The revised international system of units (SI) April 17th 2019 APS Mid-Atlantic Senior Physicists Group College Park, MD Stephan Schlamminger+, Darine Haddad, Frank Seifert, Leon Chao, David Newell, Jon Pratt
[email protected] The art of measurement has a long history
Egyptian wall painting in the tomb of Rekh-mi-re’ (1440 BC) Chinese Han dynasty (9 BC)
Vernier caliper
One of the earliest record of geometrical measurements.
Physical Measurement Laboratory
Quantities, units .. Numerical value
Quantity Unit ! = 1.2 & ! = ! [!]
Physical Measurement Laboratory Quantities, units .. Numerical value
Quantity Unit ! = 1.2 m ! = ! [!] ! = 4 ft
Physical Measurement Laboratory Units for many quantities new Unit ! = #×% = 0.8 m× 1.2 m = 0.96 m. Δ1 0.8 m 4 / = = = 8 Δ2 0.1 s 1 Do we need an infinite amount of units to measure the quantities in our lives?
Physical Measurement Laboratory Units for many quantities new Unit ! = #×% = 0.8 m× 1.2 m = 0.96 m. Δ1 0.8 m 4 / = = = 8 Δ2 0.1 s 1 Do we need an infinite amount of units to measure the quantities in our lives? No, we can use a set of base units and combine these to new units.
A system of units
Physical Measurement Laboratory The international system of units (SI)
traces back to the meter convention International Prototype of the meter
held from March 1st – May 20th 1875 in Paris. International Prototype of the kilogram 17 signatory states.
Physical Measurement Laboratory Historical evolution before 1789 since 1875 1980 107 m c
regional weights and measures international w/m international w/m decreed by regional rulers Earth sets standard fundamental constants “For all times, for all people” Physical Measurement Laboratory The present SI has seven base units
Physical Measurement Laboratory Do not confuse the logos
Physical Measurement Laboratory The present SI has seven base units
Physical Measurement Laboratory The present SI has seven base units
! = 299 792 458 m/s
Physical Measurement Laboratory The present SI has seven base units
! = 299 792 458 m/s
Physical Measurement Laboratory The present SI has seven base units 34 ,-. = 683 lm W
! = 299 792 458 m/s
Physical Measurement Laboratory The present SI has seven base units 34 ,-. = 683 lm W
! = 299 792 458 m/s
Physical Measurement Laboratory The present SI has seven base units 34 ,-. = 683 lm W
! = 299 792 458 m/s
Physical Measurement Laboratory The present SI has seven base units 34 ,-. = 683 lm W
! = 299 792 458 m/s
Physical Measurement Laboratory The definition of the kilogram The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. (1889)
Physical Measurement Laboratory Physical Measurement Laboratory Long term stability and accessibility
Physical Measurement Laboratory Why change the present SI?
Brian Josephson Klaus von Klitzing
awarded the Nobel Prize in 1973 awarded the Nobel Prize in 1985
Josephson effect integral quantum Hall effect
Quantum voltage Quantum resistance
ℎ ! = # ' 2& 1 ℎ * = # &, Josephson constant von Klitzing constant 2& ( = ) ℎ ℎ * = - &,
Physical Measurement Laboratory Quantum leap in electrical metrology V/V D
C.A. Hamilton, Rev. Sci. Instr. 71 ,3611 (2000). R.E. Elmquist et al., J. Res. NIST 106 ,65 (2001).
