Editing Metrology (section)

==Physical quantities==
{{excerpt|Physical quantity|files=0}}

=== Definition of units ===
The [[International System of Units]] (SI) defines seven base units: [[length]], [[mass]], [[time]], [[electric current]], [[thermodynamic temperature]], [[amount of substance]], and [[luminous intensity]].<ref name="NIST_SI">{{cite web|title=SI base units|url=http://physics.nist.gov/cuu/Units/units.html|website=The NIST Reference on Constants, Units, and Uncertainty|publisher=National Institute of Standards and Technology|access-date=15 February 2017|url-status=live|archive-url=https://web.archive.org/web/20170119053614/http://physics.nist.gov/cuu/Units/units.html|archive-date=19 January 2017}}</ref> By convention, each of these units are considered to be mutually independent and can be constructed directly from their defining constants.<ref name="SI 9th edition">{{SIbrochure9th}}</ref>{{rp|129}} All other SI units are constructed as products of powers of the seven base units.<ref name="SI 9th edition"/>{{rp|129}}

{| class="wikitable"
|-
|+SI base units and standards
|-
! Base quantity !! Name !! Symbol !! Definition
|-
| Time || [[second]]|| s || The duration of 9192631770 periods of the radiation corresponding to the transition between the two [[Hyperfine structure|hyperfine]] levels of the [[ground state]] of the [[Isotopes of caesium#Caesium-133|caesium-133]] atom<ref name="SI 9th edition"/>{{rp|130}}
|-
| Length || [[metre]]|| m || The length of the path travelled by light in a [[vacuum]] during a time interval of 1/299792458 of a second<ref name="SI 9th edition"/>{{rp|131}}
|-
| Mass || [[kilogram]]|| kg || Defined ([[2019 revision of the SI|as of 2019]]) by "... taking the fixed numerical value of the [[Planck constant]], ''h'', to be {{val|fmt=commas|6.62607015|e=-34}} when expressed in the unit {{nowrap|J s}}, which is equal to {{nowrap|kg m<sup>2</sup> s<sup>−1</sup>}} ..."<ref name="SI 9th edition"/>{{rp|131}}
|-
| Electric current || [[ampere]]|| A || Defined (as of 2019) by "... taking the fixed numerical value of the [[elementary charge]], ''e'', to be {{val|fmt=commas|1.602176634|e=-19}} when expressed in the unit C, which is equal to {{nowrap|A s}} ..."<ref name="SI 9th edition"/>{{rp|132}}
|-
| Thermodynamic temperature || [[kelvin]]|| K || Defined (as of 2019) by "... taking the fixed numerical value of the [[Boltzmann constant]], ''k'', to be {{val|fmt=commas|1.380649|e=-23}} when expressed in the unit {{nowrap|J K<sup>−1</sup>}}, which is equal to {{nowrap|kg m<sup>2</sup> s<sup>−2</sup> K<sup>−1</sup>}} ..."<ref name="SI 9th edition"/>{{rp|133}}
|-
| Amount of substance || [[Mole (unit)|mole]] || mol || Contains (as of 2019) "... exactly {{val|fmt=commas|6.02214076|e=23}} elementary entities. This number is the fixed numerical value of the [[Avogadro constant]], ''N''<sub>A</sub>, when expressed in the unit mol<sup>−1</sup> ..."<ref name="SI 9th edition"/>{{rp|134}}
|-
| Luminous intensity || [[candela]] || cd || The luminous intensity, in a given direction, of a source emitting monochromatic radiation of a frequency of {{val|540|e=12|u=Hz}} with a radiant intensity in that direction of 1/683 watt per [[steradian]]<ref name="SI 9th edition"/>{{rp|135}}
|}

