The Revised International System of Units (SI) and the change to Quantum standards with a focus on the realisation of the ampere and kelvin

Test & Measurement 2018

Wynand LouwDirector RIIDCIPM member

Elke Roik, Das Längenmaßsystem im alten Ägypten. Christian-Rosenkreutz-Verlag, Hamburg 1993. 407p, 298 x 210 mm, 106 fig. ISBN 3-929322, DM 129

Measurement and the SI

http://www.celticnz.org/images/Easter%20Island/

http://www.the13thenumeration.com/Blog13/wp-content/uploads/2012/11/The_Cubit_P3.gif

http://681586233295146057.weebly.com/cryptography-ciphers--hidden-texts.html

Eratosthenes, 240 B.C.

The idea to use natural phenomena as measures/units

Measurement and the SI

http://www.wikiwand.com/en/Ancient_Mesopotamian_units_of_measurement

A set of old Babylonian weights from 1 mina to 3 shekels

https://commons.wikimedia.org/w/index.php?curid=40081337

By Jononmac46

Measurement and the SI

By Meister der Jahângîr-Memoiren -https://commons.wikimedia.org/w/index.php?curid=155125

By Avantiputra7 - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=33202416

http://www.ancientpages.com/2016/11/03/gnomon-ancient-time-measuring-instrument-used-by-babylonians-egyptians-and-chinese/

Measurement and the SI

By Meister der Jahângîr-Memoiren -https://commons.wikimedia.org/w/index.php?curid=155125

These weights conform to the standard Harappan binary weight system. The smallest weight in this series is 0,856 g and the most common weight is approximately 13,7 g, which is in the 16th ratio. In the large weights the system become a decimal increase where the largest weight is 100 times the weight of the 16th ratio in the binary system. Harappa Archaeological Research Project.

By Nomu420 - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=30787089

Measurement and the SI

https://commons.wikimedia.org/w/index.php?curid=2028026

Measurement and the SI

Image credit: NASA / CXC / M.Weiss

1 metre is 1/10 millionth of the distance from the north pole to the equator

•By Basil Swindells•National Physical Laboratory,, TeddingtonThe creation of the decimal metric system at the time of

the French Revolution and the subsequent deposition of

two platinum standards representing the metre and the

kilogram, on 22 June 1799, in the Archives de la

République in Paris can be seen as the first step in the

development of the present International System of

Units.

Measurement and the SI

After the signing of the Metre Convention on 20 May

1875, which created the BIPM and established the

CGPM and the CIPM, work began on the construction

of new international prototypes of the metre and

kilogram. In 1889 the 1st CGPM sanctioned the

international prototypes for the metre and the

kilogram. Together with the astronomical second as

the unit of time, these units constituted a three-

dimensional mechanical unit system similar to the CGS

system, but with the base units metre, kilogram, and

second, the MKS system.

Measurement and the SI

Following an international inquiry by the BIPM, which

began in 1948, the 10th CGPM, in 1954, approved the

introduction of the ampere, the kelvin and the candela

as base units, respectively, for electric current,

thermodynamic temperature and luminous intensity. The

name International System of Units, with the

abbreviation SI, was given to the system by the 11th

CGPM in 1960. At the 14th CGPM in 1971, after lengthy

discussions between physicists and chemists, the current

version of the SI was completed by adding the mole as

the base unit for amount of substance, bringing the total

number of base units to seven.

Measurement and the SI

The International

System of UnitsSupplement 2014:

Updates to the 8th edition (2006) of the SI Brochure

Preamble

This document gives the list of the most significant changes to be made to the 8th edition

of the SI Brochure that appeared in 2006. They are based on recommendations made by

the Consultative Committee for Units (CCU) at its 19th, 20th and 21st meetings and

approved by the International Committee for Weights and Measures (CIPM) at its

103rd meeting in March 2014. The intention is not to conduct a comprehensive review of

the full text, but to update the most significant items in order to harmonize them with the

most recent recommendations and to update references to other documents. It includes the

new definition of the astronomical unit for length adopted in 2012 by the XXVIII General

Assembly of the International Astronomical Union (IAU).

MODIFICATION OF THE ORDER OF BASE UNITS IN THE EXPRESSION OF

DERIVED UNITS

This follows Decision CIPM/103-17 taken at Session I of the 103rd meeting of the CIPM

in March 2014 (see also pages 16 and 17 of the Report of the 21st meeting of the CCU,

2013).