Physical Measurement Laboratory From “artifacts” to quantum standards
Weston cell Thomas-type resistor
Josephson Junction Quantum Hall Device Array
Physical Measurement Laboratory A schism in metrology
SI units conventional units (base and derived)
kg A A90 m s V Ω90 V90 … W Ω W90 F … …
Physical Measurement Laboratory A schism in metrology
SI units conventional units presently (base and derived) ! "# = 1 + 9.83×10-. ! kg A A90 Ω m s V V "# = 1 + 1.77×10-. Ω90 90 Ω … W Ω W90 … … 1 F "# = 1 + 17.9×10-. W
Physical Measurement Laboratory Fundamental constants – better than artifacts
Fundamental constants are: • stable • accessible • scale invariant • measurements can be improved B.W. Petley, Physical constants and the SI, NPL News Jan.1987. ! = 299 792 458 m/s
given given unknown given Physical Measurement Laboratory Four additional constants will be fixed on 5/20/19
+
ℎ !A # $
Physical Measurement Laboratory The new defining constants
Planck constant ℎ = 6.626 070 15×10+,- kgm1s+3 kg
Physical Measurement Laboratory The new defining constants
Planck constant ℎ = 6.626 070 15×10+,- kgm1s+3 kg
1, +3 Avogadro constant 45 = 6.022 140 76×10 mol mol
Physical Measurement Laboratory The new defining constants
Planck constant ℎ = 6.626 070 15×10+,- kgm1s+3 kg
1, +3 Avogadro constant 45 = 6.022 140 76×10 mol mol
Boltzmann constant 9 = 1.380 649×10+1, kgm1s1K+3 K
Physical Measurement Laboratory The new defining constants
Planck constant ℎ = 6.626 070 15×10+,- kgm1s+3 kg
1, +3 Avogadro constant 45 = 6.022 140 76×10 mol mol
Boltzmann constant 9 = 1.380 649×10+1, kgm1s1K+3 K
Elementary charge > = 1.602 176 6341 ×10+3?As A
Physical Measurement Laboratory The new SI has seven defining constants
Physical Measurement Laboratory ℎ
Ha
H. Kubbinga, A tribute to Max Planck, Physical Measurement Laboratory Europhysics News 49, 27 (2018) About h In a classical In a quantum oscillator, oscillator, the system’s the system’s energy is energy is continuous. discrete.
E E 9⁄2 ℎ% 7⁄2 ℎ% 5⁄2 ℎ% 3⁄2 ℎ% 1⁄2 ℎ% 0 0
Physical Measurement Laboratory The Planck constant The constant of quantum mechanics……
ℎ = 6.626 070 15×10+,- kg m1s+3
…..is measured in units kilogram (and m and s). h Physical Measurement Laboratory Two ways to connect h to the kilogram
X-Ray Crystal Density Method (XRCD) Kibble balance
Photo: PTB Physical Measurement Laboratory Two ways to connect h to the kilogram
• Use a small mass • Quantum electrical standards
+ + • Scale • ) = , . = * ,- / 0,
• - ! ∝ ℎ * + • 1 = 23 4 • $ = & ⋅ ( ⋅ !
• 5,6 = 57,8+
X-Ray Crystal Density Method (XRCD) Kibble balance
Physical Measurement Laboratory X-Ray Crystal Density Method
1 1 ! = & ()*) " 2 ' +) X-Ray Crystal Density Method
1 1 ,- ! = & ()*) & = 2 ℎ " 2 ' +) ' *)( X-Ray Crystal Density Method
1 1 ,- ! = & ()*) & = 2 ℎ " 2 ' +) ' *)(
&/0 = 1 &' 1 ≈ 51 400 X-Ray Crystal Density Method
1 1 ,- ! = & ()*) & = 2 ℎ " 2 ' +) ' *)(
&/0 = 1 &' 1 ≈ 51 400
)> &6789: = ; &/0 ; ≈ 2.15×10 X-Ray Crystal Density Method
1 1 ,- ! = & ()*) & = 2 ℎ " 2 ' +) ' *)(
&/0 = 1 &' 1 ≈ 51 400
)> &6789: = ; &/0 ; ≈ 2.15×10 A 1; ≈ 1.1×10?@ 9B ≈ 1×10CD 1; How to count large numbers Macroscopic volume, Microscopic volume, Macroscopic Volume ×Bottles volume of a molar mass volume of a unit cell: Microscopic Volume W
L h 4 ⋅ 6 ⋅ 7 1 = ×10 2 8 ⋅ 9 ⋅ ℎ w H l 10 bottles per unit cell
Pictures and pedagogic concept shamelessly stolen from Peter Becker, PTB How to count large numbers Macroscopic volume, Microscopic volume, Macroscopic Volume ×Bottles volume of a molar mass volume of a unit cell: Microscopic Volume
h 4 ⋅ 6 ⋅ 7 1 = ×10 2 8 ⋅ 9 ⋅ ℎ w l 2> 10 bottles per 4 unit cell ? = B>C 3 How to count large numbers Macroscopic volume, Microscopic volume, Macroscopic Volume ×Bottles volume of a molar mass volume of a unit cell: Microscopic Volume
4 ⋅ 6 ⋅ 7 1 = ×10 2 8 ⋅ 9 ⋅ ℎ
