International Atomic Time (TAI, from its French nametemps atomique international)[1] is a high-precisionatomiccoordinatetime standard based on the notional passage ofproper time on Earth'sgeoid.[2] TAI is aweighted average of the time kept by over 450atomic clocks in over 80 national laboratories worldwide.[3] It is a continuous scale of time, withoutleap seconds, and it is the principal realisation ofTerrestrial Time (with a fixed offset ofepoch). It is the basis forCoordinated 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 6 January 2026, UTC is exactly 37 seconds behind TAI;[4] this has been the case since 1 January 2017, 00:00:00 UTC, immediately after the most recentleap second was put into effect.[5] The 37 seconds result from the initial difference of 10 seconds at the start of 1972, plus 27 leap seconds in UTC since 1972. In 2022, theGeneral Conference on Weights and Measures decided to abandon the leap second by or before 2035, at which point the difference between TAI and UTC will remain fixed.[6]
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, bothJulian days and theGregorian calendar are used. TAI in this form was synchronised withUniversal Time at the beginning of 1958, and the two have drifted apart ever since, due primarily to the slowing rotation of the Earth.
TAI is aweighted average of the time kept by over 450atomic clocks in over 80 national laboratories worldwide.[3] The majority of the clocks involved arecaesium clocks; theInternational System of Units (SI) definition of thesecond is based oncaesium.[7] The clocks are compared usingGPS signals andtwo-way satellite time and frequency transfer.[8] Due to thesignal averaging TAI is anorder of magnitude more stable than its best constituent clock.
The participating institutions each broadcast, inreal time, a frequency signal withtimecodes, 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 formUTC(NPL) in the UTC form, whereNPL here identifies theNational Physical Laboratory, UK. The TAI form may be denotedTAI(NPL). The latter is not to be confused withTA(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. TheInternational Bureau of Weights and Measures (BIPM, France) combines these measurements to retrospectively calculate the weighted average that forms the most stable time scale possible.[3] This combined time scale is published monthly in "Circular T"[9] and is thecanonical TAI. This time scale is expressed in the form of tables of differences UTC − UTC(k) (equal to TAI − TAI(k)) for each participating institutionk. 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 ofTerrestrial Time (TT).
Early atomic time scales consisted ofquartz clocks 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 theNational Physical Laboratory, UK (NPL). It was used as a basis for calibrating the quartz clocks at theRoyal Greenwich Observatory and to establish a time scale, called Greenwich Atomic (GA). TheUnited States Naval Observatory began the A.1 scale on 13 September 1956, using anAtomichron commercial atomic clock, followed by the NBS-A scale at theNational Bureau of Standards,Boulder, Colorado on 9 October 1957.[10]
TheInternational Time Bureau (BIH) began a time scale, Tm or AM, in July 1955, using both local caesium clocks and comparisons to distant clocks using the phase ofVLF radio signals. The BIH scale, A.1, and NBS-A were defined by anepoch at the beginning of 1958[a] The procedures used by the BIH evolved, and the name for the time scale changed:A3 in 1964[12] andTA(BIH) in 1969.[13]
The SI second was defined in terms of the caesium atom in 1967. From 1971 to 1975, theGeneral Conference on Weights and Measures and theInternational Committee for Weights and Measures made a series of decisions that designated the BIPM time scale International Atomic Time (TAI).[14]
In the 1970s, it became clear that the clocks participating in TAI were ticking at different rates due togravitational 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 thegeoid (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 nameEAL (Échelle Atomique Libre, meaningFree Atomic Scale).[15]
The instant that the gravitational correction started to be applied serves as the epoch forBarycentric Coordinate Time (TCB),Geocentric Coordinate Time (TCG), andTerrestrial Time (TT), which represent three fundamental time scales in theSolar System.[16] All three of these time scales were defined to read JD 2443144.5003725 (1 January 1977 00:00:32.184) exactly at that instant.[b] TAI was henceforth a realisation of TT, with the equation TT(TAI) = TAI + 32.184 s.[17]
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."[18]
Contrary to TAI, UTC is adiscontinuous 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 approximatedUT2. Afterwards, these adjustments were made only in whole seconds to approximateUT1. 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 asnavigation, which require a source of Universal Time continue to be well served by the public broadcast of UTC.[19]
By 1964 BIH realized that some atomic chronometers were much better than others, and they constructed A3 based on the best 3
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