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((Short description|Time standard based on atomic clocks))
((Use dmy dates|date=August 2022))
((Use British English|date=April 2020))

'''International Atomic Time''' (abbreviated '''TAI''', from its French name '''((lang|fr|temps atomique international))'''<ref>Temps atomique 1975((elucidate|date=April 2020))</ref>) is a high-precision [[Atomic clock|atomic]] [[coordinate time|coordinate]] [[time standard]] based on the notional passage of [[proper time]] on Earth's [[geoid]].<ref>((Cite journal|title=Is the International Atomic Time TAI a coordinate time or a proper time?|journal=Celestial Mechanics|volume=38|issue=2|pages=155–161 |bibcode=1986CeMec..38..155G|last1=Guinot|first1=B.|year=1986|doi=10.1007/BF01230427|s2cid=120564915))</ref> TAI is a [[weighted average]] of the time kept by over 450 [[atomic clock]]s in over 80 national laboratories worldwide.<ref name="Time n.d." /> It is a continuous scale of time, without [[leap seconds]], and it is the principal realisation of [[Terrestrial Time]] (with a fixed offset of [[epoch (astronomy)|epoch]]). It is the basis for [[Coordinated Universal Time]] (UTC), which is used for civil timekeeping all over the Earth's surface and which has leap seconds.

UTC deviates from TAI by a number of whole seconds. ((as of|2017|01|01)), when another [[leap second]] was put into effect,<ref name="Bulletin C 52">((cite web|url=http://hpiers.obspm.fr/eoppc/bul/bulc/bulletinc.52|first=Christian|last=Bizouard|title=Bulletin C 52|lang=en|publisher=[[IERS]]|location=Paris|date=6 July 2016|access-date=31 December 2016|archive-date=13 August 2017|archive-url=https://web.archive.org/web/20170813224025/https://hpiers.obspm.fr/eoppc/bul/bulc/bulletinc.52|url-status=live))</ref> UTC is currently exactly 37 seconds behind TAI. The 37 seconds result from the initial difference of 10 seconds at the start of 1972, plus 27 leap seconds in UTC since 1972.

TAI may be reported using traditional means of specifying days, carried over from non-uniform time standards based on the rotation of the Earth. Specifically, both [[Julian day]]s and the [[Gregorian calendar]] are used. TAI in this form was synchronised with [[Universal Time]] at the beginning of 1958, and the two have drifted apart ever since, due primarily to the slowing rotation of the Earth.

== Operation ==
TAI is a [[weighted average]] of the time kept by over 450 [[atomic clock]]s in over 80 national laboratories worldwide.<ref name="Time n.d.">((cite book
|title = BIPM Annual Report on Time Activities
|url = https://webtai.bipm.org/ftp/pub/tai/annual-reports/bipm-annual-report/annual_report_2020.pdf
|lang=en
|page = 9
|publisher = International Bureau of Weights and Measures
|volume = 15
|date = 2020
|isbn = 978-92-822-2280-5
|issn = 1994-9405
|access-date = 16 June 2022
|archive-url=https://web.archive.org/web/20210814134522/https://webtai.bipm.org/ftp/pub/tai/annual-reports/bipm-annual-report/annual_report_2020.pdf
|archive-date=14 August 2021
|url-status=live))</ref> The majority of the clocks involved are [[caesium clock]]s; the [[International System of Units]] (SI) definition of the [[second]] is based on [[caesium]].((sfn|McCarthy|Seidelmann|2009|p=207, 214)) The clocks are compared using [[Global Positioning System|GPS]] signals and [[two-way satellite time and frequency transfer]].<ref>((citation |title=Explanatory Supplement of BIPM Circular T |publisher=[[International Bureau of Weights and Measures]] |url=https://webtai.bipm.org/ftp/pub/tai/other-products/notes/explanatory_supplement_v0.6.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://webtai.bipm.org/ftp/pub/tai/other-products/notes/explanatory_supplement_v0.6.pdf |archive-date=2022-10-09 |url-status=live |date=12 July 2021 |access-date=16 June 2022))</ref>  Due to the [[signal averaging]] TAI is an [[order of magnitude]] more stable than its best constituent clock.