2> DE C 4 C C ? = B> ?FG = DE = 8IJJE 3 How to count large numbers Macroscopic volume, Microscopic volume, Macroscopic Volume ×Bottles volume of a molar mass volume of a unit cell: Microscopic Volume
4 ⋅ 6 ⋅ 7 1 = ×10 2 8 ⋅ 9 ⋅ ℎ
2> FG C 4 C C ? = B> ?DE = FG = 8IJJG 3 How to count large numbers Macroscopic volume, Microscopic volume, Macroscopic Volume ×atoms volume of a molar mass volume of a unit cell: Microscopic Volume
4 456 0 = 3 ×8 6 16 2:;;<
25 A< 6 4 6 6 > = 45 >?@ = A< = 8:;;< 3 How to count large numbers Macroscopic volume, Microscopic volume, Macroscopic Volume ×atoms volume of a molar mass volume of a unit cell: Microscopic Volume
4 456 0 = 3 ×8 6 16 2:;;<
6 6 >?@ = A< = 8:;;< Pictures: PTB How to count large numbers Macroscopic volume, Microscopic volume, Macroscopic Volume ×atoms volume of a molar mass volume of a unit cell: Microscopic Volume
4 456 0 = 3 ×8 6 16 2:;;<
Pictures: PTB Two points to emphasize
# & ) ! = 12 2 &''(
Unitless number Two points to emphasize Measured in Germany and Japan in m
# & ) ! = & ≈ 0.1 m 12 2 &''(
Measured in Italy in m
Unitless number 1 ≈ 5×105 /0( 1 &''( ≈ 2.0×10 m 223 Different Isotopes of Silicon !"# = % !& !"# = '()%() !& + '(+%(+ !& + ',-%,- !& Natural Si 91.8 % 4.8 % 3.3 % '() 92.2 %
'(+ 4.7 % ',- 3.1 %
Enriched Si 34 35 '() 99.9958 % 99.9956 % 4.2×10 1.1×10 34 '(+ 4.1×10 35 ',- 1.1×10 Different Isotopes of Silicon
Natural Si data from N.V. Abrosimov et al. Metrologia 54 599 (2017) !"# 92.2 %
!"$ 4.7 % !%& 3.1 %
Enriched Si
!"# 99.9958 % ,- !"$ 4.1×10 ,. !%& 1.1×10 XRCD: Putting it all together
. $% ) , ! = ℎ ' / 60 70 − !9:;0<0= + !?@A;B<: & ( 6 2 ,''- 01'2,'4..-
The quantities printed in black are known. For each crystal the following quantities need to be measured:
• Diameter , sphere interferometer • Lattice parameter ,''- absolute, relative, modelled • Isotopic abundances 6'2, 6'4 mass spectrometry) • Impurities, vacancies !9:;0<0= infrared absorption spectroscopy • Surface layer !?@A;B<: XPS, XRF, ellipsometry Kibble balance formerly known as watt balance
• Principle was invented in 1975 by Bryan Kibble. • Was used to realize the ampere. • After the discovery of the quantum Hall effect by Klaus von Klitzing in 1980 it could be used to measure ℎ. • From May 20th 2019 forward it can be used to realize the unit of mass.
Bryan Kibble 1938 - 2016 Mechanics, E & M, Quantummechanics
Quantum- Mechanical mechanical h Kibble balance Precision mechanical Quantum electrical device that links Electrical measurement mechanical to electrical standards, i.e., quantities Josephson Effect quantum Hall effect.
Physical Measurement Laboratory The Lorentz force Facts on the Lorentz A charge moving in a force: q v magnetic field experiences a force: • Perpendicular to B. • Perpendicular to v. F 7⃗ = 9:⃗×< • Proportional to B, i.e. B more B more F. For a current in a wire: B l • Perpendicular to wire. 7⃗ = FG⃗×< • Perpendicular to B. I • Proportional to B. simplified: F • Proportional to I. 7 = F Physical Measurement Laboratory Motor (force mode): A Motor is a Generator l Cause: Current, I I Effect: Force, F F ? = ABC Circuit is completed, B current can flow. Cause: velocity, v Generator (velocity mode): l Effect: Voltage, U D = EBC Circuit is open, current can NOT flow. v Voltage is called the induced B voltage or EMF. U Motor (force mode): A Motor is a Generator l I F 5 = 789 B 5 789 7 : = = : ;89 ; Generator (velocity mode): l : = ;89 v B U Better Geometry Top view: B Magnetic flux density B, a fraction of 1 T Coil, several hundred turns Side view: B A coil in a radial field is the preferred geometry for modern watt $ Even better: !" ∝ balances. " Get a feel for the numbers • B = 0.5 T • l = 1,000 m • Force mode: A current of 0.01 A is flowing through the wire. Calculate the Force produced by the coil. • ! = Get a feel for the