P. Lenoir

Photo TJQ

Label on the case containing the Metre of the Archives

Photo TJQ

In conformity with the law of the 18^th Germinal an 3 (7 April 1795). Presented on 4^th Messidor an 7 (22 June 1799)

(made by) F. Fortin

Label on the case containing the Metre of the Archives

The Kilogram of the Archives.

Photo TJQ

After 1795 what were the real definitions of the metre and kilogram?

The metre is one ten millionth of the quarter of the terrestrial meridian which, deduced from the

measurements of Pierre-Francois Méchain and Jean- Baptiste Delambre, was:

5 130 740 toise du Pérou, thus

1 mètre = 443,296 lignes of the toise du Pérou or was it

the length of the Metre of the Archives

The kilogram is the mass of one cubic decimetre of water at the temperature of melting ice

or was it

the mass of the Kilogram of the Archives.

Photo TJQ

The Pavillon de Breteuil in the 1920s

James Clerk Maxwell,

British Association for the Advancement of Science, Liverpool, 1870

“The idea of referring all measurements to a unit of length taken from nature was seized upon by mathematicians as soon as the existence of such a unit and the possibility

of determining it became known. They saw it as the only way to exclude all that was arbitrary from a system of measurement and to conserve it unchanged, so that no event or revolution in the world could cast uncertainty upon it.

They felt that with such a system, belonging exclusively to no

one nation, one could hope that it would be adopted by all.”

Relative standard

deviation about the mean:

5 ppm!

Taken from Base du Système métrique by J-B Delambre

Base units of the SI today

A K

mol s

cd

kg

m

Triple point of water

Caesium clock

Speed of light

“One can reduce to three the units that seem most appropriate as the base; the length of a pendulum, the quarter of the length of the equator and finally the length of a quarter of a meridian. The length of a pendulum has the advantage of being the easiest to determine and, in consequence, the easiest to verify if some accident happens that renders it necessary. Furthermore, those who wish to adopt this measure already adopted by another country, or having adopted it wish to verify it, would not obliged to send observers to the place where it was originally established. In addition, the law of the length of a pendulum is well known,

confirmed by experiment and can be used without

fearing small errors.”