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.