numbers • B = 0.5 T • l = 1,000 m • Force mode: A current of 0.01 A is flowing through the wire. Calculate the Force produced by the coil. • ! = # $% = 0.01 A 0.5 T 1000 m = 5 N Get a feel for the numbers • B = 0.5 T • l = 1,000 m • Velocity mode: The coil is moving with 2 mm/s through the magnetic field. Calculate the induced voltage • ! = Get a feel for the numbers • B = 0.5 T • l = 1,000 m • Velocity mode: The coil is moving with 2 mm/s through the magnetic field. Calculate the induced voltage m • ! = #$% = 0.002 0.5 T 1000 m s = 1 V Avogadro and Planck Avogadro and Planck Avogadro and Planck ! = # $% Avogadro and Planck ! = # $% Two modes of the Kibble balance Force mode Velocity mode !" = % &' ( = # &' !" % = ( # mass !"# = (% !" (% ! = "# % &' & # & Measurement of the induced voltage coil 23/ = +4 + = -./ nullmeter PJVS ≈ −+ Josephson effect /01 /03 • Predicted in 1962 by Brian Josephson Ψ- = .-% Ψ2 = .2% • Weak link between two superconductors ) = 42 − 4- V +1 ℎ 1 d) V ! = 2% 2' d* n = 0 or Ic I I -1 ℎ ! = + 2% DC only with AC Measurement of the electrical current current coil source /01 = 34 I I ammeter Measurement of the electrical current current coil current coil source 567 = 84 source I I 1 I 567 = 8 3 R ammeter 81 5 = 367 PJVS V nullmeter 1 = 3 4 Quantum Hall effect Discovered by Klaus v. Klitzing 1980 $" & !" = = % '() ' ( = + & * ℎ 1 ℎ ! = " + '. !/ ≈ 25.8 5Ω Two modes of the Kibble balance Force mode Velocity mode !" = % &' ( = # &' !" % = ( # mass !"# = (% !" ) !"# = ℎ, , 4 - . % &' # & ) , , & ! = ℎ - . 4 "# The Kibble balance requires g ! " = 4.4×10*+ # m g 1 m2g Physical Measurement Laboratory 1 of 4 interferometer Knife edge pivot Physical Measurement Laboratory Busy main mass side Counter mass side with dead weight Physical Measurement Laboratory Installation of the coil 2 of 6 coils for x/y and Θx/Θy damping 1 of 3 corner cubes for inter- ferometer Coil inside air gap Physical Measurement Laboratory How well do we know h? Physical Measurement Laboratory Kibble balances work at 1kg, but don’t have to Physical Measurement Laboratory The sweet spot Easy! A table top Kibble balance is a great research project Physical Measurement Laboratory Difficulty of building a Kibble balance Physical Measurement Laboratory The Boltzmann constant ! Three methods, capable of " = 2 ×10)* # - #/ 1. Acoustic Gas thermometry -- Speed of sound + = for a , . 0 U monoatomic gas +, T R T 5/3 2. Johnson Noise thermometry – Noise voltage 12 = 4456∆8 T = C ;< p 3. Dielectric gas constant thermometry -- 9 = 9 + , #/ Acoustic Gas Thermometry Acoustic resonance Microwave resonance to infer the volume Triaxial elliptical resonator to get acoustic wavelength 100 TM11 Resonance 80 60 Signal 40 20 0 2110 2111 Frequency (MHz) Resonator is precisely machined 10 Range ± 3.9 nm 0 -10 Bare Ellipsoid -20 With Acoustic Transducers -30 -40 (21.5 - 62 °C) 032 600)/nm a ( -50 Range ± 9.3 nm -60 1 2 3 4 5 6 7 8 Mode (TM1n) Next steps The General conference of weights and measures (CGPM) will vote on the revision of the new SI on November 16th. If accepted the new SI will come in effect on May 20 2019. Physical Measurement Laboratory Masses people measured massive black hole international prototype of the kilogram rest mass of the electron Summary • Transition from 7 base units to 7 defining constant. • Principle of the X-ray Crystal Density Method • Principle of the Kibble balance Physical Measurement Laboratory Thank you for your attention Physical Measurement Laboratory Thank you to my wonderful colleagues • Darine Haddad • Leon Chao • Frank Seifert • David Newell • Jon Pratt Physical Measurement Laboratory Extraordinary CCM G-1, comparison Three < 5 x 10-8, reveals One < 2 x 10-8 35 μg shift. Physical Measurement Laboratory Physical Measurement Laboratory Physical Measurement Laboratory