The participating institutions each broadcast, in [[real-time data|real time]], a frequency signal with [[timecode]]s, which is their estimate of TAI.  Time codes are usually published in the form of UTC, which differs from TAI by a well-known integer number of seconds.  These time scales are denoted in the form ''UTC(NPL)'' in the UTC form, where ''NPL'' here identifies the [[National Physical Laboratory, UK]]. The TAI form may be denoted ''TAI(NPL)''.  The latter is not to be confused with ''TA(NPL)'', which denotes an independent atomic time scale, not synchronised to TAI or to anything else.

The clocks at different institutions are regularly compared against each other.  The [[International Bureau of Weights and Measures]] (BIPM, France), combines these measurements to retrospectively calculate the weighted average that forms the most stable time scale possible.<ref name="Time n.d."/>  This combined time scale is published monthly in "Circular T",<ref>((citation |title=Circular T |publisher=[[International Bureau of Weights and Measures]] |url=https://www.bipm.org/en/time-ftp/circular-t |access-date=16 June 2022))</ref> and is the [[canonical form|canonical]] TAI.  This time scale is expressed in the form of tables of differences UTC − UTC(''k'') (equal to TAI − TAI(''k'')) for each participating institution ''k''.  The same circular also gives tables of TAI − TA(''k''), for the various unsynchronised atomic time scales.

Errors in publication may be corrected by issuing a revision of the faulty Circular T or by errata in a subsequent Circular T.  Aside from this, once published in Circular T, the TAI scale is not revised.  In hindsight, it is possible to discover errors in TAI and to make better estimates of the true proper time scale.  Since the published circulars are definitive, better estimates do not create another version of TAI; it is instead considered to be creating a better realisation of [[Terrestrial Time]] (TT).

== History ==
Early atomic time scales consisted of [[quartz clock]]s with frequencies calibrated by a single atomic clock; the atomic clocks were not operated continuously. Atomic timekeeping services started experimentally in 1955, using the first caesium atomic clock at the [[National Physical Laboratory (United Kingdom)|National Physical Laboratory, UK (NPL)]]. It was used as a basis for calibrating the quartz clocks at the [[Royal Greenwich Observatory]] and to establish a time scale, called Greenwich Atomic (GA). The [[United States Naval Observatory]] began the A.1 scale on 13 September 1956, using an [[Atomichron]] commercial atomic clock, followed by the NBS-A scale at the [[National Bureau of Standards]], [[Boulder, Colorado]] on 9 October 1957.((sfn|McCarthy|Seidelmann|2009|pages=199–200))

The [[International Time Bureau]] (BIH) began a time scale, T<sub>m</sub> or AM, in July 1955, using both local caesium clocks and comparisons to distant clocks using the phase of [[VLF]] radio signals. The BIH scale, A.1, and NBS-A were defined by an [[Epoch (date reference)|epoch]] at the beginning of 1958((efn|They were set to read Julian Date 2436204.5 (1 January 1958 00:00:00) at the corresponding [[UT2]] instant. However, each observatory used its own value of UT2.((sfn|Guinot|2000|page=181)))) The procedures used by the BIH evolved, and the name for the time scale changed: ''A3'' in 1964<ref>((cite web |last1=Allen |first1=Steve |title=The epoch of TAI is 1961-01-01T20:00:00 UT2 |url=https://www.ucolick.org/~sla/leapsecs/taiepoch.html |publisher=UCO/Lick Observatory |quote=By 1964 BIH realized that some atomic chronometers were much better than others, and they constructed A3 based on the best 3 |lang=en|access-date=21 January 2019|archive-date=10 October 2021|archive-url=https://web.archive.org/web/20211010014537/https://www.ucolick.org/~sla/leapsecs/taiepoch.html |url-status=live ))</ref> and ''TA(BIH)'' in 1969.((sfn|McCarthy|Seidelmann|2009|pages=200–201))