Since the base units are the reference points for all measurements taken in SI units, if the reference value changed all prior measurements would be incorrect. Before 2019, if a piece of the international prototype of the kilogram had been snapped off, it would have still been defined as a kilogram; all previous measured values of a kilogram would be heavier.<ref name=BGtoM>{{cite web|last1=Goldsmith|first1=Mike|title=A Beginner's Guide to Measurement|url=http://www.npl.co.uk/upload/pdf/NPL-Beginners-Guide-to-Measurement.pdf|publisher=National Physical Laboratory|access-date=16 February 2017|url-status=live|archive-url=https://web.archive.org/web/20170329111015/http://www.npl.co.uk/upload/pdf/NPL-Beginners-Guide-to-Measurement.pdf|archive-date=29 March 2017}}</ref> The importance of reproducible SI units has led the BIPM to complete the task of defining all SI base units in terms of [[physical constant]]s.<ref name=redef>{{cite web|title=On the future revision of the SI|url=http://www.bipm.org/en/measurement-units/rev-si/|publisher=Bureau International des Poids et Mesures|access-date=16 February 2017|url-status=dead|archive-url=https://web.archive.org/web/20170215111649/http://www.bipm.org/en/measurement-units/rev-si/|archive-date=15 February 2017}}</ref>

By defining SI base units with respect to physical constants, and not artefacts or specific substances, they are realisable with a higher level of precision and reproducibility.<ref name = redef/> As of the revision of the SI on 20 May 2019 the [[kilogram]], [[ampere]], [[kelvin]], and [[Mole (unit)|mole]] are defined by setting exact numerical values for the [[Planck constant]] (''{{Math|h}}''), the [[elementary electric charge]] (''{{Math|e}}''), the [[Boltzmann constant]] (''{{Math|k}}''), and the [[Avogadro constant]] ({{Math|''N''<sub>A</sub>}}), respectively. The [[second]], [[metre]], and [[candela]] have previously been defined by physical constants (the [[caesium standard]] (Δ''ν''<sub>Cs</sub>), the [[speed of light]] (''{{Math|c}}''), and the [[luminous efficacy]] of {{val|540|e=12|u=Hz}} visible light radiation (''K''<sub>cd</sub>)), subject to correction to their present definitions. The new definitions aim to improve the SI without changing the size of any units, thus ensuring continuity with existing measurements.<ref name=Kuehne>
{{cite web
 |first=Michael|last=Kühne
 |title=Redefinition of the SI
 |url=http://www.its9.org/symposium_program.html#SI_Redefinition_Keynote_Abstract
 |work=Keynote address, ITS<sup>9</sup> (Ninth International Temperature Symposium)
 |location=Los Angeles
 |access-date=1 March 2012|date=22 March 2012
 |publisher=NIST
 |archive-url=https://web.archive.org/web/20130618064512/http://www.its9.org/symposium_program.html|archive-date=18 June 2013
 |url-status=dead
}}</ref><ref name="SI 9th edition"/>{{rp|123,128}}

=== Realisation of units ===

[[File:CGKilogram.jpg|thumb|alt=Computer-generated image of a small cylinder|Computer-generated image realising the international prototype of the kilogram (IPK), made from an alloy of 90-per cent platinum and 10-per cent iridium by weight]]
The [[Realisation (metrology)|realisation]] of a unit of measure is its conversion into reality.<ref name=OED>{{OED|Realise}}</ref> Three possible methods of realisation are defined by the [[Joint Committee for Guides in Metrology#VIM: International vocabulary of metrology|international vocabulary of metrology]] (VIM): a physical realisation of the unit from its definition, a highly-reproducible measurement as a reproduction of the definition (such as the [[quantum Hall effect]] for the [[ohm]]), and the use of a material object as the measurement standard.<ref>{{cite book|title=International vocabulary of metrology—Basic and general concepts and associated terms (VIM)|date=2012|publisher=[[International Bureau of Weights and Measures]] on behalf of the Joint Committee for Guides in Metrology|page=46|edition=3rd|url=http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2012.pdf|access-date=1 March 2017|url-status=live|archive-url=https://web.archive.org/web/20170317223139/http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2012.pdf|archive-date=17 March 2017}}</ref>