1799 “Kg des archives”, 1 dm3 of H20 at 4 C

1875 Signing of ‘Metre Convention’

1889 IPK and 40 copies produced

1946, 1989, 2014 Periodic verification

1946 development of nettoyage-lavage (BIPM) cleaning method

Nettoyage (washing) Lavage (cleaning)

“The kilogram is the unit of mass; it is equal to the

mass of the International Prototype of the Kilogram”

Periodic verification

IPK

50 µg =

0,05 ppm

50 µg is …

the mass of a dust

particle of

0,34 mm diameter

A measurement system in terms of invariants of nature…

A measurement system in terms of invariants of nature…

Need to get rid of the last physical artefact unit standard

Find a way to allow independent realisations of all the base units

It must reflect the advances in Science, i.e. reflect

increasing accuracy of both realisations and measurement requirements

Definitions of units do not need to be changed over time

A measurement system in terms of invariants of nature…

A measurement system in terms of defining constants…

The new definitions are based on fixed

numerical values of the Planck constant

(h), the elementary charge (e), the

Boltzmann constant (k) and the Avogadro

constant (NA), as well as on other three

physical constants whose numerical

values are already fixed in the present SI or a similar formulation.

Two pathways to the kilogram

Amedeo Avogadro 1776 - 1856 Max Planck 1858 - 1947

𝑁𝐴ℎ =𝑀𝑝𝑐𝛼

2

2𝑅∞ ൗ𝑚𝑝

𝑚𝑒

E = hfE = mc2

hf = mc

Counting atoms (Avogadro)Comparing mechanical and electrical watt (Kibble Balance)

single-mode dual-phase operating

principle

A measurement system in terms of invariants of nature…

The 9th Edition of the SI Brochure

2.1 Definition of the SI

The International System of Units, the SI, is the system of units in which

• the unperturbed ground state hyperfine splitting frequency of the

caesium 133 atom Cs is 9 192 631 770 Hz,

• the speed of light in vacuum c is 299 792 458 m/s,

• the Planck constant h is 6.626 070 040 ×1034 J s,

• the elementary charge e is 1.602 176 620 8 ×1019 C,

• the Boltzmann constant k is 1.380 648 52 ×1023 J/K,

• the Avogadro constant NA is 6.022 140 857 ×1023 mol-1,

• the luminous efficacy Kcd of monochromatic radiation of frequency

540 ×1012 hertz is 683 lm/W.

The numerical values of the seven defining constants have no uncertainty.

Redefinition of the kelvin Actual definition:1/273,16 of the temperature of the triple point of water (TPW)

Weakness in the actual definition:Dependence on the properties of the water sample,especially the isotopic composition

Credit NIST

21 other defining points are specified,

ranging from the freezing point of

helium to the freezing point of copper

https://www.researchgate.net/On-the-left-prototype-of-a-sealed-copper-cell-for-the-realization-of-the-triple-point-of_fig2_270273329 [accessed 28 Sep, 2018

Redefinition of the kelvin

Implementing the new Kelvinhttp://projects.npl.co.uk/ink/

Redefinition of the kelvin

Implementing the new Kelvin: http://projects.npl.co.uk/ink/

The background data to PLTS-2000 (TX ≡ T). The discrepancy in the different data sets at

the lower temperatures grows rapidly to 6% at ~0.0001 K leading to a large uncertainty increase in the PLTS-2000

T2000/mK

Redefinition of the kelvin

Redefinition of the kelvin

Planned explicit-constant definition:

The kelvin, symbol K, is the SI unit of thermodynamic temperature; its magnitude is set by fixing the numerical value of the Boltzmann constant to be equal to exactly 1,380 65X × 10-23 when it is expressed in the SI unit s-2 m2 kg K-1, which is equal to J K-1

k = 1,380 65X × 10-23 J/K

This means, the kelvin will be defined in terms of the SI derived unit of energy, the joule

27

Primary-thermometry methods: AGT

TransducerReceiver

d

Equation of state for an ideal gas

2 kTu

m

u Speed of sound in the limit of zero

Heat-capacity ratio (cp / cV)

k Boltzmann constant

T Temperature

m mass of a gas particle

Frequency

Standing waves in a resonator

To be measured:➢ frequency a

➢ dimensions viamicrowaves m, pyknometry, or CMM

Quasi spheres and microwaves:

2

m

a

0

2

0

ATPW0 )(

)(lim

p

pc

NT

Mk

p

❖ Absolute AGT: u(T) / T of order 1 ppm❖ Relative AGT: measurement of u ratios❖ Review paper: Metrologia 2014