The SI second was defined in terms of the caesium atom in 1967. From 1971 to 1975 the [[General Conference on Weights and Measures]] and the [[International Committee for Weights and Measures]] made a series of decisions that designated the BIPM time scale International Atomic Time (TAI).((sfn|McCarthy|Seidelmann|2009|pages=203–204))

In the 1970s, it became clear that the clocks participating in TAI were ticking at different rates due to [[gravitational time dilation]], and the combined TAI scale, therefore, corresponded to an average of the altitudes of the various clocks. Starting from the Julian Date 2443144.5 (1 January 1977 00:00:00 TAI), corrections were applied to the output of all participating clocks, so that TAI would correspond to proper time at the [[geoid]] ([[mean sea level]]).  Because the clocks were, on average, well above sea level, this meant that TAI slowed by about one part in a trillion. The former uncorrected time scale continues to be published under the name ''EAL'' (''Échelle Atomique Libre'', meaning ''Free Atomic Scale'').((sfn|McCarthy|Seidelmann|2009|p=215))

The instant that the gravitational correction started to be applied serves as the epoch for [[Barycentric Coordinate Time]] (TCB), [[Geocentric Coordinate Time]] (TCG), and [[Terrestrial Time]] (TT), which represent three fundamental time scales in the solar system.<ref>((cite journal|last1=Brumberg|first1=V.A.|last2=Kopeikin|first2=S.M.|title=Relativistic time scales in the solar system|journal=[[Celestial Mechanics and Dynamical Astronomy]]|issn=0923-2958|volume=48|issue=1|pages=23–44|date=March 1990|doi=10.1007/BF00050674|bibcode=1990CeMDA..48...23B|s2cid=120112678))</ref>  All three of these time scales were defined to read JD 2443144.5003725 (1 January 1977 00:00:32.184) exactly at that instant.((efn|The 32.184 second offset is to provide continuity with the older [[ephemeris time]].)) TAI was henceforth a realisation of TT, with the equation TT(TAI) = TAI + 32.184&nbsp;s.((sfn|McCarthy|Seidelmann|2009|p=218&ndash;219))

The continued existence of TAI was questioned in a 2007 letter from the BIPM to the ITU-R which stated, "In the case of a redefinition of UTC without leap seconds, the CCTF would consider discussing the possibility of suppressing TAI, as it would remain parallel to the continuous UTC."<ref>((cite web
 |title=CCTF 09-27 
 |url=http://www.bipm.org/cc/CCTF/Allowed/18/CCTF_09-27_note_on_UTC-ITU-R.pdf 
 |lang=en
 |date=3 September 2007
 |publisher=International Bureau of Weights and Measures 
 |access-date=24 September 2018
 |archive-url=https://web.archive.org/web/20120316100907/http://www.bipm.org/cc/CCTF/Allowed/18/CCTF_09-27_note_on_UTC-ITU-R.pdf 
 |archive-date=16 March 2012
 |url-status=dead 
))</ref>

== Relation to UTC ==
Contrary to TAI, UTC is a [[discontinuous]] time scale. It is occasionally adjusted by leap seconds. Between these adjustments, it is composed of segments that are mapped to atomic time by a constant offset. From its beginning in 1961 through December 1971, the adjustments were made regularly in fractional leap seconds so that UTC approximated [[UT2]].  Afterward, these adjustments were made only in whole seconds to approximate [[UT1]]. This was a compromise arrangement in order to enable a publicly broadcast time scale. The less frequent whole-second adjustments meant that the time scale would be more stable and easier to synchronize internationally. The fact that it continues to approximate UT1 means that tasks such as [[navigation]] which require a source of Universal Time continue to be well served by the public broadcast of UTC.((sfn|McCarthy|Seidelmann|2009|p=227&ndash;229))

== See also ==
* [[Clock synchronization]]
* [[Time and frequency transfer]]

== Notes ==
((Notelist))