=== Standards ===
{{see also|Measurement#Standards}}

A [[Standard (metrology)|standard]] (or etalon) is an object, system, or experiment with a defined relationship to a unit of measurement of a physical quantity.<ref>Phillip Ostwald,Jairo Muñoz, ''Manufacturing Processes and Systems (9th Edition)''John Wiley & Sons, 1997 {{ISBN|978-0-471-04741-4}} page 616</ref> Standards are the fundamental reference for a system of weights and measures by realising, preserving, or reproducing a unit against which measuring devices can be compared.<ref name=FCM/> There are three levels of standards in the hierarchy of metrology: primary, secondary, and working standards.<ref name="silva">{{cite book|last1=de Silva|first1=G. M. S|title=Basic Metrology for ISO 9000 Certification|date=2012|publisher=Routledge|location=Oxford|isbn=978-1-136-42720-6|pages=12–13|edition=Online-Ausg.|url=https://books.google.com/books?id=0akABAAAQBAJ&q=standards+hierarchy+metrology&pg=PA13|access-date=17 February 2017|url-status=live|archive-url=https://web.archive.org/web/20180227045858/https://books.google.com/books?id=0akABAAAQBAJ&pg=PA13&lpg=PA13&dq=standards+hierarchy+metrology&source=bl&ots=VMyW0MPSAL&sig=kziWErFv0k_dtc-EjphSzdVjV_8&hl=en&sa=X&ved=0ahUKEwjW3tzX_5fSAhVh6IMKHR2RCoUQ6AEIfTAU#v=onepage&q=standards%20hierarchy%20metrology&f=false|archive-date=27 February 2018}}</ref> Primary standards (the highest quality) do not reference any other standards. Secondary standards are calibrated with reference to a primary standard. Working standards, used to calibrate (or check) measuring instruments or other material measures, are calibrated with respect to secondary standards. The hierarchy preserves the quality of the higher standards.<ref name = "silva"/> An example of a standard would be [[gauge blocks]] for length. A gauge block is a block of metal or ceramic with two opposing faces ground precisely flat and parallel, a precise distance apart.<ref>{{cite web|last1=Doiron|first1=Ted|last2=Beers|first2=John|title=The Gauge Block Handbook|url=https://www.nist.gov/sites/default/files/documents/calibrations/mono180.pdf|publisher=NIST|access-date=23 March 2018}}</ref> The length of the path of light in vacuum during a time interval of 1/299,792,458 of a second is embodied in an artefact standard such as a gauge block; this gauge block is then a primary standard which can be used to calibrate secondary standards through mechanical comparators.<ref>{{cite web|title=e-Handbook of Statistical Methods|url=https://www.itl.nist.gov/div898/handbook/mpc/section3/mpc312.htm|publisher=NIST/SEMATECH|access-date=23 March 2018}}</ref>

=== Traceability and calibration===

[[File:Traceability Pyramid.png|thumb|upright=1.5|alt=Pyramid illustrating the relationship between traceability and calibration|Metrology traceability pyramid]]
Metrological traceability is defined as the "property of a measurement result whereby the result can be related to a reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty".<ref name=VIM>{{Cite book |url= http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf |title= International vocabulary of metrology – basic and general concepts and associated terms |publisher= Joint Committee on Guides for Metrology (JCGM) |year= 2008 |edition= 3 |url-status= dead |archive-url= https://web.archive.org/web/20110110120304/http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf |archive-date= 2011-01-10 |access-date= 2014-06-13 }}</ref> It permits the comparison of measurements, whether the result is compared to the previous result in the same laboratory, a measurement result a year ago, or to the result of a measurement performed anywhere else in the world.<ref name=WMO>{{cite web|title=Metrological Traceability for Meteorology|url=https://www.wmo.int/pages/prog/www/IMOP/publications/Flyers/Traceability_flyer.pdf|publisher=World Meteorological Organization Commission for Instruments and Methods of Observation|access-date=2 March 2017|url-status=live|archive-url=https://web.archive.org/web/20170317094030/http://www.wmo.int/pages/prog/www/IMOP/publications/Flyers/Traceability_flyer.pdf|archive-date=17 March 2017}}</ref> The chain of traceability allows any measurement to be referenced to higher levels of measurements back to the original definition of the unit.<ref name=FCM/>