Acoustic Gas Thermometry

Nature Physics volume 12, pages 7–11 (2016)

Applications of AGT

By Nomu420 - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=30787089

Acoustic thermometers could be used in hostile industrial environments (image courtesy of iStockphoto)

Effects of the redefinition of the kelvin

Direct realisation by primary thermometry

Benefits particularly below 20 K and above 1300 K

Definition independent of any material, no favoured fixed point,no favoured measurement method, no error propagation from TPW

No immediate impact on the status of ITS-90 and PLTS-2000

Most precise temperature measurements from about 25 K to 1235 K will continue to be traceable to SPRTs calibrated according to the ITS-90

Relative uncertainty in the determination of k is transferred to TTPW

The TTPW value will not change in the foreseeable future

Click to edit Master title style

p. 3114th international metrology symposium NMIJ – 25 April 2018

Electrical units in the revised SI

“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 metre apart in vacuum, would produce between these conductors a force equal to 2 × 10−7 Newton per metre of length.”

“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 1.602 176 634 ×10-19 C”

ampere never better than IPK

A measurement system in terms of invariants of nature…Practical realisation of the volt

The volt V can be realised using the Josephson effect and the value of the Josephson constant KJ

With the revised SI:• KJ,90 conventional value replaced by value

based on the values of h and e• Present uncertainty of 410-7 removed

Impact:• All calculations for voltage measurements based on the AC

Josephson effects need to use the new value (# digits?)• Step change of 0,107 ppm

Only just visible at practical measurements using Zener-based voltage standards, but 100 times greater than the present realisations of the quantum standard!

Practical realisations of the ohm

The ohm can be realised using

1. the quantum Hall effect and the value of the Von Klitzing constant RK

2. a calculable capacitor and the value of o

With the revised SI:RK,90 conventional value replaced by value based on the values of h and ePresent uncertainty of 110-7 removed

Impact:All calculations for resistance measurements based on the quantum Hall effect need to use the new value (# digits?)Step change of 0,018 ppm only visible in best realisations of

the (quantum) standard

Practical realisations of the ampere

3 options to realise the ampere

• Using Single Electron Transport device, unit relation A = C/s, and the value of e and a realisation of the second s

• Using Ohm’s law, the unit relation A = V/Ω,and the practical realisations of the units volt V and ohm Ω, based on the Josephson and quantum Hall effects

• Using the relation I = C·dU/dt, the unit relation A = F·V/s, and practical realisations of units volt V and farad F and of the SI base unit second s (applying a voltage ramp dU/dt to a capacitor of capacitance C)

Magnetic constant o and related quantities

The relations between μ0 , ε0 , Z0 and c remain unaltered• ε0 = 1/μ0c2

• Z0 = μ0c = (μ0/ε0)1/2

with c = 299 792 458 m s–1

However, μ0 no longer has the exact value 4π10–7 N A–2 and must be determined experimentally via

c, h and e are exact in the revised SI μ0 , ε0 , Z0 will have the same relative uncertainty as the fine structure constant

The revised SI has a major impact on electrical units:

Present electrical quantum standards become direct realisations of the SI units of V, R, I

Advances in these quantum standards lead to direct improvement of realisation of the units

Other practical consequences:

• Small step change in V only just visible at industry level

• RK and KJ values need to be updated, per a certain fixed date, in all software of NMIs and industry

• μ0 no longer exact, must be determined experimentally

• Impact step changes on other quantities practically negligible

Summary of Impact on Electrical

What do I need to do in preparation for the ‘Revised SI’?

• Familiarise yourself with the revised SI (e.g. via www.bipm.org)

• Review traceability requirements of your ‘best’ standards

• Check QA documents and SW on conventional values RK-90 and KJ-90

What do I need to do on or immediately following implementation day?

• Change KJ-90 of your JAVS to KJ = 483 597,848 416 984 GHz/V

• uV > 0.268 µV/V, uR > 0.045 µ/: no action until next recalibration

• uV 0.268 µV/V, uR 0.045 µ/: apply numerically correction, or recalibrate

(uV, uR is uncertainty of reference standard)

Courtesy Dr Gert Rietveld, President CCEM

A measurement system in terms of invariants of nature…

The draft 9th Edition of the SI Brochure

The value Q of a quantity is the product of a number {Q} and a unit [Q]:

Q = {Q}[Q]

The unit is a particular example of the value of a quantity, defined by convention, which is used as a reference, and the number is the ratio of the value of the quantity to the unit.

So a metre = 1ˑm= m

Is a unit a quantity value??