== References ==
((Refbegin))
* ((cite web
|title=History of TAI−UTC
|url=http://maia.usno.navy.mil/ser7/tai-utc.dat
|lang=en
|archive-url=https://web.archive.org/web/20191019051734/http://maia.usno.navy.mil/ser7/tai-utc.dat
|url-status=dead
|archive-date=19 October 2019
|publisher=Time Service Dept., United States Naval Observatory
|date=2009
|access-date=4 January 2010
))
* ((cite web 
|title=International Atomic Time 
|url=http://www.bipm.org/en/scientific/tai/tai.html 
|lang=en
|publisher=[[International Bureau of Weights and Measures]] 
|access-date=24 January 2020
|archive-url=https://web.archive.org/web/20110110113226/http://www.bipm.org/en/scientific/tai/tai.html 
|archive-date=10 January 2011
|url-status=live 
))
((Refend))

=== Footnotes ===
((Reflist))

== Bibliography ==
((Refbegin))
* (( cite book 
| last = Guinot
| first = B
| chapter = History of the Bureau International de l'Heure
| title = Polar Motion: Historical and Scientific Problems
| url = https://books.google.com/books?id=pFDwAAAAMAAJ
| lang=en
| series = ASP Conference Series, Vol. 208
| isbn = 1-58381-039-0
| date = 2000
| volume = 208
| page = 175
| bibcode = 2000ASPC..208..175G 
| archive-url=https://web.archive.org/web/20220801225534/https://www.google.com/books/edition/Polar_Motion/pFDwAAAAMAAJ?hl=en
| archive-date=1 August 2022
| url-status=live
))
* ((Cite book 
|title=Time: From Earth Rotation to Atomic Physics 
|url=https://books.google.com/books?id=7NdrK4e77CIC 
|lang=en
|author-link=Dennis D. McCarthy 
|last1=McCarthy 
|first1=Dennis D. 
|last2=Seidelmann 
|first2=Kenneth P. 
|isbn=978-3-527-40780-4 
|publisher=[[Wiley-VCH Verlag GmbH & Co. KGaA]] 
|location=Weinheim 
|year=2009 
|access-date=12 June 2021
|archive-date=3 February 2021
|archive-url=https://web.archive.org/web/20210203233222/https://books.google.com/books?id=7NdrK4e77CIC 
|url-status=live 
))
((Refend))

== External links ==
* [https://www.bipm.org/en/time-metrology BIPM technical services: Time Metrology]
* [https://web.archive.org/web/20060923185936/http://www.npl.co.uk/time/ Time and Frequency Section - National Physical Laboratory, UK]
* [http://hpiers.obspm.fr IERS website]
* [https://www.nist.gov/pml/time-and-frequency-division/popular-links/web-clock-faq  NIST Web Clock FAQs]
* [http://www.ucolick.org/~sla/leapsecs/timescales.html History of time scales]
* [https://www.nist.gov/pml/div688/grp50/primary-frequency-standards.cfm NIST-F1 Cesium Fountain Atomic Clock]
* ((cite web|url=http://inms-ienm.nrc-cnrc.gc.ca/research/optical_frequency_projects_e.html#femtosecond|title=Optical frequency comb for metrology and timekeeping|lang=en|archive-url=https://web.archive.org/web/20090125051853/http://inms-ienm.nrc-cnrc.gc.ca/research/optical_frequency_projects_e.html#femtosecond |archive-date=25 January 2009))
* [http://jjy.nict.go.jp/index-e.html Japan Standard Time Project, NICT, Japan]
* ((citation |url=https://webtai.bipm.org/ftp/pub/tai/annual-reports/bipm-annual-report/TIMESERVICES/timeservices.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://webtai.bipm.org/ftp/pub/tai/annual-reports/bipm-annual-report/TIMESERVICES/timeservices.pdf |archive-date=2022-10-09 |url-status=live |publisher=Bureau International des Poids et Mesures |title=Time Dissemination Services))
* [http://www.ipses.com/eng/In-depth-analysis/Standard-of-time-definition Standard of time definition: UTC, GPS, LORAN and TAI]

((Time Topics))
((Time measurement and standards))
((Authority control))

[[Category:Time scales]]

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