Traceability is obtained directly through [[calibration]], establishing the relationship between an indication on a standard traceable measuring instrument and the value of the comparator (or comparative measuring instrument). The process will determine the measurement value and uncertainty of the device that is being calibrated (the comparator) and create a traceability link to the measurement standard.<ref name = VIM/> The four primary reasons for calibrations are to provide traceability, to ensure that the instrument (or standard) is consistent with other measurements, to determine accuracy, and to establish reliability.<ref name=FCM/> Traceability works as a pyramid, at the top level there is the international standards, which beholds the world's standards. The next level is the national Metrology institutes that have primary standards that are traceable to the international standards. The national Metrology institutes standards are used to establish a traceable link to local laboratory standards, these laboratory standards are then used to establish a traceable link to industry and testing laboratories. Through these subsequent calibrations between national metrology institutes, calibration laboratories, and industry and testing laboratories the realisation of the unit definition is propagated down through the pyramid.<ref name=WMO/> The traceability chain works upwards from the bottom of the pyramid, where measurements done by industry and testing laboratories can be directly related to the unit definition at the top through the traceability chain created by calibration.<ref name = BGtoM/>

=== Uncertainty  ===

[[Measurement uncertainty]] is a value associated with a measurement which expresses the spread of possible values associated with the [[measurand]]—a quantitative expression of the doubt existing in the measurement.<ref name="EUROLAB">{{cite book|title=Guide to the Evaluation of Measurement Uncertainty for Quantitative Test Results|date=August 2006|publisher=EUROLAB|location=Paris, France|page=8|url=http://www.eurolab.org/documents/EL_11_01_06_387%20Technical%20report%20-%20Guide%20Measurement%20uncertainty.pdf|access-date=2 March 2017|url-status=live|archive-url=https://web.archive.org/web/20161123053518/http://www.eurolab.org/documents/EL_11_01_06_387%20Technical%20report%20-%20Guide%20Measurement%20uncertainty.pdf|archive-date=23 November 2016}}</ref> There are two components to the uncertainty of a measurement: the width of the uncertainty interval and the confidence level.<ref name="BGtoU">{{cite journal|last1=Bell|first1=Stephanie|title=A Beginner's Guide to Uncertainty of Measurement|journal=Technical Review- National Physical Laboratory|date=March 2001|publisher=National Physical Laboratory|location=Teddington, Middlesex, United Kingdom|issn=1368-6550|edition=Issue 2|url=https://www.wmo.int/pages/prog/gcos/documents/gruanmanuals/UK_NPL/mgpg11.pdf|access-date=2 March 2017|url-status=live|archive-url=https://web.archive.org/web/20170503205533/https://www.wmo.int/pages/prog/gcos/documents/gruanmanuals/UK_NPL/mgpg11.pdf|archive-date=3 May 2017}}</ref> The uncertainty interval is a range of values that the measurement value expected to fall within, while the confidence level is how likely the true value is to fall within the uncertainty interval. Uncertainty is generally expressed as follows:<ref name = FCM/>
:<math>Y = y \pm U</math>  
:Coverage factor: ''k'' = 2
Where ''y'' is the measurement value and ''U'' is the uncertainty value and ''k'' is the coverage factor{{efn|Equivalent to standard deviation if the uncertainty distribution is normal}} indicates the confidence interval. The upper and lower limit of the uncertainty interval can be determined by adding and subtracting the uncertainty value from the measurement value. The coverage factor of ''k'' = 2 generally indicates a 95% confidence that the measured value will fall inside the uncertainty interval.<ref name = FCM/> Other values of ''k'' can be used to indicate a greater or lower confidence on the interval, for example ''k'' = 1 and ''k'' = 3 generally indicate 66% and 99.7% confidence respectively.<ref name="BGtoU"/> The uncertainty value is determined through a combination of statistical analysis of the calibration and uncertainty contribution from other errors in measurement process, which can be evaluated from sources such as the instrument history, manufacturer's specifications, or published information.<ref name="BGtoU"/>